Patent Publication Number: US-10790912-B2

Title: Visualizing arbitrary pulse shapes and schedules in quantum computing applications

Description:
BACKGROUND 
     The subject disclosure relates to pulse shapes and schedules in quantum computing applications, and more specifically, to visualizing arbitrary pulse shapes and schedules in quantum computing applications. 
     SUMMARY 
     The following presents a summary to provide a basic understanding of one or more embodiments of the invention. This summary is not intended to identify key or critical elements, or delineate any scope of the particular embodiments or any scope of the claims. Its sole purpose is to present concepts in a simplified form as a prelude to the more detailed description that is presented later. In one or more embodiments described herein, devices, systems, computer-implemented methods, and/or computer program products that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications are described. 
     According to an embodiment, a system can a processor that can execute computer executable components stored in memory. The system can further comprise a collection component that can receive a pulse schedule of pulse data and control parameters of a quantum device comprising default pulse data of the quantum device. The system can further comprise a plotting component that can generate a plot of the pulse schedule based on the pulse data, the control parameters, and the default pulse data. The system can further comprise a visualization component that can generate a display of the pulse schedule. 
     According to an embodiment, a computer-implemented method can comprise executing, by a processor, computer executable components stored in memory. The computer-implemented method can further comprise receiving, by a device operatively coupled to the processor, a pulse schedule of pulse data and control parameters of a quantum device comprising default pulse data of the quantum device. The computer-implemented method can further comprise generating, by the device, a plot of the pulse schedule based on the pulse data, the control parameters, and the default pulse data. The computer-implemented method can further comprise generating, by the device, a display of the pulse schedule. 
     According to another embodiment, a computer program product that can facilitate generating a visualization associated with a quantum device. The computer program product can comprise a computer readable storage medium having program instructions embodied therewith, the program instructions can be executable by a processor to cause the processor to execute, by the processor, computer executable components stored in memory. The program instructions can be further executable to cause the processor to receive, by the processor, a pulse schedule of pulse data and control parameters of a quantum device comprising default pulse data of the quantum device. The program instructions can be further executable to cause the processor to generate, using the processor, a plot of the pulse schedule based on the pulse data, the control parameters, and the default pulse data. The program instructions can be further executable to cause the processor to generate, using the processor, a display of the pulse schedule. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a block diagram of an example, non-limiting system that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. 
         FIG. 2  illustrates a block diagram of an example, non-limiting system that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. 
         FIG. 3  illustrates a block diagram of an example, non-limiting system that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. 
         FIG. 4  illustrates an example, non-limiting visualization that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. 
         FIG. 5  illustrates an example, non-limiting visualization that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. 
         FIG. 6  illustrates an example, non-limiting visualization that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. 
         FIGS. 7A, 7B, and 7C  illustrate example, non-limiting visualizations that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. 
         FIG. 8  illustrates an example, non-limiting visualization that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. 
         FIG. 9A  illustrates a flow diagram of an example, non-limiting computer-implemented method that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. 
         FIG. 9B  illustrates a flow diagram of an example, non-limiting computer-implemented method that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. 
         FIG. 10  illustrates a block diagram of an example, non-limiting operating environment in which one or more embodiments described herein can be facilitated. 
     
    
    
     DETAILED DESCRIPTION 
     The following detailed description is merely illustrative and is not intended to limit embodiments and/or application or uses of embodiments. Furthermore, there is no intention to be bound by any expressed or implied information presented in the preceding Background or Summary sections, or in the Detailed Description section. 
     One or more embodiments are now described with reference to the drawings, wherein like referenced numerals are used to refer to like elements throughout. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a more thorough understanding of the one or more embodiments. It is evident, however, in various cases, that the one or more embodiments can be practiced without these specific details. It is noted that the drawings of the present application are provided for illustrative purposes only and, as such, the drawings are not drawn to scale. 
     Quantum computing is generally the use of quantum-mechanical phenomena for the purpose of performing computing and information processing functions. Quantum computing can be viewed in contrast to classical computing, which generally operates on binary values with transistors. That is, while classical computers can operate on bit values that are either 0 or 1, quantum computers operate on quantum bits that comprise superpositions of both 0 and 1, can entangle multiple quantum bits (qubits), and use interference. 
     Quantum computing hardware is different from classical computing hardware. In particular, superconducting quantum circuits generally rely on Josephson junctions, which can be fabricated on a semiconductor substrate. A Josephson junction generally manifests the Josephson effect of a supercurrent, where current can flow indefinitely across a Josephson junction without an applied voltage. One or more Josephson junctions can be embedded in a superconducting circuit to form a quantum bit (qubit). A plurality of such qubits can be arranged in a superconducting quantum circuit fabricated on a semiconductor substrate, which can further comprise microwave readout resonators coupled to the respective qubits that facilitate reading quantum information of the qubits. Such a superconducting quantum circuit and microwave readout resonators can be integrated onto a semiconducting substrate to form an integrated quantum processor that can execute computations and information processing functions that are substantially more complex than can be executed by classical computing devices (e.g., general-purpose computers, special-purpose computers, etc.). 
     Building quantum computers with longer coherence times and lower gate errors requires going beyond simple pulse definitions (e.g., Gaussian pulse shapes) as the underlying control for gate operations and moving to more complex single-pulse or multi-pulse schemes based on, for instance, quantum optimal control, dynamical decoupling, and/or machine learning algorithms Being generated by machine algorithms, these complex and often times non-analytic pulse shapes and schedules are better understood through visualization. 
       FIG. 1  illustrates a block diagram of an example, non-limiting system  100  that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. According to several embodiments, system  100  can comprise a visualization system  102  and/or a quantum device  116 . In some embodiments, visualization system  102  can comprise a memory  104 , a processor  106 , a collection component  108 , a plotting component  110 , a visualization component  112 , and/or a bus  114 . In some embodiments, quantum device  116  can comprise a quantum device specification  118 . 
     It should be appreciated that the embodiments of the subject disclosure depicted in various figures disclosed herein are for illustration only, and as such, the architecture of such embodiments are not limited to the systems, devices, and/or components depicted therein. For example, in some embodiments, system  100 , visualization system  102  and/or quantum device  116  can further comprise various computer and/or computing-based elements described herein with reference to operating environment  1000  and  FIG. 10 . In several embodiments, such computer and/or computing-based elements can be used in connection with implementing one or more of the systems, devices, components, and/or computer-implemented operations shown and described in connection with  FIG. 1  or other figures disclosed herein. 
     According to multiple embodiments, memory  104  can store one or more computer and/or machine readable, writable, and/or executable components and/or instructions that, when executed by processor  106 , can facilitate performance of operations defined by the executable component(s) and/or instruction(s). For example, memory  104  can store computer and/or machine readable, writable, and/or executable components and/or instructions that, when executed by processor  106 , can facilitate execution of the various functions described herein relating to visualization system  102 , collection component  108 , plotting component  110 , visualization component  112 , quantum device  116 , quantum device specification  118 , and/or another component associated with system  100  and/or visualization system  102 , as described herein with or without reference to the various figures of the subject disclosure. 
     In some embodiments, memory  104  can comprise volatile memory (e.g., random access memory (RAM), static RAM (SRAM), dynamic RAM (DRAM), etc.) and/or non-volatile memory (e.g., read only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), etc.) that can employ one or more memory architectures. Further examples of memory  104  are described below with reference to system memory  1016  and  FIG. 10 . Such examples of memory  104  can be employed to implement any embodiments of the subject disclosure. 
     According to multiple embodiments, processor  106  can comprise one or more types of processors and/or electronic circuitry that can implement one or more computer and/or machine readable, writable, and/or executable components and/or instructions that can be stored on memory  104 . For example, processor  106  can perform various operations that can be specified by such computer and/or machine readable, writable, and/or executable components and/or instructions including, but not limited to, logic, control, input/output (I/O), arithmetic, and/or the like. In some embodiments, processor  106  can comprise one or more central processing unit, multi-core processor, microprocessor, dual microprocessors, microcontroller, System on a Chip (SOC), array processor, vector processor, and/or another type of processor. Further examples of processor  106  are described below with reference to processing unit  1014  and  FIG. 10 . Such examples of processor  106  can be employed to implement any embodiments of the subject disclosure. 
     In some embodiments, visualization system  102 , memory  104 , processor  106 , collection component  108 , plotting component  110 , visualization component  112 , and/or another component of visualization system  102  as described herein can be communicatively, electrically, and/or operatively coupled to one another via a bus  114  to perform functions of system  100 , visualization system  102 , and/or any components coupled therewith. In several embodiments, bus  114  can comprise one or more memory bus, memory controller, peripheral bus, external bus, local bus, and/or another type of bus that can employ various bus architectures. Further examples of bus  114  are described below with reference to system bus  1018  and  FIG. 10 . Such examples of bus  114  can be employed to implement any embodiments of the subject disclosure. 
     In some embodiments, visualization system  102  and/or quantum device  116  can comprise any type of component, machine, device, facility, apparatus, and/or instrument that comprises a processor and/or can be capable of effective and/or operative communication with a wired and/or wireless network. All such embodiments are envisioned. For example, visualization system  102  and/or quantum device  116  can comprise a server device, a computing device, a general-purpose computer, a special-purpose computer, a quantum computing device (e.g., a quantum computer, a quantum processor, etc.), a tablet computing device, a handheld device, a server class computing machine and/or database, a laptop computer, a notebook computer, a desktop computer, a cell phone, a smart phone, a consumer appliance and/or instrumentation, an industrial and/or commercial device, a digital assistant, a multimedia Internet enabled phone, a multimedia players, and/or another type of device. 
     In some embodiments, visualization system  102  and/or quantum device  116  can be coupled (e.g., communicatively, electrically, operatively, etc.) to one or more external systems, sources, and/or devices (e.g., computing devices, communication devices, etc.) via a data cable (e.g., coaxial cable, High-Definition Multimedia Interface (HDMI), recommended standard (RS)  232 , Ethernet cable, etc.). In some embodiments, visualization system  102  and/or quantum device  116  can be coupled (e.g., communicatively, electrically, operatively, etc.) to one or more external systems, sources, and/or devices (e.g., computing devices, communication devices, etc.) via a network. 
     According to multiple embodiments, such a network can comprise wired and wireless networks, including, but not limited to, a cellular network, a wide area network (WAN) (e.g., the Internet) or a local area network (LAN). For example, visualization system  102  and/or quantum device  116  can communicate with one or more external systems, sources, and/or devices, for instance, computing devices (and vice versa) using virtually any desired wired or wireless technology, including but not limited to: wireless fidelity (Wi-Fi), global system for mobile communications (GSM), universal mobile telecommunications system (UMTS), worldwide interoperability for microwave access (WiMAX), enhanced general packet radio service (enhanced GPRS), third generation partnership project (3GPP) long term evolution (LTE), third generation partnership project 2 (3GPP2) ultra mobile broadband (UMB), high speed packet access (HSPA), Zigbee and other 802.XX wireless technologies and/or legacy telecommunication technologies, BLUETOOTH®, Session Initiation Protocol (SIP), ZIGBEE®, RF4CE protocol, WirelessHART protocol, 6LoWPAN (IPv6 over Low power Wireless Area Networks), Z-Wave, an ANT, an ultra-wideband (UWB) standard protocol, and/or other proprietary and non-proprietary communication protocols. In such an example, visualization system  102  and/or quantum device  116  can thus include hardware (e.g., a central processing unit (CPU), a transceiver, a decoder), software (e.g., a set of threads, a set of processes, software in execution) or a combination of hardware and software that facilitates communicating information between visualization system  102  and/or quantum device  116  and external systems, sources, and/or devices (e.g., computing devices, communication devices, etc.). 
     According to multiple embodiments, visualization system  102  can comprise one or more computer and/or machine readable, writable, and/or executable components and/or instructions that, when executed by processor  106 , can facilitate performance of operations defined by such component(s) and/or instruction(s). Further, in numerous embodiments, any component associated with visualization system  102 , as described herein with or without reference to the various figures of the subject disclosure, can comprise one or more computer and/or machine readable, writable, and/or executable components and/or instructions that, when executed by processor  106 , can facilitate performance of operations defined by such component(s) and/or instruction(s). For example, collection component  108 , plotting component  110 , visualization component  112 , and/or any other components associated with visualization system  102  as disclosed herein (e.g., communicatively, electronically, and/or operatively coupled with and/or employed by visualization system  102 ), can comprise such computer and/or machine readable, writable, and/or executable component(s) and/or instruction(s). Consequently, according to numerous embodiments, visualization system  102  and/or any components associated therewith as disclosed herein, can employ processor  106  to execute such computer and/or machine readable, writable, and/or executable component(s) and/or instruction(s) to facilitate performance of one or more operations described herein with reference to visualization system  102  and/or any such components associated therewith. 
     In some embodiments, visualization system  102  can facilitate performance of operations executed by and/or associated with collection component  108 , plotting component  110 , visualization component  112 , quantum device  116 , quantum device specification  118 , and/or another component associated with visualization system  102  as disclosed herein. For example, as described in detail below, visualization system  102  can facilitate: executing computer executable components stored in memory; receiving a pulse schedule of pulse data and control parameters of a quantum device comprising default pulse data of the quantum device; generating a plot of the pulse schedule; generating a display of the pulse schedule; interpolating discrete pulses received from the quantum device; generating a display of time duration of the pulse schedule; generating a display of channels associated with the pulse schedule; generating a display of conditional execution of the pulse schedule; computing phase change associated with the quantum device, and concurrently generating a visualization of the phase change with the visualization of the pulse schedule; and/or computing conditional pulse operations associated with the quantum device, and concurrently generating a visualization of the conditional pulse operations with the visualization of the pulse schedule. 
     In some embodiments, visualization system  102  can facilitate automated (e.g., without instruction from a human) visualization of one or more arbitrary pulse shapes that can be generated from a discrete data set and/or analytical formulation (e.g., Gaussian or hyperbolic-Tangent pulse shapes). In some embodiments, visualization system  102  can further facilitate automated visualization of one or more schedules of pulses (pulse schedules) that can be used to generate the gate dynamics of a quantum device (e.g., a quantum computer). In some embodiments, such schedules of pulses (pulse schedules) can comprise a collection of the arbitrary pulse shapes described above. 
     In some embodiments, visualization system  102  can facilitate automated (e.g., without instruction from a human) plotting of one or more arbitrary pulse shapes and/or one or more pulse schedules, where such arbitrary pulse shapes can be defined by a discrete set of amplitudes (e.g., a discrete set of complex amplitudes) or an analytic formula (e.g., Gaussian pulse shape). In some embodiments, visualization system  102  can further facilitate automated interpolation of discrete pulses using information obtained from a quantum device on which a pulse schedule is set to be run. 
     In some embodiments, visualization system  102  can further facilitate automated (e.g., without instruction from a human) computation and/or display of information including, but not limited to: time duration of pulse schedules; channels on which such pulse schedules act; information related to conditional execution (e.g., conditional pulse operations); phase changes; time-step set by control hardware (e.g., unit of time on hardware pulses); measurement time; buffer time (e.g., time in between pulses when converting from a quantum assembly language (qasm) model to a pulse model comprising, for instance, a sequence of pulses); a pulse library (e.g., a collection of default pulses that can be defined, calibrated, and/or periodically recalibrated to run on a certain quantum device); and/or other information. 
     As referenced herein, quantum assembly language (qasm) can comprise an instruction set that can indicate which qubit, which gate, and/or pairs of qubits to work on. As reference herein, a qubit can be represented as a vector that starts at the center of a sphere and points to the surface of the sphere (e.g., a Bloch sphere), where such vector can indicate what the qubit is doing. As reference herein, quantum assembly language (qasm) can comprise a concept of gates, where a gate can rotate the point of a vector representing the qubit to another location on the surface of such a sphere. As referenced herein, quantum assembly language (qasm) can comprise a sequence of gates, thereby comprising a gate-based model. As referenced herein, quantum assembly language (qasm) can comprise the canonical quantum computing model. Any gate can perform a rotation of such a vector representing a qubit. Having multiple gates on multiple qubits and arranging such gates and/or qubits in a specific order(s) can facilitate execution of a quantum computation. 
     In some embodiments, visualization system  102  can further facilitate automated visualization of such information described above along with (e.g., simultaneously with) such arbitrary pulse shapes and/or pulse schedules described above. In should be appreciated that visualization system  102  can provide a solution to the issue of complex pulse and pulse schedule visualization by automating the process starting from a pulse or collection of pulses, communicating with a quantum device and interpolating discrete data sets, if necessary, and plotting the pulse or pulse schedules in an automated manner (e.g., without instruction from a human). 
     In some embodiments, visualization system  102  can facilitate automated (e.g., without instruction from a human) generation of a visualization that can comprise pulse shapes and/or pulse schedules that can correspond to and/or be input to one or more input channels of one or more respective qubits of a quantum device (e.g., a quantum computer). In some embodiments, such pulse shapes can comprise defined pulse shapes, where one or more attributes of a pulse shape (e.g., shape, amplitude, length, etc.) can be defined by an entity (e.g., a human user). In some embodiments, such pulse schedules can comprise pulse schedules that can be generated by visualization system  102  (e.g., via plotting component  110  as described below) based on one or more control parameters of a quantum device (e.g., quantum device specification  118  described below), where such control parameters can comprise default pulse data of the quantum device. In some embodiments, such pulse schedules can further comprise one or more of the defined pulse shapes described above. 
     In some embodiments, such input channels described above can comprise electrical couplings (e.g., electrical connections) to one or more qubits of such a quantum device that can facilitate transmitting signals (e.g., microwave signals) comprising pulse shapes and/or pulse schedules to such one or more respective qubits of a quantum device (e.g., quantum device  116 ). In these embodiments, such pulse shapes and/or pulse schedules can constitute a computer program (e.g., a quantum-based computer program) that can be run on such a quantum device to perform one or more quantum computations and/or data processing. 
     In some embodiments, visualization system  102  can facilitate: creating a pulse schedule using information obtained from quantum device  116  (e.g., control parameters, pulse library, etc.); sending the pulse schedule to quantum device  116 ; obtaining result values as a return (e.g., result values of a quantum computation performed by quantum device  116  based on the pulse schedule); iterating through and modifying the pulse schedule (e.g., via interpolation of discrete data points obtained from quantum device  116 ) to generate a second pulse schedule; sending the second pulse schedule to quantum device  116 ; obtaining result values as a return (e.g., result values of a quantum computation performed by quantum device  116  based on the second pulse schedule); iterating through and modifying the second pulse schedule to generate a third pulse schedule and repeating these steps as needed. In some embodiments, visualization system  102  can provide visualizations of such pulse schedules between each iteration (e.g., visualizations  400 ,  500 ,  600 ,  700   a ,  700   b ,  700   c ,  800 , etc.), where such pulse schedules can be used to implement pulse-level control of a quantum device (e.g., quantum device  116 ). In these embodiments, each of the visualizations can comprise a compilation of all pulse schedule data of a certain iteration, and/or other data related thereto, in a single visual display that can facilitate improved ingestion and/or interpretation of such data by an entity (e.g., a human user). 
     According to multiple embodiments, collection component  108  can receive a pulse schedule of pulse data and control parameters of a quantum device comprising default pulse data of the quantum device. For example, collection component  108  can receive a pulse schedule of pulse data (e.g., pulse definitions) that can be generated (e.g., via plotting component  110  as described below) based on information such as, for instance, control parameters of a quantum device (e.g., quantum device  116 ) that can comprise default pulse data of the quantum device. In some embodiments, collection component  108  can receive such control parameters by querying a quantum device as described below. In some embodiments, such a pulse schedule can be defined by a discrete set of amplitudes or an analytic formula (e.g., as described above). In some embodiments, such pulse data of a pulse schedule can comprise one or more pulse definitions that can comprise one or more attributes of a pulse (e.g., shape, amplitude, length, etc.), which can be defined by an entity (e.g., a human user). In some embodiments, such a pulse schedule comprising one or more pulse definitions can be referred to herein as pulse quantum object (qobj). 
     In some embodiments, collection component  108  can query a quantum device (e.g., quantum device  116 ) to obtain information about the quantum device. For example, collection component  108  can query an application programming interface (API) (not illustrated in the figures) that can obtain information such as, for instance, control parameters (e.g., a configuration file) of quantum device  116  including, but not limited to: time-step set by control hardware (e.g., unit of time on hardware pulses), measurement time, buffer time (e.g., time in between pulses when converting from a quantum assembly language (qasm) model to a pulse model), and/or a pulse library (e.g., a collection of default pulses that can be defined, calibrated, and/or periodically recalibrated to run on quantum device  116 ); select parameters (e.g., return values) about quantum device  116  that provide the pulses quantum device  116  supports; the time scales quantum device  116  supports; data about how the pulses are arranged; how many channels are allowed by quantum device  116 ; and/or other information. In some embodiments, such information (e.g., control parameters) about the quantum device (e.g., quantum device  116 ) can be obtained by collection component  108  from such a quantum device and used by plotting component  110  to construct one or more pulse schedules as described below. 
     In some embodiments, to facilitate querying a quantum device (e.g., quantum device  116 ) to obtain information about a quantum device such as, for instance, control parameters of the quantum device, collection component  108  can employ one or more application programming interface (API) calls to query the quantum device. In these embodiments, such a quantum device can generate the control parameters and transmit them (e.g., via a network such as, for example, the Internet) to a database (e.g., memory  104 ), which collection component  108  can query to obtain the control parameters. In some embodiments, the control parameters can be coded on the quantum device and change periodically (e.g., once a day, every time the quantum device is calibrated, etc.). For example, the quantum device can comprise a default set of pulses (also referred to herein as the pulse library), which can be an input to plotting component  110  to generate the pulse schedules. In some embodiments, such a default set of pulses can cause the quantum device to perform one or more certain actions. In some embodiments, the quantum device can have some small fluctuation on a time scale of 12-24 hours and thus, recalibration of what the instructions to the quantum device mean in terms of the default pulses can be required, so the default pulses can change (e.g., the default pulses can be recalibrated every time the quantum device is recalibrated). In some embodiments, the quantum device (e.g., quantum device  116 ) can transmit recalibrated pulses to the database described above (e.g., memory  104 ) where they can be queried by collection component  108 . In some embodiments, due to such quantum device and/or pulse recalibrations, collection component  108  can query (e.g., via API calls) quantum device  116  and/or the database described above on a regular basis (e.g., once every minute, once every hour, once every day, etc.). 
     According to multiple embodiments, plotting component  110  can generate a plot of a pulse schedule based on pulse data of a pulse schedule and/or control parameters of a quantum device comprising default pulse data of the quantum device. For example, plotting component  110  can generate a plot of a pulse schedule (e.g., created by plotting component  110  as described below) based on pulse data of the pulse schedule (e.g., pulse definitions) and/or control parameters of a quantum device (e.g., control parameters of quantum device  116  that can be obtained by collection component  108 ), where such control parameters can comprise default pulse data of the quantum device (e.g., pulse library  312  described below). 
     In some embodiments, to facilitate generating a pulse schedule, plotting component  110  can extract one or more items from control parameters (e.g., a configuration file) corresponding to a quantum device (e.g., from the control parameters of quantum device  116  described above). For example, plotting component  110  can extract items including, but not limited to: time-step set by control hardware (e.g., unit of time on hardware pulses); measurement time; buffer time (e.g., time in between pulses when converting from a quantum assembly language (qasm) model to a pulse model); a pulse library (e.g., a collection of default pulses that can be defined, calibrated, and/or periodically recalibrated to run on a certain quantum device), and/or other items. 
     In some embodiments, to facilitate generating a pulse schedule, plotting component  110  can sort one or more pulses by channel (e.g., if time-ordered) and compute the length of the pulse schedule (e.g., using time or change in time (dt)). In some embodiments, to facilitate generating a pulse schedule, plotting component  110  can merge defined pulse definitions (e.g., defined by a human user) with the pulse library of the quantum device and interpolate discrete pulse data, if desired, where such discrete pulse data can comprise a collection of data points that when interpolated (e.g., via interpolation component  202  as described below with reference to  FIG. 2 ) can constitute a Gaussian pulse. 
     In some embodiments, pulse files (pulses) obtained by collection component  108  from a quantum device (e.g., quantum device  116 ) can be provided in chronological order, with no additional structure and plotting component  110  can arrange such pulses to generate a pulse schedule. In some embodiments, plotting component  110  can arrange such pulses by utilizing information such as, for instance, control parameters obtained from quantum device  116  as described above that can provide data about which pulses come before and/or after a certain pulse. In some embodiments, plotting component  110  can layout the pulses according to channel, start time, and in embodiments where start times are dependent on previous channel pulses (e.g., persistent value pulses), compute the start time and/or end time of such pulses. In some embodiments, such ordering of the pulses can comprise a separate input file to plotting component  110  (e.g., separate from the pulse files and/or other information obtained from the quantum device), where such a separate input file can comprise the instruction set that can enable construction of a pulse schedule. In some embodiments, constructing the pulse schedule can constitute developing a quantum-based computer program to perform one or more quantum computations and/or data processing on the quantum device (e.g., quantum device  116 ) from which the parameters are obtained. 
     In some embodiments, to facilitate generating a pulse schedule, for example, a pulse schedule generated based on control parameters obtained from a quantum device (e.g., quantum device  116 ), plotting component  110  (and/or analysis component  204  described below with reference to  FIG. 2 ) can calculate the phase change (also referred to herein as frame change) by computing the cumulative phase change on a given channel as a function of time and multiplying pulses at these times by the cumulated phase. As referenced herein, a phase change can comprise an exponential function (e.g., expressed as e i·Θ ) that can be represented by an arrow (e.g., a vector) in the x-y plane, where the amount of each x and y component can be determined by the angle Θ (theta), which can indicate the amount of real component and imaginary component. As referenced herein, phase change or frame change can mean that after some time t when the phase change occurs, the values of all pulses subsequent to the phase change (e.g., pulses after the time of the phase change) are modified, as they rotate into the complex plane (e.g., imaginary plane) and thereafter comprise a complex component and a real component. As a phase change (or a frame change) alters the pulses that come after the phase change, in some embodiments, the subsequent pulses can be modified by the action of the phase change, which can be performed by plotting component  110 . 
     According to multiple embodiments, visualization component  112  can generate a display of a pulse schedule. For example, visualization component  112  can generate a visual display of a pulse schedule that can be generated by plotting component  110  (e.g., as described above) based on control parameters of quantum device  116 . Examples of such a visual display can comprise visualizations  400 ,  500 ,  600 ,  700   a ,  700   b ,  700   c , and/or  800  described below and illustrated in  FIGS. 4, 5, 6, 7A, 7B, 7C , and/or  8 , respectively. In some embodiments, visualization component  112  can render such a visual display (e.g., visualizations  400 ,  500 ,  600 ,  700   a ,  700   b ,  700   c , and/or  800 ) on a display component (e.g., a monitor, a screen, output device  1040  described below with reference to  FIG. 10 , etc.) by employing a user interface of visualization system  102  (e.g., a graphical user interface (GUI)). 
     In some embodiments, visualization component  112  can generate a display of time duration of a pulse schedule. For example, visualization component  112  can generate a visual display of time duration (e.g., in terms of nanoseconds (ns)) of a pulse schedule that can be generated by plotting component  110  (e.g., as described above) based on control parameters of quantum device  116 . Examples of such a visual display can comprise visualizations  400 ,  500 ,  600 ,  700   a ,  700   b ,  700   c , and/or  800  described below and illustrated in  FIGS. 4, 5, 6, 7A, 7B, 7C , and/or  8 , respectively. 
     In some embodiments, visualization component  112  can generate a display of channels associated with a pulse schedule. For example, visualization component  112  can generate a visual display of channels (e.g., control channels, input channels, etc.) associated with a pulse schedule that can be generated by plotting component  110  (e.g., as described above) based on control parameters of quantum device  116 . Examples of such a visual display can comprise visualizations  400 ,  500 ,  600 ,  700   a ,  700   b ,  700   c , and/or  800  described below and illustrated in  FIGS. 4, 5, 6, 7A, 7B, 7C , and/or  8 , respectively. 
     In some embodiments, visualization component  112  can generate a display of conditional execution of a pulse schedule. For example, visualization component  112  can generate a visual display of conditional execution (e.g., a conditional pulse) of a pulse schedule that can be generated by plotting component  110  (e.g., as described above) based on control parameters of quantum device  116 . An example, of such a visual display can comprise visualization  700   a  described below and illustrated in  FIG. 7A . 
     According to multiple embodiments, quantum device  116  can comprise a superconducting system. For example, quantum device  116  can comprise a superconducting system including, but not limited to, a quantum computing device (e.g., quantum computer, quantum processor, quantum hardware, quantum simulator, etc.), a superconducting chip, a superconducting quantum bit circuit (qubit circuit) fabricated on a semiconductor substrate (e.g., a silicon substrate), a circuit quantum electrodynamic (circuit-QED) system, and/or another superconducting system. In some embodiments, quantum device  116  can comprise one or more qubits that can be coupled (e.g., electrically) to visualization system  102  via one or more control channels (e.g., input channels) such as, for example, drive channel  306 , measure channel  308 , and/or additional control channel  310  as described below with reference to  FIG. 3 . 
     According to multiple embodiments, quantum device specification  118  can comprise information corresponding to quantum device  116 . For example, quantum device specification  118  can comprise the control parameters of quantum device  116  described above. For instance, quantum device specification  118  can comprise control parameters (e.g., a configuration file) of quantum device  116  including, but not limited to: time-step set by control hardware (e.g., unit of time on hardware pulses), measurement time, buffer time (e.g., time in between pulses when converting from a quantum assembly language (qasm) model to a pulse model), and/or a pulse library (e.g., a collection of default pulses that can be defined, calibrated, and/or periodically recalibrated to run on quantum device  116 ); select parameters (e.g., return values) about quantum device  116  that provide the pulses quantum device  116  supports; the time scales quantum device  116  supports; data about how the pulses are arranged; how many channels are allowed by quantum device  116 ; and/or other information. Additionally, or alternatively, in some embodiments, quantum device specification  118  can further comprise one or more defined pulse files (e.g., defined pulse shapes that can be defined by an entity such as, for instance, a human user) and/or one or more pulse schedules (e.g., pulse schedules generated by plotting component  110  as described above). 
       FIG. 2  illustrates a block diagram of an example, non-limiting system  200  that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. Repetitive description of like elements and/or processes employed in respective embodiments is omitted for sake of brevity. In some embodiments, system  200  can comprise visualization system  102 , which can comprise an interpolation component  202  and/or an analysis component  204 . 
     According to multiple embodiments, interpolation component  202  that interpolates discrete pulses received from a quantum device. For example, interpolation component  202  can interpolate discrete data points of one or more default pulses (e.g., the pulse library) obtained from quantum device  116  (e.g., via collection component  108  as described above with reference to  FIG. 1 ), where such discrete data points can be derived from sampling an analytical mathematical function (e.g., Gaussian, hyperbolic-Tangent, and/or similar functions). In some embodiments, interpolation component  202  can interpolate such discrete data points of such one or more default pulses (e.g., the pulse library) obtained from quantum device  116  to generate smooth continuous functions such as, for example, Gaussian curves that can represent such default pulses. 
     According to multiple embodiments, analysis component  204  can compute phase change associated with a quantum device. For example, analysis component  204  can compute a phase change associated with a quantum device by employing a function (e.g., compute_frame_change) in Python. In some embodiments, analysis component  204  can employ such a function in Python to: compute values of pulses occurring after each phase change; compute how long a persistent value should last; and/or determine what is conditional and what is not. In some embodiments, performing such operations described here can constitute creating callable data structures (e.g., callable data structures of tables  404 ,  604 ,  704   a ,  704   b , and/or  704   c  described below and illustrated in  FIGS. 4, 6, 7A, 7B , and/or  7 C, respectively. 
     In some embodiments, analysis component  204  can employ such a function in Python to compute a pulse value at a certain time t, where such a function can compute such a pulse value by determining whether one or more phase changes happen and accumulating all such phase changes, determining whether a pulse is a persistent value pulse, and/or determining other information. In some embodiments, such a function in Python that can be employed by analysis component  204  can perform such a pulse value computation described above and return a pulse value (e.g., point in time value) that can comprise a real component and an imaginary component (e.g., real pulse component  410  and complex pulse component  412 , respectively, described below with reference to  FIG. 4 ). In these embodiments, visualization component  112  can concurrently generate a visualization of the phase change with a visualization of the pulse schedule (e.g., via visualizations  400 ,  500 ,  600 ,  700   a ,  700   b ,  700   c , and/or  800  as described below and illustrated in  FIGS. 4, 5, 6, 7A, 7B, 7C , and/or  8 , respectively). 
     In some embodiments, analysis component  204  can compute conditional pulse operations associated with a quantum device. For example, analysis component  204  can compute such conditional pulse operations associated with a quantum device by employing the function in Python described above. In this example, visualization component  112  can concurrently generate a visualization of the conditional pulse operations with a visualization of the pulse schedule (e.g., via visualization  700   a  and/or visualization  700   c  as described below and illustrated in  FIGS. 7A and/or 7C , respectively). 
       FIG. 3  illustrates a block diagram of an example, non-limiting system  300  that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. Repetitive description of like elements and/or processes employed in respective embodiments is omitted for sake of brevity. 
     In some embodiments, system  300  can comprise a user-layer  302 , a device-layer  304 , a drive channel  306  (denoted d i (t) in  FIG. 3 ), a measure channel  308  (denoted m i (t) in  FIG. 3 ), an additional control channel  310  (denoted u i (t) in  FIG. 3 ), a pulse library  312 , and/or defined settings  314 . In some embodiments, system  300  can comprise an example, non-limiting alternative embodiment of system  100  and/or system  200 , where user-layer  302  can comprise visualization system  102  and device-layer  304  can comprise quantum device  116 , which can comprise quantum device specification  118 . 
     In some embodiments, drive channel  306 , measure channel  308 , and/or additional control channel  310  can comprise input channels coupled (e.g., electrically) to one or more respective qubits of a quantum device (e.g., one or more respective qubits of quantum device  116 ), where such input channels can be used to control and/or measure such respective qubits. In some embodiments, each qubit of such a quantum device can be coupled (e.g., electrically) to a drive channel (e.g., drive channel  306 ), a measure channel (e.g., measure channel  308 ), and/or an additional control channel (e.g., additional control channel  310 ). In some embodiments, drive channel  306 , measure channel  308 , and/or additional control channel  310  can facilitate transmitting signals (e.g., microwave signals) comprising pulse shapes and/or pulse schedules to such one or more respective qubits of a quantum device (e.g., quantum device  116 ). In these embodiments, such pulse shapes and/or pulse schedules can constitute a computer program (e.g., a quantum-based computer program) that can be run on such a quantum device to perform one or more quantum computations and/or data processing. 
     In some embodiments, drive channel  306  can be used to drive (e.g., control) a qubit of a quantum device (e.g., quantum device  116 ). For example, drive channel  306  can be used to control a state of a qubit by inputting the one or more pulse shapes and/or pulse schedules into drive channel  306 , where such state of a qubit can be represented by a vector on a sphere of radius 1 (e.g., a Bloch sphere of radius 1). In this example, since +z=10&gt; and −z=11&gt;, this is called the z-representation. In this example, classically, a state of a qubit (also referred to herein as a state vector or a qubit state vector) can only point up or down and some quantum applications require rotating a state vector of a qubit to arbitrary points on the sphere. In this example, rotation of a qubit state vector can be performed by applying “gates”, for instance, starting at 10&gt;. In this example, drive channel  306  can be utilized to drive a qubit by rotating the qubit state vector around the sphere (e.g., to apply gates). In some embodiments, with respect to an x-gate, drive channel  306  can be used to rotate π around an x-axis of such a sphere. In some embodiments, with respect to a y-gate, drive channel  306  can be used to rotate π around a y-axis of such a sphere. In some embodiments, with respect to a z-gate, drive channel  306  can be used to rotate π around a z-axis of such a sphere. In some embodiments, with respect to a Hadamard Gate, drive channel  306  can be used to rotate the qubit state vector onto the equator of such a sphere (e.g., real quantum gate). For example, with respect to a Hadamard Gate, drive channel  306  can be used to rotate the qubit state vector around ({circumflex over (x)}+{circumflex over (z)})/√{square root over (2)} by π, which can provide a vector that points in the +x direction. 
     In some embodiments, measure channel  308  can be used to measure (e.g., via a readout device not illustrated in the figures) a qubit of a quantum device (e.g., quantum device  116 ). For example, measure channel  308  can be used to measure a state of a qubit (e.g., a quantum state, a logic state, etc.) of quantum device  116 . 
     In some embodiments, additional control channel  310  can be used to drive (e.g., control) one or more parameters (e.g., quantum-based parameters) of a qubit in a quantum device (e.g., quantum device  116 ) and/or the quantum device itself. For example, additional control channel  310  can be used to control such one or more parameters of the qubit and/or the quantum device by inputting the one or more pulse shapes and/or pulse schedules into additional control channel  310 . 
     In some embodiments, pulse library  312  can comprise one or more default pulse definitions (e.g., default pulse shapes, amplitude, length, etc.) of a certain quantum device (e.g., quantum device  116 ) that can be utilized (e.g., by visualization system  102 , a human user, etc.) to implement certain operations on the quantum device. In these embodiments, such default pulse definitions can comprise the pulse definitions that can change every time the quantum device is recalibrated (e.g., once every hour, once every 24 hours, etc.), where such pulse definitions can constitute hardware defined pulse definitions that can be calibrated and recalibrated periodically for a certain quantum device (e.g., quantum device  116 ). 
     In some embodiments, defined settings  314  can comprise defined pulse shapes (also referred to herein as pulse definitions). For example, defined settings  314  can comprise defined pulse shapes, where one or more attributes of a pulse shape (e.g., shape, amplitude, length, etc.) can be defined by an entity (e.g., a human user). 
       FIG. 4  illustrates an example, non-limiting visualization  400  that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. Repetitive description of like elements and/or processes employed in respective embodiments is omitted for sake of brevity. 
     In some embodiments, visualization  400  can comprise a plot  402  and a table  404 . In some embodiments, plot  402  can comprise a plot of pulse schedule data that can correspond to one or more input channels coupled (e.g., electrically) to a qubit in a quantum device. For example, plot  402  can comprise a plot of pulse schedule data of drive channel  306 , measure channel  308 , and/or additional control channel  310  coupled (e.g., electrically) to a qubit (e.g., a qubit denoted as qubit 0) of a quantum device (e.g., quantum device  116 ). 
     In some embodiments, table  404  can comprise one or more callable data structures that can return the value of a channel (e.g., drive channel  306 ) at a given instance in time, where such data structures can account for phase changes and/or other special pulses that modify all subsequent pulses (e.g., pulses occurring at a later time). For example, table  404  can comprise time data  420  and/or phase angle data  422  as illustrated in  FIG. 4 , where such data can correspond to pulse schedule data of plot  402 . For instance, in some embodiments, time data  420  can comprise a time of a phase change in a pulse schedule on drive channel  306  and phase angle data  422  can comprise a phase angle of such phase change expressed in terms of radians, for instance. 
     In some embodiments, the x-axis of plot  402  can represent time (e.g., nanoseconds (ns)). In some embodiments, the y-axis of plot  402  can represent amplitude of discrete pulses on each input channel. For example, the y-axis of plot  402  can represent amplitude of: pulse  406 , real pulse component  410 , and/or complex pulse component  412  of drive channel  306 ; measurement pulse  414  of measure channel  308 ; and/or additional control pulse  416  and/or persistent value pulse  418  of additional control channel  310 . In some embodiments, the y-axis of plot  402  can comprise amplitude of discrete pulses in terms of a unitless value. In some embodiments, pulse  406 , real pulse component  410 , and complex pulse component  412  can comprise Gaussian pulses. In some embodiments, pulse  406 , real pulse component  410 , and complex pulse component  412  can collectively constitute an example of a pulse schedule as described herein in accordance with one or more embodiments of the subject disclosure. 
     In some embodiments, as described above, each qubit of a quantum device can have three (3) input channels coupled thereto (e.g., electrically). For example, qubit 0 of visualization  400  can be electrically coupled to drive channel  306 , measure channel  308 , and/or additional control channel  310  (e.g., denoted d 0 , m 0 , u 0  in  FIG. 4 ), where such input channels can be used to control and/or measure qubit 0. In some embodiments, drive channel  306  (d 0 ) can be used to drive qubit 0 (e.g., control qubit 0). In some embodiments, measure channel  308  (m 0 ) can be used to do one or more measurements of qubit 0 (e.g., measurement of a quantum state or logic state of qubit 0), where measurement pulse  414  can represent such a measurement. In some embodiments, additional control channel  310  (u 0 ) can be similar to drive channel  306  and it can be used to control system parameters of qubit 0. 
     In some embodiments, phase change  408  can flip a qubit state vector from 0 to 1. In some embodiments, phase change  408  can implement a rotation of a subsequent pulse value into the complex plane (e.g., imaginary plane). For example, as illustrated by time data  420  and phase angle data  422  in table  404 , at time=60 ns on plot  402 , phase change  408  can implement a rotation of a subsequent pulse value by 0.2 radians, thereby generating real pulse component  410  and complex pulse component  412 . 
     In some embodiments, persistent value pulse  418  can comprise a pulse having a fixed numerical value that can remain fixed for a time that can be determined based the timing of a pulse that follows such a persistent value pulse. For example, persistent value pulse  418  can comprise a fixed value pulse having variable length timing that can be determined based on the timing of the pulse following persistent value pulse  418 . 
       FIG. 5  illustrates an example, non-limiting visualization  500  that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. Repetitive description of like elements and/or processes employed in respective embodiments is omitted for sake of brevity. 
     In some embodiments, visualization  500  can comprise an example, non-limiting alternative embodiment of visualization  400 , where plot  502  can comprise an example, non-limiting alternative embodiment of plot  402 . In some embodiments, plot  502  can comprise a three-dimensional (3D) embodiment of plot  402 . In some embodiments, plot  502  can comprise a plot of pulse schedule data that can correspond to one or more input channels coupled (e.g., electrically) to respective qubits in a quantum device. For example, plot  502  can comprise a plot of pulse schedule data of one or more drive channels  306   a ,  306   n  (e.g., respectively denoted as d 0  and d 2  in  FIG. 5 ), one or more measure channels  308   a ,  308   b ,  308   n  (e.g., respectively denoted as m 0 , m 1 , and m 2  in  FIG. 5 ), and/or one or more additional control channels  310   a  (where n can represent a total quantity of such respective channels). In these embodiments, drive channel  306   a , measure channel  308   a , and/or additional control channel  310   a  can be coupled (e.g., electrically) to a first qubit (e.g., a qubit that can be denoted as qubit 0). In these embodiments, measure channel  308   b  can be coupled (e.g., electrically) to a second qubit (e.g., a qubit that can be denoted as qubit 1). In these embodiments, drive channel  306   n  and/or measure channel  308   n  can be coupled (e.g., electrically) to a third qubit (e.g., a qubit that can be denoted as qubit n). 
     In some embodiments, drive channels  306   a ,  306   n  can respectively comprise one or more pulses  406   a ,  406   n , one or more phase changes  408   a ,  408   n , one or more real pulse components  410   a ,  410   n , and/or one or more complex pulse components  412   a ,  412   n  (where n can represent a total quantity of such components). In some embodiments, measure channels  308   a ,  308   b ,  308   n  can respectively comprise one or more measurement pulses  414   a ,  414   b ,  414   n  (where n can represent a total quantity of such components). In some embodiments, additional control channel  310   a  can comprise one or more additional control pulses  416   a.    
       FIG. 6  illustrates an example, non-limiting visualization  600  that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. Repetitive description of like elements and/or processes employed in respective embodiments is omitted for sake of brevity. 
     In some embodiments, visualization  600  can comprise an example, non-limiting alternative embodiment of visualization  400  and/or visualization  500 . In some embodiments, visualization  600  can comprise a plot  602  and/or a table  604 . In some embodiments, plot  602  can comprise an example, non-limiting alternative embodiment of plot  402  and/or plot  502 . In some embodiments, table  604  can comprise an example, non-limiting alternative embodiment of table  404 . 
     In some embodiments, plot  602  can comprise a plot of pulse schedule data that can correspond to one or more drive channels coupled (e.g., electrically) to respective qubits in a quantum device. For example, plot  602  can comprise a plot of pulse schedule data of drive channels  306   a ,  306   b ,  306   n  (where n can represent a total quantity of drive channels  306 ) that can be coupled (e.g., electrically) to respective qubits of a quantum device (e.g., quantum device  116 ). In some embodiments, drive channel  306   a  (e.g., denoted as d 0  in  FIG. 6 ) can be coupled (e.g., electrically) to a first qubit (e.g., a qubit that can be denoted as qubit 0). In some embodiments, drive channel  306   b  (e.g., denoted as d 1  in  FIG. 6 ) can be coupled (e.g., electrically) to a second qubit (e.g., a qubit that can be denoted as qubit 1). In some embodiments, drive channel  306   n  (e.g., denoted as d 2  in  FIG. 6 ) can be coupled (e.g., electrically) to a third qubit (e.g., a qubit that can be denoted as qubit 2). 
     In some embodiments, table  604  can comprise one or more callable data structures that can return the value of one or more channels (e.g., drive channels  306   a ,  306   b ,  306   n ) at a given instance in time, where such data structures can account for phase changes and/or other special pulses that modify all subsequent pulses (e.g., pulses occurring at a later time). For example, table  604  can comprise time data  606 , channel identity data  608 , and/or phase angle data  610  as illustrated in  FIG. 6 , where such data can correspond to pulse schedule data of plot  602 . For instance, in some embodiments, time data  606  can comprise a time of a phase change in a pulse schedule on a drive channel (e.g., drive channel  306   a ,  306   b ,  306   n ) and phase angle data  610  can comprise a phase angle of such phase change expressed in terms of radians, for instance. 
       FIGS. 7A, 7B, and 7C  illustrate example, non-limiting visualizations  700   a ,  700   b ,  700   c  that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. Repetitive description of like elements and/or processes employed in respective embodiments is omitted for sake of brevity. 
     In some embodiments, visualization  700   a  ( FIG. 7A ) can comprise an example, non-limiting alternative embodiment of visualizations  400 ,  500 , and/or  600 . In some embodiments, visualization  700   a  can comprise a plot  702   a  and/or a table  704   a . In some embodiments, plot  702   a  can comprise an example, non-limiting alternative embodiment of plot  402  and/or plot  602 . In some embodiments, table  704   a  can comprise an example, non-limiting alternative embodiment of table  404  and/or table  604 . 
     In some embodiments, plot  702   a  can comprise a plot of pulse schedule data that can correspond to one or more input channels coupled (e.g., electrically) to a qubit in a quantum device. For example, plot  702   a  can comprise a plot of pulse schedule data of drive channel  306  and/or measure channel  308  that can be coupled (e.g., electrically) to a qubit (e.g., a qubit denoted as qubit 0) of a quantum device (e.g., quantum device  116 ). In some embodiments, plot  702   a  can comprise one or more conditional pulses  706  (e.g., denoted as COND in  FIG. 7A ). In some embodiments, conditional pulse  706  can provide information about how the quantum-based computer program described herein branches. 
     In some embodiments, table  704   a  can comprise one or more callable data structures that can return the value of one or more channels (e.g., drive channel  306 ) at a given instance in time, where such data structures can account for phase changes, conditional pulses, conditional pulse operations, and/or other special pulses that modify all subsequent pulses (e.g., pulses occurring at a later time). For example, table  704   a  can comprise time data  708  and/or conditional pulse data  710  as illustrated in  FIG. 7A , where such data can correspond to pulse schedule data of plot  702   a . For instance, in some embodiments, time data  708  can comprise a time of a conditional pulse (e.g., conditional pulse  706 ) in a pulse schedule on a drive channel (e.g., drive channel  306 ) and conditional pulse data  710  can comprise conditional pulse data of such conditional pulse (e.g., mask &amp;&amp; register==value where mask, register, and value can be binary strings, arrays, of hex values). 
     In some embodiments, visualization  700   b  ( FIG. 7B ) can comprise an example, non-limiting alternative embodiment of visualizations  400 ,  500 ,  600 , and/or  700   a . In some embodiments, visualization  700   b  can comprise a plot  702   b  and/or a table  704   b . In some embodiments, plot  702   b  can comprise an example, non-limiting alternative embodiment of plot  402 , plot  602 , and/or plot  702   a . In some embodiments, table  704   b  can comprise an example, non-limiting alternative embodiment of table  404 , table  604 , and/or table  704   a.    
     In some embodiments, visualization  700   c  ( FIG. 7C ) can comprise an example, non-limiting alternative embodiment of visualizations  400 ,  500 ,  600 ,  700   a , and/or  700   b . In some embodiments, visualization  700   c  can comprise a plot  702   c  and/or a table  704   c . In some embodiments, plot  702   c  can comprise an example, non-limiting alternative embodiment of plot  402 , plot  602 , plot  702   a , and/or plot  702   b . In some embodiments, table  704   c  can comprise an example, non-limiting alternative embodiment of table  404 , table  604 , table  704   a , and/or table  704   b.    
       FIG. 8  illustrates an example, non-limiting visualization  800  that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. Repetitive description of like elements and/or processes employed in respective embodiments is omitted for sake of brevity. 
     In some embodiments, visualization  800  can comprise an example, non-limiting alternative embodiment of visualizations  400 ,  500 ,  600 ,  700   a ,  700   b , and/or  700   c . In some embodiments, visualization  800  can comprise an interactive visual display of a pulse schedule. In some embodiments, visualization  800  can comprise one or more interactive pulses  802  and/or interactive measurement pulses  804 . In some embodiments, selection (e.g., by an entity such as, for instance, a human user) of such an interactive pulse  802  and/or an interactive measurement pulse  804  can cause visualization system  102  and/or visualization component  112  to display (e.g., in a subfigure) information corresponding to such an interactive pulse  802  and/or an interactive measurement pulse  804  (e.g., the pulse function, the Gaussian pulse, the amplitude, etc.). In some embodiments, visualization  800  can comprise one or more phase changes  806  that can be represented by vertical lines as illustrated in  FIG. 8 . In some embodiments, visualization  800  can comprise one or more conditional pulses  808 , which can be represented by a pattern as illustrated in  FIG. 8 . 
     In some embodiments, visualization system  102  can be associated with various technologies. For example, visualization system  102  can be associated with quantum computing technologies, quantum computing architecture technologies, quantum hardware technologies, signal processing technologies, quantum computer programming technologies, superconducting quantum circuit technologies, quantum bit (qubit) technologies, circuit quantum electrodynamics (circuit-QED) technologies, and/or other technologies. 
     In some embodiments, visualization system  102  can provide technical improvements to systems, devices, components, operational steps, and/or processing steps associated with the various technologies identified above. For example, visualization system  102  can facilitate visualization of abstract pulses of a quantum computing model, thereby facilitating improved development of a quantum computing algorithm or a quantum computing device. 
     In some embodiments, visualization system  102  can provide technical improvements to a processing unit (e.g., processor  106 ) associated with a quantum computing device (e.g., a quantum processor, quantum hardware etc.), a circuit-QED system and/or a superconducting quantum circuit. For example, by generating visualizations of abstract pulses of a quantum computing model as described above, visualization system  102  can facilitate improved performance of such a processing unit (e.g., processor  106 ) by reducing the number of processing cycles such processing unit completes to develop and/or enable execution of a pulse schedule (e.g., a pulse-level quantum computing program) that can be executed by a quantum device. In some embodiments, an advantage of visualization system  102  is that it can facilitate generation and/or visualization of a pulse schedule that can be useful to an entity (e.g., a human user) developing quantum computing algorithms and/or quantum devices (e.g., quantum computers), as pulses of such pulse schedule are currently abstracted away in the standard quantum computing model (e.g., not visually displayed) where such entities manipulate gates, the pulses are underneath each gate, and the pulses do not necessarily correspond to the strict definition of a gate. 
     In some embodiments, visualization system  102  can employ hardware or software to solve problems that are highly technical in nature, that are not abstract and that cannot be performed as a set of mental acts by a human. In some embodiments, some of the processes described herein may be performed by one or more specialized computers (e.g., one or more specialized processing units, a specialized quantum computer, etc.) for carrying out defined tasks related to the various technologies identified above. In some embodiments, visualization system  102  or components thereof, can be employed to solve new problems that arise through advancements in technologies mentioned above, employment of quantum computing systems, cloud computing systems, computer architecture, and/or another technology. 
     It is to be appreciated that visualization system  102  can utilize various combinations of electrical components, mechanical components, and circuitry that cannot be replicated in the mind of a human or performed by a human, as the various operations that can be executed by visualization system  102  or components thereof as described herein are operations that are greater than the capability of a human mind. For instance, the amount of data processed, the speed of processing such data, or the types of data processed by visualization system  102  over a certain period of time can be greater, faster, or different than the amount, speed, or data type that can be processed by a human mind over the same period of time. 
     According to several embodiments, visualization system  102  can also be fully operational towards performing one or more other functions (e.g., fully powered on, fully executed, etc.) while also performing the various operations described herein. It should be appreciated that such simultaneous multi-operational execution is beyond the capability of a human mind. It should also be appreciated that visualization system  102  can include information that is impossible to obtain manually by an entity, such as a human user. For example, the type, amount, or variety of information included in visualization system  102 , collection component  108 , plotting component  110 , visualization component  112 , quantum device  116 , quantum device specification  118 , interpolation component  202 , and/or analysis component  204  can be more complex than information obtained manually by a human user. 
       FIG. 9A  illustrates a flow diagram of an example, non-limiting computer-implemented method  900   a  that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. Repetitive description of like elements and/or processes employed in respective embodiments is omitted for sake of brevity. 
     In some embodiments, at  902   a , the computer-implemented method can comprise receiving (e.g., via visualization system  102  and/or collection component  108 ) inputs comprising pulse schedule (e.g., a pulse schedule generated by plotting component  110 ), pulse definitions (e.g., pulse definitions defined by an entity such as, for instance, a human user), and/or control parameters corresponding to a quantum device (e.g., control parameters described above with reference to  FIG. 1 , quantum device specification  118 , etc.). 
     In some embodiments, at  904   a , the computer-implemented method can comprise extracting (e.g., via visualization system  102 , collection component  108 , and/or plotting component  110 ) time-step set by control hardware, measurement time, buffer time, and/or pulse library from the control parameters. For example, visualization system  102 , collection component  108 , and/or plotting component  110  can extract such information by reading (e.g., via processor  106 ) it from a configuration file (e.g., control parameters) obtained from quantum device or reading it from a file designed to model a quantum device. 
     In some embodiments, at  906   a , the computer-implemented method can comprise sorting (e.g., via visualization system  102 , collection component  108 , and/or plotting component  110 ) pulses (e.g., pulse definitions and/or default pulses of a pulse library obtained by collection component  108  from a quantum device) by channel, if time-ordered (e.g., drive channel  306 , measure channel  308 , additional control channel  310 , etc.). For example, visualization system  102 , collection component  108 , and/or plotting component  110  can sort such pulses by channel and/or start time (e.g., determine start time if pulse is dependent on previous pulses on same channel). 
     In some embodiments, at  908   a , the computer-implemented method can comprise computing (e.g., via visualization system  102  and/or plotting component  110 ) the length of the pulse schedule. 
     In some embodiments, at  910   a , the computer-implemented method can comprise merging (e.g., via visualization system  102  and/or plotting component  110 ) pulse definitions with pulse library (e.g., pulse library  312 ). For example, visualization system  102  and/or plotting component  110  can merge user pulse definitions and a quantum device pulse library (e.g., pulse library  312 ) into single data structure. 
     In some embodiments, at  912   a , the computer-implemented method can comprise interpolating (e.g., via visualization system  102 , plotting component  110 , and/or interpolation component  202 ) discrete pulse data, if desired (e.g., discrete pulse data obtained by collection component  108  from a quantum device). For example, visualization system  102 , plotting component  110 , and/or interpolation component  202  can interpolate such discrete pulse data using polynomial interpolation (e.g., cubic-polynomial interpolation). 
     In some embodiments, at  914   a , the computer-implemented method can comprise creating (e.g., via visualization system  102 , plotting component  110 , and/or analysis component  204 ) callable data structures (e.g., time data  420 , phase angle data  422 , time data  708 , conditional pulse data  710 , etc.) that return the value of a channel (e.g., drive channel  306 , measure channel  308 , additional control channel  310 , etc.) at a given instance in time. For example, visualization system  102 , plotting component  110 , and/or analysis component  204  can create such callable data structures by composing callable data structures such as, for instance, functions built up from pulse schedule data (e.g., time data  420 , phase angle data  422 , time data  708 , conditional pulse data  710 , etc.) that return the value of a channel (e.g., drive channel  306 , measure channel  308 , additional control channel  310 , etc.) at a given instance in time. 
     In some embodiments, at  916   a , the computer-implemented method can comprise displaying all information in a visual format (e.g., via visualization system  102  and/or visualization component  112 ). 
       FIG. 9B  illustrates a flow diagram of an example, non-limiting computer-implemented method  900   b  that can facilitate visualizing arbitrary pulse shapes and schedules in quantum computing applications in accordance with one or more embodiments described herein. Repetitive description of like elements and/or processes employed in respective embodiments is omitted for sake of brevity. 
     In some embodiments, at  902   b , the computer-implemented method can comprise executing, by a device operatively coupled to a processor (e.g., processor  106 ), computer executable components stored in memory (e.g., memory  104 ). 
     In some embodiments, at  904   b , the computer-implemented method can comprise receiving (e.g., via visualization system  102  and/or collection component  108 ), by the device, a pulse schedule of pulse data (e.g., a pulse schedule generated by plotting component  110 ) and control parameters of a quantum device (e.g., control parameters described above with reference to  FIG. 1 , quantum device specification  118 , etc.) comprising default pulse data (e.g., pulse library  312 ) of the quantum device. 
     In some embodiments, at  906   b , the computer-implemented method can comprise generating (e.g., via visualization system  102  and/or plotting component  110 ), by the device, a plot of the pulse schedule (e.g., plots  402 ,  502 ,  602 ,  702   a ,  702   b ,  702   c , and/or  800 ). 
     In some embodiments, at  908   b , the computer-implemented method can comprise generating (e.g., via visualization system  102  and/or visualization component  112 ), by the device, a display of the pulse schedule (e.g., visualizations  400 ,  500 ,  600 ,  700   a ,  700   b ,  700   c , and/or  800 ). 
     For simplicity of explanation, the computer-implemented methodologies are depicted and described as a series of acts. It is to be understood and appreciated that the subject innovation is not limited by the acts illustrated and/or by the order of acts, for example acts can occur in various orders and/or concurrently, and with other acts not presented and described herein. Furthermore, not all illustrated acts can be required to implement the computer-implemented methodologies in accordance with the disclosed subject matter. In addition, those skilled in the art will understand and appreciate that the computer-implemented methodologies could alternatively be represented as a series of interrelated states via a state diagram or events. Additionally, it should be further appreciated that the computer-implemented methodologies disclosed hereinafter and throughout this specification are capable of being stored on an article of manufacture to facilitate transporting and transferring such computer-implemented methodologies to computers. The term article of manufacture, as used herein, is intended to encompass a computer program accessible from any computer-readable device or storage media. 
     In order to provide a context for the various aspects of the disclosed subject matter,  FIG. 10  as well as the following discussion are intended to provide a general description of a suitable environment in which the various aspects of the disclosed subject matter can be implemented.  FIG. 10  illustrates a block diagram of an example, non-limiting operating environment in which one or more embodiments described herein can be facilitated. Repetitive description of like elements employed in other embodiments described herein is omitted for sake of brevity. 
     With reference to  FIG. 10 , a suitable operating environment  1000  for implementing various aspects of this disclosure can also include a computer  1012 . The computer  1012  can also include a processing unit  1014 , a system memory  1016 , and a system bus  1018 . The system bus  1018  couples system components including, but not limited to, the system memory  1016  to the processing unit  1014 . The processing unit  1014  can be any of various available processors. Dual microprocessors and other multiprocessor architectures also can be employed as the processing unit  1014 . The system bus  1018  can be any of several types of bus structure(s) including the memory bus or memory controller, a peripheral bus or external bus, and/or a local bus using any variety of available bus architectures including, but not limited to, Industrial Standard Architecture (ISA), Micro-Channel Architecture (MSA), Extended ISA (EISA), Intelligent Drive Electronics (IDE), VESA Local Bus (VLB), Peripheral Component Interconnect (PCI), Card Bus, Universal Serial Bus (USB), Advanced Graphics Port (AGP), Firewire (IEEE 1394), and Small Computer Systems Interface (SCSI). 
     The system memory  1016  can also include volatile memory  1020  and nonvolatile memory  1022 . The basic input/output system (BIOS), containing the basic routines to transfer information between elements within the computer  1012 , such as during start-up, is stored in nonvolatile memory  1022 . Computer  1012  can also include removable/non-removable, volatile/non-volatile computer storage media.  FIG. 10  illustrates, for example, a disk storage  1024 . Disk storage  1024  can also include, but is not limited to, devices like a magnetic disk drive, floppy disk drive, tape drive, Jaz drive, Zip drive, LS-100 drive, flash memory card, or memory stick. The disk storage  1024  also can include storage media separately or in combination with other storage media. To facilitate connection of the disk storage  1024  to the system bus  1018 , a removable or non-removable interface is typically used, such as interface  1026 .  FIG. 10  also depicts software that acts as an intermediary between users and the basic computer resources described in the suitable operating environment  1000 . Such software can also include, for example, an operating system  1028 . Operating system  1028 , which can be stored on disk storage  1024 , acts to control and allocate resources of the computer  1012 . 
     System applications  1030  take advantage of the management of resources by operating system  1028  through program modules  1032  and program data  1034 , e.g., stored either in system memory  1016  or on disk storage  1024 . It is to be appreciated that this disclosure can be implemented with various operating systems or combinations of operating systems. A user enters commands or information into the computer  1012  through input device(s)  1036 . Input devices  1036  include, but are not limited to, a pointing device such as a mouse, trackball, stylus, touch pad, keyboard, microphone, joystick, game pad, satellite dish, scanner, TV tuner card, digital camera, digital video camera, web camera, and the like. These and other input devices connect to the processing unit  1014  through the system bus  1018  via interface port(s)  1038 . Interface port(s)  1038  include, for example, a serial port, a parallel port, a game port, and a universal serial bus (USB). Output device(s)  1040  use some of the same type of ports as input device(s)  1036 . Thus, for example, a USB port can be used to provide input to computer  1012 , and to output information from computer  1012  to an output device  1040 . Output adapter  1042  is provided to illustrate that there are some output devices  1040  like monitors, speakers, and printers, among other output devices  1040 , which require special adapters. The output adapters  1042  include, by way of illustration and not limitation, video and sound cards that provide a means of connection between the output device  1040  and the system bus  1018 . It should be noted that other devices and/or systems of devices provide both input and output capabilities such as remote computer(s)  1044 . 
     Computer  1012  can operate in a networked environment using logical connections to one or more remote computers, such as remote computer(s)  1044 . The remote computer(s)  1044  can be a computer, a server, a router, a network PC, a workstation, a microprocessor based appliance, a peer device or other common network node and the like, and typically can also include many or all of the elements described relative to computer  1012 . For purposes of brevity, only a memory storage device  1046  is illustrated with remote computer(s)  1044 . Remote computer(s)  1044  is logically connected to computer  1012  through a network interface  1048  and then physically connected via communication connection  1050 . Network interface  1048  encompasses wire and/or wireless communication networks such as local-area networks (LAN), wide-area networks (WAN), cellular networks, etc. LAN technologies include Fiber Distributed Data Interface (FDDI), Copper Distributed Data Interface (CDDI), Ethernet, Token Ring and the like. WAN technologies include, but are not limited to, point-to-point links, circuit switching networks like Integrated Services Digital Networks (ISDN) and variations thereon, packet switching networks, and Digital Subscriber Lines (DSL). Communication connection(s)  1050  refers to the hardware/software employed to connect the network interface  1048  to the system bus  1018 . While communication connection  1050  is shown for illustrative clarity inside computer  1012 , it can also be external to computer  1012 . The hardware/software for connection to the network interface  1048  can also include, for exemplary purposes only, internal and external technologies such as, modems including regular telephone grade modems, cable modems and DSL modems, ISDN adapters, and Ethernet cards. 
     The present invention may be a system, a method, an apparatus and/or a computer program product at any possible technical detail level of integration. The computer program product can include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present invention. The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium can be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer readable storage medium can also include the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire. 
     Computer readable program instructions described herein can be downloaded to respective computing/processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and/or a wireless network. The network can comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and/or edge servers. A network adapter card or network interface in each computing/processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing/processing device. Computer readable program instructions for carrying out operations of the present invention can be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, configuration data for integrated circuitry, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++, or the like, and procedural programming languages, such as the “C” programming language or similar programming languages. The computer readable program instructions can execute entirely on the user&#39;s computer, partly on the user&#39;s computer, as a stand-alone software package, partly on the user&#39;s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can be connected to the user&#39;s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) can execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present invention. 
     Aspects of the present invention are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer readable program instructions. These computer readable program instructions can be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer readable program instructions can also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function/act specified in the flowchart and/or block diagram block or blocks. The computer readable program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational acts to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams can represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the blocks can occur out of the order noted in the Figures. For example, two blocks shown in succession can, in fact, be executed substantially concurrently, or the blocks can sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions. 
     While the subject matter has been described above in the general context of computer-executable instructions of a computer program product that runs on a computer and/or computers, those skilled in the art will recognize that this disclosure also can or can be implemented in combination with other program modules. Generally, program modules include routines, programs, components, data structures, etc. that perform particular tasks and/or implement particular abstract data types. Moreover, those skilled in the art will appreciate that the inventive computer-implemented methods can be practiced with other computer system configurations, including single-processor or multiprocessor computer systems, mini-computing devices, mainframe computers, as well as computers, hand-held computing devices (e.g., PDA, phone), microprocessor-based or programmable consumer or industrial electronics, and the like. The illustrated aspects can also be practiced in distributed computing environments in which tasks are performed by remote processing devices that are linked through a communications network. However, some, if not all aspects of this disclosure can be practiced on stand-alone computers. In a distributed computing environment, program modules can be located in both local and remote memory storage devices. 
     As used in this application, the terms “component,” “system,” “platform,” “interface,” and the like, can refer to and/or can include a computer-related entity or an entity related to an operational machine with one or more specific functionalities. The entities disclosed herein can be either hardware, a combination of hardware and software, software, or software in execution. For example, a component can be, but is not limited to being, a process running on a processor, a processor, an object, an executable, a thread of execution, a program, and/or a computer. By way of illustration, both an application running on a server and the server can be a component. One or more components can reside within a process and/or thread of execution and a component can be localized on one computer and/or distributed between two or more computers. In another example, respective components can execute from various computer readable media having various data structures stored thereon. The components can communicate via local and/or remote processes such as in accordance with a signal having one or more data packets (e.g., data from one component interacting with another component in a local system, distributed system, and/or across a network such as the Internet with other systems via the signal). As another example, a component can be an apparatus with specific functionality provided by mechanical parts operated by electric or electronic circuitry, which is operated by a software or firmware application executed by a processor. In such a case, the processor can be internal or external to the apparatus and can execute at least a part of the software or firmware application. As yet another example, a component can be an apparatus that provides specific functionality through electronic components without mechanical parts, wherein the electronic components can include a processor or other means to execute software or firmware that confers at least in part the functionality of the electronic components. In an aspect, a component can emulate an electronic component via a virtual machine, e.g., within a cloud computing system. 
     In addition, the term “or” is intended to mean an inclusive “or” rather than an exclusive “or.” That is, unless specified otherwise, or clear from context, “X employs A or B” is intended to mean any of the natural inclusive permutations. That is, if X employs A; X employs B; or X employs both A and B, then “X employs A or B” is satisfied under any of the foregoing instances. Moreover, articles “a” and “an” as used in the subject specification and annexed drawings should generally be construed to mean “one or more” unless specified otherwise or clear from context to be directed to a singular form. As used herein, the terms “example” and/or “exemplary” are utilized to mean serving as an example, instance, or illustration. For the avoidance of doubt, the subject matter disclosed herein is not limited by such examples. In addition, any aspect or design described herein as an “example” and/or “exemplary” is not necessarily to be construed as preferred or advantageous over other aspects or designs, nor is it meant to preclude equivalent exemplary structures and techniques known to those of ordinary skill in the art. 
     As it is employed in the subject specification, the term “processor” can refer to substantially any computing processing unit or device comprising, but not limited to, single-core processors; single-processors with software multithread execution capability; multi-core processors; multi-core processors with software multithread execution capability; multi-core processors with hardware multithread technology; parallel platforms; and parallel platforms with distributed shared memory. Additionally, a processor can refer to an integrated circuit, an application specific integrated circuit (ASIC), a digital signal processor (DSP), a field programmable gate array (FPGA), a programmable logic controller (PLC), a complex programmable logic device (CPLD), a discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. Further, processors can exploit nano-scale architectures such as, but not limited to, molecular and quantum-dot based transistors, switches and gates, in order to optimize space usage or enhance performance of user equipment. A processor can also be implemented as a combination of computing processing units. In this disclosure, terms such as “store,” “storage,” “data store,” data storage,” “database,” and substantially any other information storage component relevant to operation and functionality of a component are utilized to refer to “memory components,” entities embodied in a “memory,” or components comprising a memory. It is to be appreciated that memory and/or memory components described herein can be either volatile memory or nonvolatile memory, or can include both volatile and nonvolatile memory. By way of illustration, and not limitation, nonvolatile memory can include read only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable ROM (EEPROM), flash memory, or nonvolatile random access memory (RAM) (e.g., ferroelectric RAM (FeRAM). Volatile memory can include RAM, which can act as external cache memory, for example. By way of illustration and not limitation, RAM is available in many forms such as synchronous RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM). Additionally, the disclosed memory components of systems or computer-implemented methods herein are intended to include, without being limited to including, these and any other suitable types of memory. 
     What has been described above include mere examples of systems and computer-implemented methods. It is, of course, not possible to describe every conceivable combination of components or computer-implemented methods for purposes of describing this disclosure, but one of ordinary skill in the art can recognize that many further combinations and permutations of this disclosure are possible. Furthermore, to the extent that the terms “includes,” “has,” “possesses,” and the like are used in the detailed description, claims, appendices and drawings such terms are intended to be inclusive in a manner similar to the term “comprising” as “comprising” is interpreted when employed as a transitional word in a claim. 
     The descriptions of the various embodiments have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.