Patent ID: 12217131

DETAILED DESCRIPTION

During operation of a Majorana-based quantum computing device (also referred to as a topological quantum computing device), respective voltages are applied to the Majorana islands and the QDs. For example, a Majorana island plunger gate voltage and a QD plunger gate voltage may be applied with respective plunger gates located proximate to the Majorana island and the QD.

When a joint parity measurement is performed, the quantum capacitance of a QD is measured when the QD is electrically coupled to a pair of MZMs. These MZMs may be located at the same Majorana island or different Majorana islands. The joint parity measurement may also make use of one or more additional QDs included in the measurement loop.

The values of the Majorana island plunger gate voltage and the QD plunger gate voltage may affect the measurement visibility of joint parity measurements. When a joint parity measurement is performed, the measurement may output a positive parity value or a negative parity value. However, the joint parity measurement may instead have an ambiguous measurement outcome. An ambiguous measurement outcome may occur when the quantum capacitance values corresponding to positive and negative parity are too close to reliably distinguish. The difference between the quantum capacitance values measured at positive and negative parity may depend upon the values of the Majorana island plunger gate voltage and the QD plunger gate voltage. Accordingly, to reduce the probability of an ambiguous measurement, it is useful to obtain voltage values for which the positive and negative parity values are highly distinguishable.

A ground state of the Majorana island may change during device operation as a result of quasiparticle poisoning (QPP). Due to this change in the ground state, the values of the Majorana island plunger gate voltage and the QD plunger gate voltage that provide high measurement visibility may change, potentially resulting in low measurement visibility for joint parity measurements that are performed after a QPP event.

There are three types of QPP that occur at Majorana-based quantum computing devices: intrinsic QPP, extrinsic QPP, and inter-component QPP. Intrinsic QPP is QPP that occurs when the fermion number of a Majorana island remains constant, but the ground states of the Majorana island are thermally excited above the superconducting gap. Thus, a quasiparticle is expelled from an MZM and may be absorbed by another MZM. In extrinsic QPP, the Majorana island exchanges fermions with a fermion source or sink outside the system of Majorana islands and QDs that are used to instantiate qubits. Inter-component QPP occurs when a Majorana island exchanges a fermion with another Majorana island or with a QD. Extrinsic and inter-component QPP change the total fermion number of the Majorana island.

Using the devices and methods discussed below, the value of the fermion number of a Majorana island may be identified during device calibration and initialized to a baseline value when preparing the quantum computing device for execution of a quantum computation. The devices and methods discussed below may be used to identify a minimum-energy resonance region corresponding to a highest-probability value of the fermion number, with respect to a given idle configuration of the Majorana island. During device calibration, the total fermion number may be set to a known value such that a joint parity measurement may be calibrated at different values of the total fermion number.

FIG.1schematically shows a computing system1that includes a quantum computing device10and a controller30.FIG.1shows, at the quantum computing device10, a Majorana island12at which a plurality of Majorana zero modes (MZMs)14are instantiated. The MZMs14instantiated at the Majorana island12form in pairs at the ends of topological superconducting nanowires. The Majorana island12may be a coherent link that includes two MZMs14, a Majorana tetron that includes four MZMs14, or a Majorana hexon that includes six MZMs14.

The quantum computing device10further includes a QD16configured to be electrically connectable to the Majorana island12via an MZM14of the plurality of MZMs14included in that Majorana island12. The quantum computing device is configured to apply a first plunger gate voltage Ngto the Majorana island12and apply a second plunger gate voltage ngto the QD16.

The quantum computing device10further includes an electrical ground18that is electrically connectable to the Majorana island12. The Majorana island12may accordingly be switchably grounded by electrically coupling the Majorana island12to the electrical ground18. In some examples, the electrical ground18is directly coupled to the Majorana island12, whereas in other examples, the electrical ground18is coupled to the Majorana island12via the QD16. These two example paths between the Majorana island12and the electrical ground18are shown inFIG.1.

The quantum computing device10further includes a capacitance sensor20. Via the capacitance sensor20, the quantum computing device10may be configured to collect quantum capacitance measurements40of a system that includes the Majorana island12and the QD16. These quantum capacitance measurements40may be transmitted to the controller30, which, as discussed in further detail below, is configured to use the quantum capacitance measurements40to identify resonance regions44.

The controller30, as shown in the example ofFIG.1, is a classical computing device that includes a processor32and memory34. The processor32may be instantiated in a single processing device or may alternatively include a plurality of processing devices. The one or more processing devices included in the processor32may, for example, include one or more central processing units (CPUs), graphics processing units (GPUs), and/or other processing devices such as specialized hardware accelerators. The memory34may be instantiated as one or more memory devices, which may include one or more volatile and/or non-volatile memory devices. In some examples, the functionality of the controller30may be achieved by a plurality of networked physical computing devices, such as a plurality of networked compute nodes located in a data center.

As discussed above, the controller30may be configured to receive sensor data from the quantum computing device10. The controller30may be further configured to generate instructions with which the components of the quantum computing device10are controlled. For example, instructions generated at the controller30may be used to set the first plunger gate voltage Ngand the second plunger gate voltage ng.

FIG.2schematically shows the Majorana island12in additional detail in an example in which the Majorana island12is a coherent link. The coherent link includes a topological superconducting nanowire22at which a first MZM14A and a second MZM14B are configured to form. The QD16is located within a semiconductor region24proximate to the second MZM14B. In addition, the electrical ground18is tunably coupled to the Majorana island12. This tunable coupling passes through the QD16in some examples.

FIG.2further shows a first plunger gate26located proximate to the topological superconducting nanowire22and a second plunger gate27located proximate to the semiconductor region24. Via the first plunger gate26and the second plunger gate27, respectively, the first plunger gate voltage Ngand the second plunger gate voltage ngare applied to the Majorana island12and the QD16as a Majorana island plunger gate voltage and a QD plunger gate voltage.

The capacitance sensor20, as shown in the example ofFIG.2, includes a microwave readout circuit60configured to output a microwave response signal62based at least in part on a quantum capacitance of the Majorana island12and the QD16. The microwave readout circuit60shown inFIG.2is coupled to an alternating current (AC) voltage source64that is configured to supply an AC driving voltage to the microwave readout circuit60. The microwave readout circuit60shown in the example ofFIG.2is capacitively coupled to the QD16.

FIG.3schematically shows an example of the Majorana island12in which the Majorana island12is a Majorana tetron. The Majorana tetron shown inFIG.3includes a first topological superconducting nanowire22A and a second topological superconducting nanowire22B coupled by a trivial superconducting nanowire23. A first MZM14A and a second MZM14B are configured to form at the ends of the first topological superconducting nanowire22A, and a third MZM14C and a fourth MZM14D are configured to form at the ends of the second topological superconducting nanowire22B.

FIG.4schematically shows another example of the Majorana island12in which the Majorana island12is a Majorana hexon. The Majorana hexon ofFIG.4includes a first topological superconducting nanowire22A, a second topological superconducting nanowire22B, and a third topological superconducting nanowire22C. A first MZM14A and a second MZM14B are configured to form at the ends of the first topological superconducting nanowire22A, a third MZM14C and a fourth MZM14D are configured to form at the ends of the second topological superconducting nanowire22B, and a fifth MZM14E and a sixth MZM14F are configured to form at the ends of the third topological superconducting nanowire22C. The Majorana hexon further includes trivial superconducting nanowires23that respectively couple the first topological superconducting nanowire22A to the second topological superconducting nanowire22B and couple the second topological superconducting nanowire22B to the third topological superconducting nanowire22C.

Although not shown inFIGS.2-4in the interest of clarity, the quantum computing device10may include respective QDs16located proximate to each of the MZMs14. These QDs16may each be connectable to corresponding capacitance sensors20and to the electrical ground18as well as to the MZMs14proximate to which they are located. In addition, a corresponding first plunger gate26may be located proximate to each of the topological superconducting nanowires22, and a corresponding second plunger gate27may be located proximate to each of the QDs16.

Returning toFIG.1, the resonance region identification performed at the controller30is discussed below. The controller30is configured to identify a plurality of resonance regions44in the microwave response signals62that are used to obtain the quantum capacitance measurements40. Each of the resonance regions44is a region located around a peak in a capacitance curve formed by the plurality of quantum capacitance measurements40. Thus, each resonance region44is an approximation of a location of the resonance peak. These resonance regions44are identified in respective sampling iterations42. The resonance regions44identified in the sampling iterations42may correspond to fermion numbers of the Majorana island12.

FIG.5shows steps that the controller30may be configured to control the quantum computing device10to perform during each of the sampling iterations42. At step70, the sampling iteration42may include electrically coupling the Majorana island12to the electrical ground18while the first plunger gate26is set to an idle voltage54. The idle voltage54may be a first plunger gate voltage Ngthat is applied when no measurement is being performed at the Majorana island12. The resonance regions44identified in the steps shown inFIG.5may be specific to the value of the idle voltage54used in step70. Accordingly, the fermion number of the Majorana island12may be reset. The fermion numbers of the Majorana island12subsequently to resetting may follow a thermal distribution46, as discussed in further detail below.

At step71, the sampling iteration42may further include disconnecting the Majorana island12from the electrical ground18. When step71is performed, the electrical connections between the Majorana island12and the QD16and between the QD16and the electrical ground18may both be opened.

At step72, the sampling iteration42may further include electrically coupling the Majorana island12to the QD16. In addition, at step72, the controller30may be configured to control the quantum computing device10to scan over a plurality of values of the first plunger gate voltage Ngand the second plunger gate voltage ngusing the capacitance sensor20. As shown inFIG.1, the controller30may accordingly obtain a plurality of quantum capacitance measurements40of the Majorana island12and the QD16at the scanned values of the first plunger gate voltage Ngand the second plunger gate voltage ng. During the scan, the quantum computing device10may be configured to scan over the plurality of values of the first plunger gate voltage Ngand the second plunger gate voltage nguntil a resonance region44over the measured values of the quantum capacitance is identified. Scanning over a plurality of values of the first plunger gate voltage Ngand the second plunger gate voltage ng, as discussed herein, refers to scanning a plurality of different voltage value pairs that each include respective values of Ngand ng, and may be performed by varying either or both of Ngand ngover the course of scanning. The quantum computing device10is further configured to output, to the controller30, respective quantum capacitance measurements40obtained at the plurality of values of the first plunger gate voltage Ngand the second plunger gate voltage ng.

In some examples, when step72is performed, the controller30may be further configured to control the quantum computing device10to set the first plunger gate voltage Ngto a predetermined first plunger gate voltage Ngduring scanning over the plurality of values of the second plunger gate voltage ng. Accordingly, the first plunger gate voltage Ngmay be kept fixed during step72. In such examples, the predetermined value of the first plunger gate voltage Ngmay differ from the idle voltage54.

At step73, the controller30is further configured to control the quantum computing device10to return the first plunger gate26to the idle voltage54and disconnect the Majorana island from the QD16. The controller30may also reset the second plunger gate voltage ngto an idle value.

Steps70,71,72, and73, as shown inFIG.5, may be performed during calibration of the quantum computing device10. In such examples, at step74, the controller30may be further configured to obtain a predetermined number of sample values of the first plunger gate voltage Ngand the second plunger gate voltage nglocated within the resonance regions44, as well as the corresponding values of the quantum capacitance. As depicted inFIG.1, the controller30is further configured to receive the quantum capacitance measurements40, and, based at least in part on the quantum capacitance measurements40, identify a respective plurality of resonance regions44associated with the sampling iterations42. The resonance regions44may correspond to values of a fermion number N of the Majorana island12.

Based at least in part on the quantum capacitance measurements40, the controller30is further configured to determine a measured distribution46of a respective plurality of resonance regions44associated with the sampling iterations42. In some examples, the measured distribution46is a thermal distribution. The thermal distribution may be a Gibbs distribution, defined as:

pN=e-β⁢E⁡(N)∑M∈ℤe-β⁢E⁡(M)

where pNis the probability of the Majorana island12having a fermion number N. By convention, the fermion number N for which the energy of the Majorana island12is minimized is defined as N=0. In addition, β=1/kBT, where KBis the Boltzmann constant and T is the temperature, and E (N) is the charging energy of the Majorana island12as a function of N.

Based at least in part on the thermal distribution46, the controller30is further configured to identify a minimum-energy resonance region52of the plurality of resonance regions44that corresponds to a minimum energy value50of the Majorana island12. The charging energy of the Majorana island12may be approximated as:
E(N)=EC(N−Ng)2

In this example, the first plunger gate voltage Ngis expressed in dimensionless form, and ECis a unit charging energy value.

FIG.6schematically shows the computing system1when the controller30identifies the minimum-energy resonance region52. As depicted inFIG.6, the resonance regions44identified by scanning over values of the second plunger gate voltage ngin each of the sampling iterations42are distributed according to a thermal distribution. In the measured distribution46, the values of the resonant voltage may be bucketed into ranges corresponding to different values of the fermion number N. The measured distribution46may indicate the number of sampling iterations42in which a respective resonance region44is detected within each of these ranges. Thus, the measured distribution46may indicate respective frequencies with which a plurality of different fermion numbers N are sampled.

The minimum-energy resonance region52that corresponds to the minimum energy value50may be the resonance region44of the plurality of resonance regions44that has a highest frequency in the thermal distribution. As depicted in the example ofFIG.6, the minimum-energy resonance region52is the resonance region44with a corresponding resonant voltage that was detected in the highest number of sampling iterations42.

Returning to the example ofFIG.1, subsequently to determining the minimum-energy resonance region52, the controller30is further configured to output a minimum-energy resonance region identification48that indicates the minimum-energy resonance region52. The minimum-energy resonance region identification48may include the values of the first plunger gate voltage Ngand the second plunger gate voltage ngthat are identified as resonance values. Ranges of values of Ngand ngin a vicinity of the minimum-energy resonance region52may be indicated in the minimum-energy resonance region identification48in some examples.

FIG.7schematically shows a sampling iteration set80including a plurality of sampling iteration subsets82at which the Majorana island12is set to different respective first plunger gate voltages Ngin different respective sampling iterations42when scanning for resonance regions44in step72. The sampling iteration set80includes each of the sampling iterations42. In the example ofFIG.7, rather than using the same value of the first plunger gate voltage Ngin each of the sampling iterations42, the controller30may be configured to control the quantum computing device10to identify the resonance regions44at a plurality of different first plunger gate voltages Ng. In such examples, the controller30may be configured to control the quantum computing device10to set the first plunger gate voltage Ngto a plurality of different values in a corresponding plurality of sampling iteration subsets82of the sampling iteration set80. In the example ofFIG.7, the first plunger gate voltage Ngis shown changing to a value Ng′ when a new sampling iteration subset82begins. Using a plurality of sampling iteration subsets82that have different values of the first plunger gate voltage Ng, the controller30may be configured to collect larger samples of resonance regions44corresponding to fermion numbers other than N=0.

In other examples in which the first plunger gate voltage Ngis modified during scanning at step72instead of the second plunger gate voltage ng, the controller30may be further configured to control the quantum computing device10to use different values of the second plunger gate voltage ngin different sampling iteration subsets82. In still other examples, both the first plunger gate voltage Ngand the second plunger gate voltage ngmay be modified over the plurality of sampling iterations42.

FIG.8shows an example resonance region plot100that depicts resonance regions44corresponding to different values of the fermion number N.FIG.8shows respective capacitance curves102,104, and106that plot thermally averaged quantum capacitanceCQas a function of the second plunger gate voltage ngfor N=0, N=1, and N=2. The capacitance curves102,104, and106have different values of the second plunger voltage ngat which their peak capacitance values occur. The first plunger gate voltage Ngis held constant in the example ofFIG.8. Accordingly, by varying the value of the second plunger voltage ng, the controller30may distinguish between the different values of N.

FIG.9shows steps that may be performed when the fermion number of the Majorana island12is initialized prior to a joint parity measurement78performed at the Majorana island12. In the example ofFIG.9, steps70,71,72, and73as discussed above with reference toFIG.5may be performed in each of one or more initialization iterations76to initialize the fermion number of the Majorana island12. During each initialization iteration76, at step70, the controller30may be further configured to control the quantum computing device to electrically couple the Majorana island12to the electrical ground18while the first plunger gate26is set to the idle voltage54. At step71, each of the initialization iterations76may further include disconnecting the Majorana island12from the electrical ground18. At step72, each of the initialization iterations76may further include scanning over a plurality of current-iteration values of the first plunger gate voltage Ngand the second plunger gate voltage ngto identify a current-iteration resonance region77. At step73, each of the initialization iterations76may further include disconnecting the Majorana island12from the electrical ground18.

The controller30may be configured to control the quantum computing device10to perform the one or more initialization iterations76until the controller identifies a current-iteration resonance region77as the minimum-energy resonance region52. Accordingly, the controller30may detect that the Majorana island has the minimum-energy fermion number N=0 corresponding to the value of the idle voltage54used in step70. If the controller30detects a current-iteration resonance region77corresponding to some other fermion number N, the controller30may control the quantum computing device10to perform another initialization iteration76. Thus, the controller30may be configured to set the quantum computing device10to the minimum-energy fermion number N=0 prior to the joint parity measurement78.

FIG.10schematically shows the computing system1in an example in which controller30is further configured to perform a QPP detection92at the Majorana island12subsequently to performing the joint parity measurement78at the Majorana island12. When the controller30performs the QPP detection92, the controller30may be further configured to control the quantum computing device10to obtain an additional quantum capacitance measurement90of the Majorana island12. This additional quantum capacitance measurement90may be obtained at the value of the first plunger gate voltage Ngused during calibration of the quantum computing device10, and at the value of the second plunger gate voltage ngidentified as the voltage at which the minimum-energy resonance region52occurs.

The controller30may be further configured to determine whether QPP has occurred at the Majorana island12based at least in part on the additional quantum capacitance measurement90and the minimum-energy resonance region identification48. The controller30may be configured to determine whether QPP has occurred by determining whether the additional quantum capacitance measurement90is approximately equal to the resonance region value of the quantum capacitance obtained during calibration. Accordingly, the controller30may be configured to determine whether the Majorana island12is in its minimum-energy state. When the controller30detects the minimum-energy resonance region52, the QPP detection92may indicate that QPP has not occurred. When the controller30does not detect the minimum-energy resonance region52, the QPP detection92may indicate that QPP has occurred. Accordingly, the controller30may be configured to determine whether QPP occurred at the Majorana island12when the joint parity measurement78was performed.

FIG.11Ashows a flowchart of a method200for use with a computing system including a quantum computing device and a controller. The steps of the method200may be performed when calibrating the quantum computing device in order to identify resonance regions corresponding to different fermion numbers of the Majorana island. The method200may additionally or alternatively be performed to initialize the fermion number of the Majorana island prior to performing a joint parity measurement.

The quantum computing device used when performing the method200includes a Majorana island at which a plurality of MZMs are instantiated. The quantum computing device further includes a QD configured to be electrically connectable to the Majorana island via an MZM of the plurality of MZMs. In addition, the quantum computing device includes an electrical ground that is electrically connectable to the Majorana island (e.g., directly or via the QD), as well as a capacitance sensor configured to measure a quantum capacitance of the QD and the Majorana island. For example, the capacitance sensor may include a microwave readout circuit configured to output a microwave response signal based at least in part on a quantum capacitance of the Majorana island and the QD.

Steps202,204,206,208, and210of the method200are performed at the quantum computing device in each of a plurality of sampling iterations. At step202, the method200includes electrically coupling the Majorana island to the electrical ground. This electrical coupling is performed while a first plunger gate located proximate to the Majorana island is set to an idle voltage. At step204, the method200further includes disconnecting the Majorana island from the electrical ground, and at step206, the method200further includes electrically coupling the Majorana island to the QD. Accordingly, the Majorana island and the QD may reach thermal equilibrium with the electrical ground before the Majorana island is disconnected from the electrical ground and coupled to the QD to prepare the Majorana island for quantum capacitance measurement.

At step208, the method200further includes, via the capacitance sensor, scanning over a plurality of values of a first plunger gate voltage of a first plunger gate located proximate to the Majorana island and a second plunger gate voltage applied to a second plunger gate located proximate to the QD. The first plunger gate voltage, the second plunger gate voltage, or both may be varied during the scanning. At step210, the method200further includes outputting, to the controller, respective quantum capacitance measurements obtained at the plurality of values of the first plunger gate voltage and the second plunger gate voltage. Accordingly, the quantum capacitance of the Majorana island and the QD are measured for different combinations of values of the plunger gate voltages. The Majorana island may be disconnected from the QD subsequently to locating the resonance region.

Steps212,214,216, and218of the method200are performed at the controller. At step212, the method200further includes receiving the quantum capacitance measurements from the capacitance sensor. As discussed above, the quantum capacitance measurements may be received in the form of microwave response signals.

At step214, the method200further includes, based at least in part on the quantum capacitance measurements, determining a measured distribution of a respective plurality of resonance regions associated with the sampling iterations. The controller may identify a resonance region by identifying the values of the first plunger gate voltage and the second plunger gate voltage for which the highest value of the quantum capacitance is measured in a given sampling iteration. The measured distribution is constructed over the course of the plurality of sampling iterations as the quantum capacitance measurements are obtained. The resonance regions associated with the sampling iterations may correspond to fermion numbers of the Majorana island.

At step216, the method200further includes identifying a minimum-energy resonance region of the plurality of resonance regions based at least in part on the measured distribution. The minimum-energy resonance region corresponds to a minimum energy value of the Majorana island. In some examples, the measured distribution is a thermal distribution, which may be a Gibbs distribution. The minimum-energy resonance region may, in such examples, be the resonance region of the plurality of resonance regions that has a highest frequency in the thermal distribution. Fitting the resonance regions to the thermal distribution may include bucketing the resonant values of the first plunger gate voltage and the second plunger gate voltage into ranges corresponding to different fermion numbers of the Majorana island. The thermal distribution may indicate respective frequencies, across the plurality of sampling iterations, with which resonance regions within those plunger gate voltage ranges are measured.

At step218, the method200further includes outputting the minimum-energy resonance region identification. Thus, the controller calibrates the quantum computing device by approximating the plunger gate voltages and corresponding quantum capacitance when the Majorana island has a minimum energy value.

FIG.11Bshows additional steps of the method200that may be performed in some examples. At step220, the method200may further include, at the quantum computing device, setting a first plunger gate voltage of the Majorana island to a predetermined first plunger gate voltage during scanning over the plurality of values of the second plunger gate voltage. Step220may be performed during step208. Thus, the quantum computing device may control for the value of the first plunger gate voltage when scanning for the resonance region.

At step222, the method200may further include identifying the resonance regions at a plurality of different first plunger gate voltages over the plurality of sampling iterations. Step222may be performed during step214. When step222is performed, the first plunger gate voltage may be set to different values in different subsets of the set of sampling iterations. Accordingly, the controller may obtain larger sample sizes for values of the fermion number other than the value corresponding to the minimum-energy resonance region. These larger sample sizes may allow the controller to more accurately calibrate the quantum computing device for identification of QPP.

FIG.11Cshows additional steps of the method200that may be performed in some examples subsequently to calibration. At step224, the method200may further include initializing the fermion number of the Majorana island. Initializing the fermion number may include performing steps226,228, and230in each of one or more initialization iterations. The one or more initialization iterations may be performed in a loop that includes steps226,228, and230until a current-iteration resonance region measured in a current initialization iteration is identified as the minimum-energy resonance region. When the minimum-energy resonance region is detected, the controller may detect that the fermion number of the Majorana island has its minimum-energy value.

At step226, step224may include electrically coupling the Majorana island to the electrical ground. At step228, step224may further include disconnecting the Majorana island from the electrical ground. At step230, step224may further include scanning over a plurality of current-iteration values of the first plunger gate voltage and the second plunger gate voltage to identify the current-iteration resonance region. In some examples, subsequently to identifying the current-iteration resonance region, the Majorana island may be decoupled from the QD.

At step232, the method200may further include performing a joint parity measurement at the Majorana island subsequently to initializing the fermion number. The joint parity measurement may be a measurement of the joint parity an MZM included in the Majorana island and one or more additional MZMs, which may be included in the same Majorana island or one or more additional Majorana islands. Thus, a quantum computation may be performed at the quantum computing device subsequently to initializing the fermion number of the Majorana island.

FIG.11Dshows further steps of the method200that may be performed subsequently to step232in some examples. At step234, the method200may further include performing a QPP detection at the Majorana island. Step234may include, at step236, obtaining an additional quantum capacitance measurement of the Majorana island. The additional quantum capacitance measurement may be collected at the values of the first plunger gate voltage and the second plunger gate voltage corresponding to the minimum-energy resonance region. At step238, step234may further include determining whether QPP has occurred at the Majorana island based at least in part on the additional quantum capacitance measurement and the minimum-energy resonance region identification. When step238is performed, the controller may determine whether resonance occurs at the previously identified minimum-energy resonant values of the first plunger gate voltage and the second plunger gate voltage. When such resonance occurs, the controller may determine that QPP has not occurred, and when such resonance does not occur, the controller may determine that QPP has occurred.

Using the systems and methods discussed above, a quantum computing device may be calibrated by identifying the first plunger gate voltage and the second plunger gate voltage that produce a resonance region when the Majorana island located proximate to the first plunger gate has a fermion number that minimizes the energy of the Majorana island. Resonant voltages for other values of the fermion number may similarly be identified. The systems and methods discussed above may also be used to initialize the fermion number of the Majorana island to the minimum-energy fermion number prior to performing a joint parity measurement.

In some embodiments, the methods and processes described herein may be tied to a computing system of one or more computing devices. In particular, such methods and processes may be implemented as a computer-application program or service, an application-programming interface (API), a library, and/or other computer-program product.

FIG.12schematically shows a non-limiting embodiment of a computing system300that can enact one or more of the methods and processes described above. Computing system300is shown in simplified form. Computing system300may embody the computing system1described above and illustrated inFIG.1. Components of computing system300may be included in one or more personal computers, server computers, tablet computers, home-entertainment computers, network computing devices, video game devices, mobile computing devices, mobile communication devices (e.g., smart phone), and/or other computing devices, and wearable computing devices such as smart wristwatches and head mounted augmented reality devices.

Computing system300includes a logic processor302volatile memory304, and a non-volatile storage device306. Computing system300may optionally include a display subsystem308, input subsystem310, communication subsystem312, and/or other components not shown inFIG.12.

Logic processor302includes one or more physical devices configured to execute instructions. For example, the logic processor may be configured to execute instructions that are part of one or more applications, programs, routines, libraries, objects, components, data structures, or other logical constructs. Such instructions may be implemented to perform a task, implement a data type, transform the state of one or more components, achieve a technical effect, or otherwise arrive at a desired result.

The logic processor may include one or more physical processors configured to execute software instructions. Additionally or alternatively, the logic processor may include one or more hardware logic circuits or firmware devices configured to execute hardware-implemented logic or firmware instructions. Processors of the logic processor302may be single-core or multi-core, and the instructions executed thereon may be configured for sequential, parallel, and/or distributed processing. Individual components of the logic processor optionally may be distributed among two or more separate devices, which may be remotely located and/or configured for coordinated processing. Aspects of the logic processor may be virtualized and executed by remotely accessible, networked computing devices configured in a cloud-computing configuration. In such a case, these virtualized aspects are run on different physical logic processors of various different machines, it will be understood.

Non-volatile storage device306includes one or more physical devices configured to hold instructions executable by the logic processors to implement the methods and processes described herein. When such methods and processes are implemented, the state of non-volatile storage device306may be transformed—e.g., to hold different data.

Non-volatile storage device306may include physical devices that are removable and/or built in. Non-volatile storage device306may include optical memory, semiconductor memory, and/or magnetic memory, or other mass storage device technology. Non-volatile storage device306may include nonvolatile, dynamic, static, read/write, read-only, sequential-access, location-addressable, file-addressable, and/or content-addressable devices. It will be appreciated that non-volatile storage device306is configured to hold instructions even when power is cut to the non-volatile storage device306.

Volatile memory304may include physical devices that include random access memory. Volatile memory304is typically utilized by logic processor302to temporarily store information during processing of software instructions. It will be appreciated that volatile memory304typically does not continue to store instructions when power is cut to the volatile memory304.

Aspects of logic processor302, volatile memory304, and non-volatile storage device306may be integrated together into one or more hardware-logic components. Such hardware-logic components may include field-programmable gate arrays (FPGAs), program- and application-specific integrated circuits (PASIC/ASICs), program- and application-specific standard products (PSSP/ASSPs), system-on-a-chip (SOC), and complex programmable logic devices (CPLDs), for example.

The terms “module,” “program,” and “engine” may be used to describe an aspect of computing system300typically implemented in software by a processor to perform a particular function using portions of volatile memory, which function involves transformative processing that specially configures the processor to perform the function. Thus, a module, program, or engine may be instantiated via logic processor302executing instructions held by non-volatile storage device306, using portions of volatile memory304. It will be understood that different modules, programs, and/or engines may be instantiated from the same application, service, code block, object, library, routine, API, function, etc. Likewise, the same module, program, and/or engine may be instantiated by different applications, services, code blocks, objects, routines, APIs, functions, etc. The terms “module,” “program,” and “engine” may encompass individual or groups of executable files, data files, libraries, drivers, scripts, database records, etc.

When included, display subsystem308may be used to present a visual representation of data held by non-volatile storage device306. The visual representation may take the form of a graphical user interface (GUI). As the herein described methods and processes change the data held by the non-volatile storage device, and thus transform the state of the non-volatile storage device, the state of display subsystem308may likewise be transformed to visually represent changes in the underlying data. Display subsystem308may include one or more display devices utilizing virtually any type of technology. Such display devices may be combined with logic processor302, volatile memory304, and/or non-volatile storage device306in a shared enclosure, or such display devices may be peripheral display devices.

When included, input subsystem310may comprise or interface with one or more user-input devices such as a keyboard, mouse, touch screen, camera, or microphone.

When included, communication subsystem312may be configured to communicatively couple various computing devices described herein with each other, and with other devices. Communication subsystem312may include wired and/or wireless communication devices compatible with one or more different communication protocols. As non-limiting examples, the communication subsystem may be configured for communication via a wired or wireless local- or wide-area network, broadband cellular network, etc. In some embodiments, the communication subsystem may allow computing system300to send and/or receive messages to and/or from other devices via a network such as the Internet.

The following paragraphs discuss several aspects of the present disclosure. According to one aspect of the present disclosure, a computing system is provided, including a quantum computing device. The quantum computing device includes a Majorana island at which a plurality of Majorana zero modes (MZMs) are instantiated. The quantum computing device further includes a quantum dot (QD) configured to be electrically connectable to the Majorana island via an MZM of the plurality of MZMs. The quantum computing device further includes an electrical ground and a capacitance sensor. The computing system further includes a controller configured to, in each of a plurality of sampling iterations, control the quantum computing device to electrically couple the Majorana island to the electrical ground while a first plunger gate located proximate to the Majorana island is set to an idle voltage. The controller is further configured to control the quantum computing device to disconnect the Majorana island from the electrical ground, electrically couple the Majorana island to the QD, and, via the capacitance sensor, scan over a plurality of values of a first plunger gate voltage applied to the first plunger gate and a second plunger gate voltage applied to a second plunger gate located proximate to the QD. The controller is further configured to control the quantum computing device to output, to the controller, respective quantum capacitance measurements obtained at the plurality of values of the first plunger gate voltage and the second plunger gate voltage. The controller is further configured to receive the quantum capacitance measurements. Based at least in part on the quantum capacitance measurements, the controller is further configured to determine a measured distribution of a respective plurality of resonance regions associated with the sampling iterations. Based at least in part on the measured distribution, the controller is further configured to identify a minimum-energy resonance region of the plurality of resonance regions that corresponds to a minimum energy value of the Majorana island. The controller is further configured to output the minimum-energy resonance region identification. The above features may have the technical effect of calibrating the first plunger gate voltage, the second plunger gate voltage, and the quantum capacitance associated with those voltages. The above features may have the additional technical effect of allowing the fermion number of the Majorana island to be initialized at a fermion number corresponding to the minimum energy value.

According to this aspect, the controller may be further configured to control the quantum computing device to set the first plunger gate voltage a predetermined first plunger gate voltage during scanning over the plurality of values of the second plunger gate voltage. The above features may have the technical effect of controlling for the value of the first plunger gate voltage when determining the values of the second plunger gate voltage at which resonance occurs.

According to this aspect, the controller may be further configured to control the quantum computing device to identify the resonance regions at a plurality of different first plunger gate voltages over the plurality of sampling iterations. The above features may have the technical effect of allowing a larger sample of resonance regions other than the minimum-energy resonance region to be measured.

According to this aspect, the resonance regions identified in the sampling iterations may correspond to fermion numbers of the Majorana island. The above features may have the technical effect of allowing the computing system to calibrate fermion number measurements and to initialize the fermion number of the Majorana island at a minimum-energy fermion number.

According to this aspect, prior to a joint parity measurement performed at the Majorana island, the controller may be further configured to initialize the fermion number of the Majorana island. The above features may have the technical effect of setting the fermion number of the Majorana island to a known baseline value at which the joint parity measurement has high measurement visibility.

According to this aspect, the controller may be configured to initialize the fermion number of the Majorana island at least in part by, in each of one or more initialization iterations performed until the controller identifies a current-iteration resonance region as the minimum-energy resonance region, controlling the quantum computing device to electrically couple the Majorana island to the electrical ground. In each of the initialization iterations, the controller may be further configured to control the quantum computing device to disconnect the Majorana island from the electrical ground and scan over a plurality of current-iteration values of the first plunger gate voltage and the second plunger gate voltage to identify the current-iteration resonance region. The above features may have the technical effect of iteratively resetting the fermion number of the Majorana island until the Majorana island is measured to be in the minimum-energy resonance region.

According to this aspect, subsequently to performing the joint parity measurement, the controller is further configured to perform a quasiparticle poisoning (QPP) detection at least in part by controlling the quantum computing device to obtain an additional quantum capacitance measurement of the Majorana island. Performing the QPP detection further includes determining whether QPP has occurred at the Majorana island based at least in part on the additional quantum capacitance measurement and the minimum-energy resonance region identification. The above features may have the technical effect of using the identification of the minimum-energy resonance region obtained during calibration to determine whether a QPP event has altered the fermion number of the Majorana island.

According to this aspect, the controller may be configured to determine whether QPP has occurred at least in part by determining whether resonance occurs at the minimum-energy resonance region. The above features may have the technical effect of determining whether a QPP event has altered the fermion number of the Majorana island.

According to this aspect, the capacitance sensor may include a microwave readout circuit configured to output a microwave response signal based at least in part on a quantum capacitance of the Majorana island and the QD. The above features may have the technical effect of allowing the quantum capacitance of the Majorana island and the QD to be measured via resonance detection.

According to this aspect, the Majorana island may be a coherent link, a Majorana tetron, or a Majorana hexon. The above features may have the technical effect of providing a structure at which the MZMs are configured to form.

According to this aspect, the measured distribution may be a thermal distribution. The minimum-energy resonance region may be the resonance region of the plurality of resonance regions that has a highest frequency in the thermal distribution. The above features may have the technical effect of allowing the controller to identify the minimum-energy resonance region by fitting the measured resonance regions to a thermal distribution.

According to this aspect, the electrical ground may be electrically coupled to the Majorana island via the QD. The above feature may have the technical effect of coupling both the Majorana island and the QD to the electrical ground in a manner that uses less wiring than separate connections to the electrical ground.

According to another aspect of the present disclosure, a method for use with a computing system including a quantum computing device and a controller is provided. The quantum computing device includes a Majorana island at which a plurality of Majorana zero modes (MZMs) are instantiated. The quantum computing device further includes a quantum dot (QD) configured to be electrically connectable to the Majorana island via an MZM of the plurality of MZMs. The quantum computing device further includes an electrical ground and a capacitance sensor. The method includes, at the quantum computing device, in each of a plurality of sampling iterations, electrically coupling the Majorana island to the electrical ground while a first plunger gate located proximate to the Majorana island is set to an idle voltage. The method further includes disconnecting the Majorana island from the electrical ground and electrically coupling the Majorana island to the QD. The method further includes, via the capacitance sensor, scanning over a plurality of values of a first plunger gate voltage of a first plunger gate located proximate to the Majorana island and a second plunger gate voltage applied to a second plunger gate located proximate to the QD. The method further includes outputting, to the controller, respective quantum capacitance measurements obtained at the plurality of values of the first plunger gate voltage and the second plunger gate voltage. At the controller, the method further includes receiving the quantum capacitance measurements. Based at least in part on the quantum capacitance measurements, the method further includes determining a measured distribution of a respective plurality of resonance regions associated with the sampling iterations. Based at least in part on the measured distribution, the method further includes identifying a minimum-energy resonance region of the plurality of resonance regions that corresponds to a minimum energy value of the Majorana island. The method further includes outputting the minimum-energy resonance region identification.

According to this aspect, the method further includes, at the quantum computing device, setting a first plunger gate voltage to a predetermined first plunger gate voltage during scanning over the plurality of values of the second plunger gate voltage. The above features may have the technical effect of controlling for the value of the first plunger gate voltage when determining the values of the second plunger gate voltage at which resonance occurs.

According to this aspect, the method may further include identifying the resonance regions at a plurality of different first plunger gate voltages over the plurality of sampling iterations. The above features may have the technical effect of allowing a larger sample of resonance regions other than the minimum-energy resonance region to be measured.

According to this aspect, the resonance regions associated with the sampling iterations may correspond to fermion numbers of the Majorana island. The above features may have the technical effect of allowing the computing system to calibrate fermion number measurements and to initialize the fermion number of the Majorana island at a minimum-energy fermion number.

According to this aspect, the method may further include initializing the fermion number of the Majorana island at least in part by, in each of one or more initialization iterations performed until a current-iteration resonance region is identified as the minimum-energy resonance region, electrically coupling the Majorana island to the electrical ground. Each of the one or more initialization iterations may further include disconnecting the Majorana island from the electrical ground. Each of the one or more initialization iterations may further include scanning over a plurality of current-iteration values of the first plunger gate voltage and the second plunger gate voltage to identify the current-iteration resonance region. The method may further include performing a joint parity measurement at the Majorana island subsequently to initializing the fermion number. The above features may have the technical effect of iteratively resetting the fermion number of the Majorana island until the Majorana island is measured to be in the minimum-energy resonance region. The above features may have the further technical effect of using the Majorana island in a quantum computation after the fermion number of the Majorana island has been initialized.

According to this aspect, the method may further include, subsequently to performing the joint parity measurement, performing a quasiparticle poisoning (QPP) detection at least in part by obtaining an additional quantum capacitance measurement of the Majorana island. Performing the QPP detection may further include determining whether QPP has occurred at the Majorana island based at least in part on the additional quantum capacitance measurement and the resonance region identification. The above features may have the technical effect of using the identification of the minimum-energy resonance region obtained during calibration to determine whether a QPP event has altered the fermion number of the Majorana island.

According to this aspect, the measured distribution may be a thermal distribution. The minimum-energy resonance region may be the resonance region of the plurality of resonance regions that has a highest frequency in the thermal distribution. The above features may have the technical effect of allowing the controller to identify the minimum-energy resonance region by fitting the measured resonance regions to a thermal distribution.

According to another aspect of the present disclosure, a computing system is provided, including a quantum computing device. The quantum computing device includes a Majorana island at which a plurality of Majorana zero modes (MZMs) are instantiated. The quantum computing device further includes a quantum dot (QD) configured to be electrically connectable to the Majorana island via an MZM of the plurality of MZMs. The quantum computing device further includes an electrical ground and a capacitance sensor. The computing system further includes a controller configured to initialize the fermion number of the Majorana island. Initializing the fermion number of the Majorana island includes, in each of one or more initialization iterations performed until the controller determines that a current-iteration resonance region is a minimum-energy resonance region of the Majorana island, controlling the quantum computing device to electrically couple the Majorana island to the electrical ground while a first plunger gate located proximate to the Majorana island is set to an idle voltage. In each of the initialization iterations, the controller is further configured to control the quantum computing device to disconnect the Majorana island from the electrical ground, and, via the capacitance sensor, scan over a plurality of current-iteration values of a first plunger gate voltage applied to the first plunger gate and a second plunger gate voltage of a second plunger gate located proximate to the QD. In each of the initialization iterations, the controller is further configured to control the quantum computing device to output, to the controller, respective quantum capacitance measurements obtained at the plurality of values of the first plunger gate voltage and the second plunger gate voltage. At the controller, each of the initialization iterations further includes receiving the quantum capacitance measurements. Based at least in part on the quantum capacitance measurements, each of the initialization iterations further includes identifying a current-iteration resonance region. Each of the initialization iterations further includes determining whether the current-iteration resonance region is the minimum-energy resonance region. The above features may have the technical effect of initializing the fermion number of the Majorana island at a fermion number corresponding to a minimum energy value.

“And/or” as used herein is defined as the inclusive or V, as specified by the following truth table:

ABA ∨ BTrueTrueTrueTrueFalseTrueFalseTrueTrueFalseFalseFalse

It will be understood that the configurations and/or approaches described herein are exemplary in nature, and that these specific embodiments or examples are not to be considered in a limiting sense, because numerous variations are possible. The specific routines or methods described herein may represent one or more of any number of processing strategies. As such, various acts illustrated and/or described may be performed in the sequence illustrated and/or described, in other sequences, in parallel, or omitted. Likewise, the order of the above-described processes may be changed.

The subject matter of the present disclosure includes all novel and non-obvious combinations and sub-combinations of the various processes, systems and configurations, and other features, functions, acts, and/or properties disclosed herein, as well as any and all equivalents thereof.