Patent Publication Number: US-2022222561-A1

Title: Efficient cooling of ion chains for quantum computation

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     The present application is a continuation application of U.S. patent application Ser. No. 16/450,779, entitled “EFFICIENT COOLING OF ION CHAINS FOR QUANTUM COMPUTATION,” and filed on Jun. 24, 2019, which in turn claims priority to and the benefit from U.S. Provisional Patent Application No. 62/692,099, entitled “EFFICIENT COOLING OF ION CHAINS FOR QUANTUM COMPUTATION,” and filed on Jun. 29, 2018, the contents of each of which are incorporated herein by reference in their entirety. 
    
    
     BACKGROUND OF THE DISCLOSURE 
     Aspects of the present disclosure generally relate to quantum systems, and more specifically, to efficient cooling of ion chains used for atomic quantum bits (qubits) in quantum computations. 
     Trapped atoms are one of the leading implementations for quantum information processing. Atomic-based qubits can be used as quantum memories, as quantum gates in quantum computers and simulators, and can act as nodes for quantum communication networks. 
     Performing entangling gates between physical qubits in an ion chain is needed to enable large-scale quantum computation. To this end, quantum computations with trapped atomic ions (qubits) use the ions&#39; combined motion to create the entangling gates. Since the initial motional state affects the gate operation, the ions are typically first cooled to near the motional ground state at the beginning of or during (if using sympathetic cooling) the quantum computation. The number of motional modes that need to be cooled is proportional to the number of ions. Traditionally, the motional modes are cooled sequentially, that is, a next motional mode is cooled only after the previous motional mode has been cooled. As the number of atomic ions increases, this causes the total cooling time to lengthen. 
     As the cooling process becomes longer, heating of the motional modes from electric field fluctuations in the ion trap electrodes can cause noise that can then overwhelm the cooling process. It thus becomes advantageous to implement faster cooling methods. Accordingly, techniques that allow for more efficient cooling of ion chains are desirable. 
     SUMMARY OF THE DISCLOSURE 
     The following presents a simplified summary of one or more aspects in order to provide a basic understanding of such aspects. This summary is not an extensive overview of all contemplated aspects, and is intended to neither identify key or critical elements of all aspects nor delineate the scope of any or all aspects. Its purpose is to present some concepts of one or more aspects in a simplified form as a prelude to the more detailed description that is presented later. 
     The disclosure describes techniques to cool a chain of ions to near the combined motional ground state that does not grow in execution time with the number of ions. By addressing each ion individually and using each ion to cool a different motional mode, it is possible to simultaneously cool multiple motional modes. In an example, it is possible to simultaneously cool one third of the total motional modes. In other examples, a different number of the total motional modes may be cooled. 
     In an aspect of the disclosure, a method for cooling of an ion chain having multiple ions is described that includes generating a sideband cooling laser beam for each ion in the ion chain; concurrently cooling two or more motional modes associated with the ions in the ion chain using the respective sideband cooling laser beam until each of the two or more motional modes reaches a motional ground state; and performing a quantum computation using the ion chain after the two or more motional modes have reached the motional ground state. 
     In another aspect of the disclosure, a quantum information processing (QIP) system for cooling of an ion chain having multiple ions is described that includes one or more optical sources configured to generate a sideband cooling laser beam for each ion in the ion chain; a beam controller configured to concurrently cool two or more motional modes associated with the ions in the ion chain using the respective sideband cooling laser beam until each of the two or more motional modes reaches a motional ground state; and an algorithms component configured to perform a quantum computation using the ion chain after the two or more motional modes have reached the motional ground state. 
     In another aspect of the disclosure, a computer-readable storage medium storing code with instructions executable by a processor for cooling of an ion chain having multiple ions is described that includes code for generating a sideband cooling laser beam for each ion in the ion chain; code for concurrently cooling two or more motional modes associated with the ions in the ion chain using the respective sideband cooling laser beam until each of the two or more motional modes reaches a motional ground state; and code for performing a quantum computation using the ion chain after the two or more motional modes have reached the motional ground state. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The appended drawings illustrate only some implementation and are therefore not to be considered limiting of scope. 
         FIG. 1A  illustrates a diagram representing of a trap holding atomic ions that form a linear crystal or lattice in accordance with aspects of the disclosure. 
         FIG. 1B  is a diagram illustrating an example of a reduced energy level diagram showing the application of laser radiation for state initialization in accordance with aspects of the disclosure. 
         FIG. 1C  is a diagram illustrating an example of a reduced energy level diagram showing the application of laser radiation for qubit state detection through fluorescence in accordance with aspects of the disclosure. 
         FIG. 2  is a diagram that illustrates an example of a sequential sideband cooling process. 
         FIG. 3  is a diagram that illustrates an example of a chain with four (4) ions confined in a potential in accordance with aspects of this disclosure. 
         FIG. 4  is a diagram that illustrates an example of a distribution of a set of N=4 motional modes in accordance with aspects of this disclosure. 
         FIGS. 5A and 5B  are diagrams that illustrate examples of a set of ion motion amplitudes for the modes in  FIG. 4  in accordance with aspects of this disclosure. 
         FIG. 6  is a diagram that illustrates an example of parallelization or concurrency of sideband cooling process in accordance with aspects of this disclosure. 
         FIG. 7  is a diagram that illustrates an example of a computer device in accordance with aspects of this disclosure. 
         FIG. 8  is a flow diagram that illustrates an example of a method in accordance with aspects of this disclosure. 
         FIG. 9A  is a block diagram that illustrates an example of a quantum information processing (QIP) system in accordance with aspects of this disclosure. 
         FIG. 9B  is a block diagram that illustrates an example of an optical controller used in connection with parallelized sideband cooling in accordance with aspects of this disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The detailed description set forth below in connection with the appended drawings is intended as a description of various configurations and is not intended to represent the only configurations in which the concepts described herein may be practiced. The detailed description includes specific details for the purpose of providing a thorough understanding of various concepts. However, it will be apparent to those skilled in the art that these concepts may be practiced without these specific details. In some instances, well known components are shown in block diagram form in order to avoid obscuring such concepts. 
     As described above, trapped atoms may be used to implement quantum information processing. Atomic-based qubits can be used as different types of devices, including but not limited to quantum memories, quantum gates in quantum computers and simulators, and nodes for quantum communication networks. Qubits based on trapped atomic ions can have very good coherence properties, can be prepared and measured with nearly 100% efficiency, and can be readily entangled with each other by modulating their Coulomb interaction with suitable external control fields such as optical or microwave fields. As used in this disclosure, the terms “atomic ions,” “atoms,” and “ions” may be used interchangeably to describe the particles that are to be confined, or are actually confined, in a trap to form a chain, a crystal, a lattice, or similar arrangement or configuration. This disclosure describes techniques in the form of methods or processes and equipment or apparatuses for cooling motional modes in a crystal of trapped atomic ions. 
     The typical ion trap geometry or structure used for quantum information and metrology purposes is the linear radio frequency (RF) Paul trap (also referred to as an RF trap or simply a Paul trap), where nearby electrodes hold static and dynamic electrical potentials that lead to an effective inhomogeneous harmonic confinement of the ions. The RF Paul trap is a type of trap that uses electric fields to trap or confine charged particles in a particular region, position, or location. When atomic ions are laser-cooled to very low temperatures in such a trap, the atomic ions form a stationary crystal of qubits (e.g., a structured arrangement of qubits), with Coulomb repulsion balancing the external confinement force. For sufficient trap anisotropy, the ions can form a linear crystal along the weak direction of confinement, and this is the arrangement typically employed for applications in quantum information and metrology. 
     The disclosure describes techniques to cool a chain of ions (e.g., a lattice or crystal of ions) to near the combined motional ground state that does not grow in execution time with the number of ions. By addressing each ion individually and using each ion to cool a different motional mode, it is possible to simultaneously cool the motional modes. In an example, it is possible to simultaneously cool one third of the total motional modes. 
       FIG. 1A  illustrates a diagram representing the trapping of atomic ions in a linear crystal  110  using, for example, a linear RF Paul trap (by using electrodes inside a vacuum chamber) in a vacuum chamber  100 . In the example shown in  FIG. 1A , a vacuum chamber in a quantum system can include a set of electrodes for trapping N (N≥1) atomic Ytterbium ions (e.g.,  171 Yb +  ions) which are confined in the linear crystal  110  and can be laser-cooled to be nearly at rest. The number of atomic ions trapped can be configurable. The atoms are illuminated with laser radiation tuned to a resonance in  171 Yb +  and the fluorescence of the atomic ions is imaged onto a camera. In an example, atomic ions can be separated by a distance  115  of about 5 microns (μm) from each other, which can be verified by fluorescence. The separation of the atomic ions is determined by a balance between the external confinement force and Coulomb repulsion. 
     Strong fluorescence of individual trapped atomic ions relies on the efficient cycling of photons with the atomic ion species chosen for strong closed optical transition that allows for laser-cooling of the motion, qubit state initialization, and efficient qubit readout. Within these atomic ions, quantum bits can be represented by two stable electronic levels, often characterized by an effective spin with the two states |↑  and |↓ , or equivalently |1  and |0 . For example,  FIG. 1B  and  FIG. 1C  show the reduced energy level diagrams  120  and  150 , respectively, for atomic ion  171 Yb +  where the qubit levels |↑  and |↓   130  are represented by the stable hyperfine levels in the ground electronic state, and are separated by frequency ω 0 /2π=12.642812 GHz. The excited electronic states |e  and |e′   140  in  171 Yb +  are themselves split by a smaller hyperfine coupling and are separated from the ground states by an optical interval having an energy corresponding to an optical wavelength of 369.53 nm. 
     Laser radiation tuned just below resonance in these optical transitions allows for Doppler laser cooling to confine the atomic ions near the bottom of the trap. Other more sophisticated forms of laser cooling can bring the atomic ions to be nearly at rest in the trap, as will be discussed in this disclosure. 
     When a bichromatic laser beam (e.g., a beam with two tones produced by sidebands resulting from optical modulation) resonant with both |↑ ↔|e  and |↓ ↔|e′  transitions is applied to the atom, it rapidly falls into the state |↓  and no longer interacts with the light field, allowing the initialization of the qubit with essentially 100% fidelity (see e.g.,  FIG. 1B ). 
     When a single laser beam resonant with the |↑ ↔|e  transition is applied, a closed cycling optical transition causes an ion in the |↑  state to fluoresce strongly while an ion in the |↓  state stays dark because the laser frequency is far from its resonance (see e.g.,  FIG. 1C ). The collection of even a small fraction of this fluorescence allows for the detection of the atomic qubit state with near-perfect efficiency or accuracy. Other atomic species may have similar initialization/detection schemes. 
     In  FIGS. 1B and 1C , all allowed transitions from the excited electronic states |e  and |e′   140  are illustrated as downward, wavy arrows. On the other hand, the applied laser radiation (which is shown as upward, straight arrows) drive these transitions for initialization to state |↓  as shown in  FIG. 1B , and for fluorescence detection of the qubit state (|↑ =fluorescence, |↓ =no fluorescence) as shown in  FIG. 1C . 
     In addition to Doppler laser cooling, a process of sideband cooling of ions is also used in which a laser beam or combination of laser beams are used to remove a single quantum or quanta of motion from the quantized, collective motion of a trapped collection of ions.  FIG. 2  shows a diagram  200  that describes a sequential technique currently used for sideband cooling. Sideband cooling proceeds with the following steps as illustrated in the diagram  200  in  FIG. 2 : (1) The ions are reset into the lower energy state using a “repump” laser beam (see e.g.,  210 ); (2) a motional dependent laser interaction transfers one quantum of motion into the state change from the lower internal energy state into the upper internal energy state (see e.g.,  220 ); (3) the ions are reset again; and (4) repeat from (2) until most or all quanta of energy are removed. 
     The timing of step (2) is varied over the repetitions indicated in step (4) to maximize the rate of quanta removal. The timings may also vary for the particular motional state being cooled. Tens to hundreds of repetitions (or more) may be needed to remove sufficient motional quanta to allow high quality quantum operations on the atoms/ions. For a chain of ions, this process may usually be repeated for each of the collective modes of motion. 
     In the example in  FIG. 2 , two motional modes (e.g., motional mode 1 ( 210   a ) and motional mode 2 ( 210   b )) are shown in connection with a ‘repump’ laser beam operation  210 , although additional motional modes can also be cooled subsequent to cooling the first two motional modes. Also shown in  FIG. 2  is the motion transfer operation  220  in which, as described in step (2) above, a motional dependent laser interaction transfers one quantum of motion into the state change from the lower internal energy state into the upper internal energy state. Each subsequent transfer is shown to take a longer time until the particular motional mode finally reaches its motional ground state and the next motional mode can be sideband cooled. 
     In contrast to the sequential (e.g., successive or serial) sideband cooling described above, this disclosure describes simultaneous or concurrent (e.g., parallel) mode cooling on multiple modes, which can greatly reduce the time needed to cool all the modes. For purposes of illustration, this concurrent or simultaneous process is being described using an example with four ions. This technique, however, can be applied to any number of ions trapped in a common trap well, or even in separate trap wells, or a combination of the two. 
       FIG. 3  shows a diagram  300  in which the four ions are fully confined in a potential (within a Paul trap, for example). For N ions, there are 3×N combined modes of motion, usually forming 3 separate groups of N modes. In this example, one of the groups of N modes is used; however, the method can address any N modes that couple to the sideband cooling laser beams (e.g., addressing beams  310   a ,  310   b ,  310   c , and  310   d ). For a chain of two or more ions, then N≥2. 
       FIG. 4  shows a diagram  400  with an example of a distribution of a set of N motional modes frequencies for N=4 modes. The motional modes can include one or more longitudinal or axial modes with respect to the ion chain, one or more transverse or radial modes with respect to the ion chain, or a combination thereof. 
       FIGS. 5A and 5B  show diagrams  500 ,  510 ,  520 , and  530  describing an example set of ion motion amplitudes for each of the N=4 modes. In the diagram  500 , a motional mode 1 (mode 1) from  FIG. 4  associated with frequency f1 is addressed by a second ion (ion 2—shaded) in the four-ion chain. In the diagram  510 , a motional mode 2 (mode 2) from  FIG. 4  associated with frequency f2 is addressed by the third ion (ion 3—shaded) in the four-ion chain. In the diagram  520 , a motional mode 3 (mode 3) from  FIG. 4  associated with frequency f3 is addressed by the fourth ion (ion 4—shaded) in the four-ion chain. In the diagram  530 , a motional mode 4 (mode 4) from  FIG. 4  and associated with frequency f4 is addressed by the first ion (ion 1—shaded) in the four-ion chain. 
     As shown in  FIG. 3 , each ion is separately addressed by a sideband cooling laser (or combination of lasers). Each addressing beam (e.g., addressing beams 1 ( 310   a ), 2 ( 310   b ), 3 ( 310   c ), and 4 ( 310   d )) is tuned to interact with a different motional mode from  FIG. 4 . For optimal cooling, the ion addressed by each beam should have a large amplitude in the motional mode, see  FIGS. 5A and 5B , to which that beam is tuned. 
     Because each beam is both localized to a particular ion in the chain and to a particular mode, the process of transferring a quantum of motion to the ion&#39;s internal state step (2) given above is largely independent for each beam and can occur simultaneously or concurrently. The resets of steps (1) and (3) are the same and common among all the ions. The sequential addressing of motional states from  FIG. 2  is replaced now by a parallel cooling of these states as shown in the diagram  600  in  FIG. 6 . This parallelization results in an N-fold decrease in the time needed to cool the chain of ions. 
     In addition to the general technique for simultaneous or concurrent sideband cooling described above, other aspects can also be implemented based on the ability to individually address ions with separate laser beams. For example, in a first aspect, the ions in the chain can be of two or more species or isotopes (e.g., one type of ion is  171 Yb +  and another type of ion is different from  171 Yb +  and used for sympathetic cooling). This allows for sympathetic cooling during the quantum operations (as opposed to waiting until the sideband cooling is completed before performing the quantum operations). In another aspect, a single motional mode may be addressed by two or more ions and two or more laser beams. The cooling pulses in this case may be applied sequentially, transferring more than one quanta into the multiple ions prior to applying the repump. In yet another aspect, the repump beam may be individually addressed such that the sideband cooling on each ion can be run asynchronous without having to align the repump pulses across all ions. 
     Additional details and context related to the techniques for simultaneous or concurrent sideband cooling of multiple motional modes by individually addressing the ions in a chain are described below. 
     Cooling of the ions in a chain (e.g., ion crystal or ion lattice) to a ground state of motion (motional ground state) is one of the starting steps for any quantum operation or computation. This is generally done through various laser interactions. One of the challenges is that the number of degrees of freedom that need to be consider to cool the ions increases as the number of ions (e.g., the number of qubits) increases. As such, as the number of ions increases so does the time it takes to cool the ions down, which can result in the unfavorable condition that more time is spent cooling the ions than performing quantum operations or computations. Moreover, the ion trap (e.g., Paul trap) may end up heating the ions, which counters the cooling performed on the ions. 
     Because the quantum information processing (QIP) systems described herein are capable of individually addressing each ion in a chain, it is possible to use these capabilities to parallelize the cooling of all of the motional modes in a set (or at least a third of all the possible motional modes). As such, it is then possible to have each ion address a different motional mode simultaneously or concurrently since they are, to a large extent, independent. Therefore, the repeated process of removing quanta can be performed on all N modes at the same time until the motional ground state is reached for all of the motional modes. 
     Motional modes may refer to normal modes of motion. For example, the ions in a chain may behave like weights on a chain of springs (e.g., couple oscillators) and their motion can be represented by a set of oscillating frequencies. Accordingly, the motional modes may correspond to the different frequencies of oscillation. The normal modes of motion may represent decoupled degrees of freedom and it may be possible to excite one without necessarily exciting the others. Because of this decoupling, it is possible for one normal mode to be hot (e.g., excited) and another normal mode to be cold (e.g., not excited). It may therefore be necessary, in order to prepare the chain of ions for quantum operations or computations, to cool the separate or decoupled normal modes of motion (e.g., motional modes). 
     Previous techniques for sideband cooling the ions relied on sequential cooling as described above. That is, a first of the motional modes is cooled, then a second one, then a third one, until all the motional modes are cooled. There are a couple of issues with these techniques. The first is that it takes a long time for this process to complete, and the second is that the earlier modes begin to heat up before the process is completed. Therefore, this sequential approach is not scalable, particularly as the number of ions needed for quantum computations and operations increases. 
     The problems associated with the sequential cooling described above can be overcome by the individual addressing of ions supported by the QIP systems described herein. The individual addressing of ions also allows for various optimization techniques. For example, in a case of N=3 (three motional modes or normal modes of motion), it may be possible to control the motion of each of the ions with a separate laser beam for each ion. So this is a case of 3 ions and 3 normal modes. One of the modes may be such that the central or middle ion does not move or participate in the motion at all. In such a case, shining a laser beam on the central or middle ion is inefficient because the middle ion is not coupled. Based on this example, it is clear that certain ions coupled more effectively to certain motional modes (e.g., the end ions in this example), and certain ions are disengaged (e.g., the central or middle ion). Accordingly, it is possible to identify which ion (or ions) is best suited to cool a particular motional mode, and then shine or provide a laser beam to that specific ion at the frequency associated with the respective motional mode to cool that motional mode through that ion. As described above, the diagram  400  in  FIG. 4  shows an example of correspondence of different frequencies to different modes for N=4, while the diagrams  500 ,  510 ,  520 , and  530  in  FIGS. 5A and 5B  show examples of how different ions can be used for different modes/frequencies. 
     As described above, the cooling is incremental and requires the removal of one quanta of energy from each of the motional modes at each step in a sequence of repeated steps (see e.g., steps (1), (2), (3), and (4) above). In general, an information qubit in the chain is set or reset to ground, then a transfer is made using a laser beam (e.g., a gate laser). All the ions are hit simultaneously or concurrently by their respective gate lasers, where each of these lasers is tuned to a particular frequency to address a specific mode (see e.g.,  FIGS. 3 and 4 ). Each laser pulls one quanta into an internal information state, which is then erased such that the information gets lost or destroyed but results in one quanta being removed from the motion. This process of having the gate beams or gate lasers interact with the ions to pull the motional information into an internal state and then erase is repeated multiple times. In some examples, more than one laser can be tuned to the same frequency to address the same mode in order to remove multiple quanta of motion from that mode at once. 
     An additional optimization that can be performed during simultaneous or concurrent sideband cooling is that the amount of time a gate laser or beam interacts with its respective ion may be different than the amount of time another gate laser or beam interacts with its own respective ion. That is, interactions with different ions to address different motional modes may take different amounts of time. 
     Another optimization that may be performed includes erasing (e.g., removing the quanta of motion) at different times for different motional modes or ions. 
     Other aspects that may need optimization include when the frequencies of certain motional modes are very close and individually addressing the motional modes may be challenging if the respective beams for these modes are close to each other. One approach may be to select the ions for each closely spaced mode using the criteria that that ion has strong coupling only to that mode and not to the other modes. The variation in coupling strengths is illustrated by the motion amplitudes in the diagrams in  FIGS. 5A and 5B . 
     Also as described above, there are typically two different stages of cooling. First, there is Doppler cooling, and second, there is sideband cooling. Doppler cooling can typically get the amount of motion quanta to a few quanta but not all the way down to the motional ground state. Therefore, Doppler cooling ends up bringing the motional modes down to a few quanta, which is a reasonable for a first cooling stage. For the sideband cooling, the remaining quanta of motion are removed to bring the motional modes to the motional ground state. In general, the number of steps or repetitions can be determined such that the removal process is performed for a predetermined number of repetitions that ensures that there is no remaining quanta of motion in any of the motional modes. 
     As shown in  FIGS. 2 and 6 , as the number of quanta gets lower, it takes longer to remove the next quanta from a motional mode (e.g., the pulse width gets wider as it takes longer time). This is in part because of the time it takes for the transition within the qubit of absorbing one of the quanta and then resetting (e.g., the process of getting entropy out of the system/mode). Because of the increased amount of time it takes to remove every additional quanta of motion, it is necessary to control the amount of time dedicated to each step or repetition, as shown by the changing pulse width of the motional transfer laser beam in  FIGS. 2 and 6 . 
     Another aspect to consider and one described above, is that because of uncontrolled electric field fluctuations in the trap electrodes, and because the ions are charged particles, the ions are going to be heated by the electrodes in the ion trap. This effect is referred to as the heating rate. Accordingly, one of the benefits of simultaneous or concurrent sideband cooling is that it is efficient and fast enough that there is sufficient time to perform quantum computations or operations before the motional modes begin to heat up again (e.g., because of the heating rate). Overall it is desirable for the cooling rate to be faster than the heating rate. 
     One thing to point out is that not all motional modes may heat up at the same rate. For example, common modes (e.g., with motion in a same direction) may be easier to excite with slow fluctuating electric fields (or electric fields that tend to be uniform over the length scale of the spatial frequency of the mode), while differential modes (e.g., with motion in different directions) may need fast fluctuating electric fields (or electric fields with high spatial frequency compared to the spatial frequency of the mode) to be excited. Accordingly, another optimization opportunity associated with concurrent or simultaneous sideband cooling is that it is possible to spend more time and more resources (e.g., laser beams) to cool down the motional modes that heat up faster and spend less time and fewer resources to cool down the motional modes that are slow to heat up. For example, it is possible to allocate more ions and laser beams to cool those motional modes that heat up faster. In one example, if there is one remaining motional mode that needs to cool it is possible to allocate two or more ions and laser beams to more quickly remove any remaining quanta of motion from that motional mode. 
     An additional benefit of the QIP system described herein (see e.g.,  FIGS. 9A and 9B ) and its application to concurrent or simultaneous sideband cooling is the ability, as described above, to perform sympathetic cooling while also performing quantum computations or operations. By using two different types of ions or isotopes, where there is at least one type (of atomic species or isotope) for computation and at least one type (of atomic species or isotope) for cooling (cooling or coolant ion) interspersed among the computational ions, it is possible to use the coolant ions to cool the nearby computational ions while the computation ions are being used to perform quantum computations or operations. One optimization opportunity is to place or position the coolant ions (sympathetic ions) where they would participate in motional modes to help cool those motional modes. 
     The various aspects described above for an efficient cooling process that includes a concurrent or simultaneous sideband cooling, along with the related examples described in connection with the four-ion chain in  FIGS. 2-6 , can be performed as methods or processes by different devices or systems. Additional details of such methods, processes, devices, or systems are further described below in connection with  FIGS. 7-9B . 
     Referring now to  FIG. 7 , illustrated is an example computer device  700  in accordance with aspects of the disclosure. The computer device  700  can represent a single computing device, multiple computing devices, or a distributed computing system, for example. The computer device  700  may be configured as a quantum computer (e.g., a quantum information processing (QIP) system), a classical computer, or a combination of quantum and classical computing functions. For example, the computer device  700  may be used to process information using quantum algorithms based on trapped ion technology and may therefore implement methods or processes for efficient cooling, including techniques involved in concurrent or simultaneous sideband cooling of motional modes. A generic example of the computer device  700  as a QIP system that can implement the techniques described herein is illustrated in an example shown in  FIGS. 9A and 9B . 
     In one example, the computer device  700  may include a processor  710  for carrying out processing functions associated with one or more of the features described herein. For example, the processor  710  may be configure to control, coordinate, and/or perform aspects of the concurrent or simultaneous sideband cooling of motional modes, as well as control, coordinate, and/or perform aspects of quantum computations or operations that take place while the cooling is being performed (e.g., sympathetic cooling). The processor  710  may include a single or multiple set of processors or multi-core processors. Moreover, the processor  710  may be implemented as an integrated processing system and/or a distributed processing system. The processor  710  may include a central processing unit (CPU), a quantum processing unit (QPU), a graphics processing unit (GPUO, or combination of those types of processors. In one aspect, the processor  710  may refer to a general processor of the computer device  700 , which may also include additional processors  710  to perform more specific functions. 
     In an example, the computer device  700  may include a memory  720  for storing instructions executable by the processor  710  for carrying out the functions described herein. In an implementation, for example, the memory  720  may correspond to a computer-readable storage medium that stores code or instructions to perform one or more of the functions or operations described herein. In one example, the memory  720  may include instructions to perform aspects of a method  800  described below in connection with  FIG. 8 . Just like the processor  710 , the memory  720  may refer to a general memory of the computer device  700 , which may also include additional memories  720  to store instructions and/or data for more specific functions. 
     Further, the computer device  700  may include a communications component  730  that provides for establishing and maintaining communications with one or more parties utilizing hardware, software, and services as described herein. The communications component  730  may carry communications between components on the computer device  700 , as well as between the computer device  700  and external devices, such as devices located across a communications network and/or devices serially or locally connected to computer device  700 . For example, the communications component  730  may include one or more buses, and may further include transmit chain components and receive chain components associated with a transmitter and receiver, respectively, operable for interfacing with external devices. 
     Additionally, the computer device  700  may include a data store  740 , which can be any suitable combination of hardware and/or software, that provides for mass storage of information, databases, and programs employed in connection with implementations described herein. For example, the data store  740  may be a data repository for operating system  760  (e.g., classical OS, or quantum OS). In one implementation, the data store  740  may include the memory  720 . 
     The computer device  700  may also include a user interface component  750  operable to receive inputs from a user of the computer device  700  and further operable to generate outputs for presentation to the user or to provide to a different system (directly or indirectly). The user interface component  750  may include one or more input devices, including but not limited to a keyboard, a number pad, a mouse, a touch-sensitive display, a digitizer, a navigation key, a function key, a microphone, a voice recognition component, any other mechanism capable of receiving an input from a user, or any combination thereof. Further, the user interface component  750  may include one or more output devices, including but not limited to a display, a speaker, a haptic feedback mechanism, a printer, any other mechanism capable of presenting an output to a user, or any combination thereof. 
     In an implementation, the user interface component  750  may transmit and/or receive messages corresponding to the operation of the operating system  760 . In addition, the processor  710  may execute the operating system  760  and/or applications or programs, and the memory  720  or the data store  740  may store them. 
     When the computer device  700  is implemented as part of a cloud-based infrastructure solution, the user interface component  750  may be used to allow a user of the cloud-based infrastructure solution to remotely interact with the computer device  700 . 
       FIG. 8  is a flow diagram that illustrates an example of a method  800  for cooling of an ion chain having multiple ions in accordance with aspects of this disclosure. In an aspect, the method  800  may be performed in a computer system (e.g., as part of the operations of the computer system) such as the computer device  700  described above, where, for example, the processor  710 , the memory  720 , the data store  740 , and/or the operating system  760  may be used to perform or control the functions of the method  800 . Similarly, the functions of the method  800  may be performed or controlled by one or more components of a QIP system such as a QIP system  900  and its components (e.g., optical controller  920  and its subcomponents) described in more detail below in connection with  FIGS. 9A and 9B . 
     At  810 , the method  800  includes generating a sideband cooling laser beam for each ion in the ion chain. 
     At  820 , the method  800  includes concurrently cooling two or more motional modes associated with the ions in the ion chain using the respective sideband cooling laser beam until each of the two or more motional modes reaches a motional ground state. 
     At  830 , the method  800  includes performing a quantum computation using the ion chain after the two or more motional modes have reached the motional ground state. 
     In another aspect of the method  800 , concurrently cooling two or more motional modes includes repeating the following sequence a number of times: resetting the ions into a lower energy state using a repump laser beam; performing a motional dependent laser interaction with the generated sideband cooling laser beams to transfer a quanta of motion from the lower energy state of the ions to a higher energy state of the ions; and resetting the ions again into the lower energy state. The number of times the sequence is repeated is a predetermined number of times that ensures that all of the two or more motional modes reach the motional ground state. The resetting the ions into a lower energy state using a repump laser beam can include resetting each of the ions into a lower energy state using a respective repump laser beam to enable asynchronous resetting of the ions. 
     In another aspect of the method  800 , a number of the two or more motional modes is proportional to a number of ions in the ion chain. 
     In another aspect of the method  800 , each of the two or more motional modes has a respective ion in the ion chain for sideband cooling using a corresponding sideband cooling laser beam. 
     In another aspect of the method  800 , the two or more motional modes include longitudinal or axial modes with respect to the ion chain, transverse or radial modes with respect to the ion chain, or a combination thereof. 
     In another aspect of the method  800 , the ions in the ion chain include ions of two or more species, with one of the species being used for sympathetic cooling, the concurrently cooling of the two or more motional modes associated with the ions in the ion chain is performed using the ions of the species used for sympathetic cooling, and the quantum computation is performed with one or more of the remaining species while the concurrent cooling is taking place. 
     In yet another aspect of the method  800 , at least one of the two or more motional modes is sideband cooled using two or more ions and two or more of the sideband cooling laser beams. 
       FIG. 9A  is a block diagram that illustrates the QIP system  900  in accordance with aspects of this disclosure. The QIP system  900  may also be referred to as a quantum computing system, a computer device, a trapped-ion quantum computer, or the like. In an aspect, the QIP system  900  may correspond to portions of a quantum computer implementation of the computer device  700  in  FIG. 7 . 
     The QIP system  900  can include a source  960  that provides atomic species (e.g., a flux of neutral atoms) to a chamber  950  having an ion trap  970  that traps the atomic species once ionized (e.g., photoionized) by an optical controller  920  (see e.g.,  FIG. 9B ). Optical sources  930  (e.g., lasers that produce beams) in the optical controller  920  may include one or more laser sources that can be used for ionization of the atomic species, control (e.g., phase control) of the atomic ions, for fluorescence of the atomic ions that can be monitored and tracked by image processing algorithms operating in an imaging system  940  in the optical controller  920 , and/or to perform the optical cooling functions described in this disclosure, including Doppler cooling and concurrent or simultaneous sideband cooling of motional modes. In an aspect, the optical sources  930  may be implemented separately from the optical controller  920 . 
     The imaging system  940  can include a high resolution imager (e.g., CCD camera) for monitoring the atomic ions while they are being provided to the ion trap or after they have been provided to the ion trap  970 . In an aspect, the imaging system  940  can be implemented separate from the optical controller  920 , however, the use of fluorescence to detect, identify, and label atomic ions using image processing algorithms may need to be coordinated with the optical controller  920 . 
     The QIP system  900  may also include an algorithms component  910  that may operate with other parts of the QIP system  900  (not shown) to perform quantum algorithms or quantum operations, including single qubit operations or multi-qubit operations as well as extended quantum computations. As such, the algorithms component  910  may provide instructions to various components of the QIP system  900  (e.g., to the optical controller  920 ) to enable the implementation of the quantum algorithms or quantum operations. In an example, the algorithms component  910  may perform, coordinate, and/or instruct the performance of quantum computations or operations after sideband cooling is complete or during sideband cooling if sympathetic cooling techniques are being applied, as described above in connection with concurrent or simultaneous sideband cooling. 
       FIG. 9B  shows at least a portion of the optical controller  920 . In this example, the optical controller  920  can include a beam controller  921 , the optical sources  930 , and the imaging system  940 . As shown by the dotted lines, one or both of the optical sources  930  and the imaging system  940  may be implemented separate from, but in communication with, the optical controller  920 . The imaging system  940  includes a CCD  941  (or similar imager or camera) and an image processing algorithms component  942 . The optical sources  930  includes a modulator  925  and multiple laser sources  935   a , . . . ,  935   b , which may be used for one or more of the functions described above (e.g., to produce laser or gate beams for cooling operations). 
     The beam controller  921  is configured to perform various aspects described herein for coherently controlling quantum phases on atomic qubits mediated by control fields, as applied to quantum logic gates, and/or in connection with generalized interactions between qubits. The beam controller  921  may include a Doppler cooling component  922  configured to use laser beams to perform a first stage of cooling of the motional modes of an ion chain (e.g., ions in a crystal or lattice in the ion trap  970 ). The beam controller  921  may also include a sideband cooling component  923  having a concurrent motional mode cooling component  924  to perform the various aspects described herein for a second stage of cooling of the motional modes of an ion chain, where the second stage of cooling involves concurrent or simultaneous (e.g., non-sequential) cooling of the motional modes. In one implementation, the Doppler cooling component  922  and the sideband cooling component  923  may be part of the same component and/or may be implemented separate from the beam controller  921  but in communication with the beam controller  921 . 
     The various components of the optical controller  920  may operate individually or in combination to perform the various functions described in this disclosure, for example, the method  800  in  FIG. 8 . Moreover, the various components of the optical controller  920  may operate with one or more of the components of the QIP system  900  to perform the various functions described in this disclosure, for example, the method  800  in  FIG. 8 . 
     Although the present disclosure has been provided in accordance with the implementations shown, one of ordinary skill in the art will readily recognize that there could be variations to the embodiments and those variations would be within the scope of the present disclosure. Accordingly, various modifications may be made by one of ordinary skill in the art without departing from the scope of the appended claims.