Tracking and mitigating quasiparticle poisoning errors in the Majorana quantum computing system

Abstract

A computing system comprising a quantum computer including Majorana islands on which Majorana zero-modes (MZMs) are instantiated. The computing system further comprises a controller configured to control the quantum computer to perform joint parity measurements on two or more MZMs. The controller is further configured to control the quantum computer to perform quasiparticle poisoning (QPP) detection on one or more Majorana islands, thereby generating error data. The error data includes one or more QPP indications associated with one or more Majorana islands. The controller is further configured to receive the error data from the quantum computer. The controller is further configured to update the cumulative error state of one or more Majorana islands based at least in part on the error data, and to perform update operations based at least in part on the cumulative error state.

Description

[Background technology]

[0001] background

[0001] Majorana-based quantum computing is a method for quantum computing that utilizes Majorana zero modes (MZMs). MZMs are instantiated in a floating superconducting region of a quantum computing device. When two or more MZMs are formed in a floating superconducting region, the superconducting region is known as a Majorana island. The parity of the MZMs contained in the Majorana island can be used to store qubits and classical bits used in quantum computing. [Overview of the project]

[0002] overview

[0002] According to one aspect of the present disclosure, a computing system is provided which includes a quantum computing device. The quantum computing device includes a plurality of Majorana islands in which a plurality of Majorana zero modes (MZMs) are instantiated. The quantum computing device further includes a plurality of quantum dots located in close proximity to the plurality of Majorana islands. The quantum computing device further includes a plurality of capacitance sensors. The computing system further includes a controller configured to control the quantum computing device to perform joint parity measurements of two or more MZMs located within one or more Majorana islands for an island-dot system which includes one or more Majorana islands and one or more quantum dots. Performing joint parity measurements includes setting the corresponding Majorana island gate voltages of one or more Majorana islands and the corresponding quantum dot gate voltages of one or more quantum dots to the respective candidate resonance values ​​located within the candidate resonance region, for each of a plurality of candidate resonance regions corresponding to a plurality of values ​​of the change in the fermion number of the island-dot system. Performing a joint parity measurement further includes detecting the microwave response signal measured in an island-dot system by capacitance sensors of multiple capacitance sensors in each of multiple candidate resonance regions. Performing a joint parity measurement further includes outputting two or more MZM joint parity values ​​based at least partially on the microwave response signal.

[0003]

[0003] According to another aspect of the present disclosure, a computing system is provided which includes a quantum computing device. The quantum computing device includes a plurality of Majorana islands in which a plurality of Majorana zero modes (MZMs) are instantiated. The computing system further includes a controller configured to control the quantum computing device to perform joint parity measurements in two or more of the plurality of MZMs. The two or more MZMs are located in one or more of the plurality of Majorana islands. The controller is further configured to control the quantum computing device to perform quasiparticle poisoning (QPP) detection in one or more Majorana islands, thereby generating error data. The error data includes one or more QPP indications associated with one or more Majorana islands. The controller is further configured to receive the error data from the quantum computing device. The controller is further configured to update the cumulative error state of one or more Majorana islands based at least in part on the error data. The controller is further configured to perform update operations based at least in part on the cumulative error state.

[0004]

[0004] This summary is provided to introduce in a simplified form a series of concepts that will be further described in the following detailed description. This summary is not intended to identify any important or essential features of the claims, nor to be used to limit the scope of the claims. Furthermore, the claims are not limited to any implementation that resolves any or all of the inconveniences described in any part of this disclosure. [Brief explanation of the drawing]

[0005] Brief explanation of the drawing [Figure 1]

[0005] A schematic representation of a computational system including a quantum computing device comprising a plurality of island dot systems and a controller including a processor and memory is shown according to one exemplary embodiment. [Figure 2]

[0006] Figure 1 shows an example of an island dot system configuration in which the Majorana Island included in the island dot system is a coherent link. [Figure 3]

[0007] Figure 1 schematically shows an island dot system including a first Majorana island and a second Majorana island, provided as Majorana Tetron. [Figure 4A]

[0008] Figure 3 shows the island-dot system when the controller controls the quantum computing device to perform joint parity measurements and quasiparticle poisoning detection. [Figure 4B]

[0008] Figure 3 shows the island-dot system when the controller controls the quantum computing device to perform joint parity measurement and quasiparticle poisoning detection. [Figure 5]

[0009] The island-dot system and controller when joint parity measurements are performed in multiple candidate resonance regions are schematically shown in the example in Figure 1. [Figure 6A]

[0010] The example in Figure 3 schematically shows plots of the energy of the island-dot system as a function of detuning energy for several different interference phase values ​​when the change in fermion number is equal to zero. [Figure 6B]

[0011] The example in Figure 3 schematically shows plots of the energy of the island-dot system as a function of detuning energy for several different interference phase values ​​when the change in the fermion number is equal to 1. [Figure 7A]

[0012] Figure 1 illustrates a schematic calculation system for performing quasiparticle poisoning detection on a quantum computing device. [Figure 7B]

[0013] The computation system is schematically shown in the example of Figure 7A, where the controller is configured to perform an update operation. [Figure 7C]

[0014] The computation system is schematically shown in the example of Figure 7A, where the controller is configured to transmit instructions for performing quantum error correction to the quantum computer. [Figure 8]

[0015] Figure 7A schematically illustrates multiple logical computation timesteps, each containing an individual physical computation timestep. [Figure 9A]

[0016] Figure 3 illustrates an example of quasiparticle poisoning between Majorana zero modes of a Majorana island included in an island-dot system. [Figure 9B]

[0016] An example of quasiparticle poisoning between Majorana zero modes of Majorana islands included in an island dot system is shown in the example in Figure 3. [Figure 10A]

[0017] Figure 1 illustrates an example of quasiparticle poisoning between Majorana zero modes of a Majorana island in another island-dot system. [Figure 10B]

[0017] An example of quasiparticle poisoning between Majorana zero modes of a Majorana island included in another island-dot system is shown in the example of Figure 1. [Figure 10C]

[0017] An example of quasiparticle poisoning between Majorana zero modes of a Majorana island included in another island-dot system is shown in the example of Figure 1. [Figure 11A]

[0018] This shows an example of quasiparticle poisoning between Majorana zero modes and quantum dots included in the island dot system shown in Figures 10A and 10C. [Figure 11B]

[0018] An example of quasiparticle poisoning between Majorana zero modes and quantum dots included in the island dot system shown in Figures 10A to 10C is presented. [Figure 11C]

[0018] An example of quasiparticle poisoning between Majorana zero modes and quantum dots included in the island dot system shown in Figures 10A to 10C is presented. [Figure 11D]

[0018] An example of quasiparticle poisoning between Majorana zero modes and quantum dots included in the island dot system shown in Figures 10A to 10C is presented. [Figure 12A]

[0019] The computational system is schematically shown in the example in Figure 1, where the controller is configured to calculate multiple estimated fermion number probabilities for different values ​​of the change in the fermion number. [Figure 12B]

[0020] The example in Figure 12A schematically shows the calculation of multiple candidate resonance regions corresponding to multiple joint parity measurement types. [Figure 13A]

[0021] Figure 5 schematically illustrates the computational system during the calibration phase, in which the controller is configured to estimate multiple candidate resonance regions. [Figure 13B]

[0022] The island-dot system during the calibration stage is schematically shown in the example in Figure 13A. [Figure 13C]

[0022] The island dot system during the calibration stage is schematically shown in the example of Figure 13A. [Figure 13D]

[0022] The island dot system during the calibration stage is schematically shown in the example of Figure 13A. [Figure 14A]

[0023] Figure 1 shows a flowchart illustrating a method for using a computing system, including a quantum computer and controller, to perform joint parity measurements. [Figure 14B]

[0024] The following shows additional steps to the method in Figure 14A, which may be performed in some examples to select a number of candidate resonance regions. [Figure 14C]

[0025] Additional steps of the method shown in Figure 14A may be performed in some examples during the calibration phase. [Figure 15A]

[0026] Figure 1 shows a flowchart illustrating a method that may be used in conjunction with a computational system to correct quasiparticle poisoning errors that occur during joint parity measurements. [Figure 15B]

[0027] The following shows additional steps of the method in Figure 15A that may be performed in an example where multiple physical calculation timesteps are executed during a logical calculation timestep. [Figure 15C]

[0028] The following shows additional steps of the method shown in Figure 15A, which may be performed in an example where a quantum computing device update operation is performed. [Figure 16]

[0029] Figure 1 shows a schematic diagram of an exemplary computing environment in which the computing system can be instantiated. [Modes for carrying out the invention]

[0006] Detailed explanation

[0030] Each Majorana island in a Majorana-based quantum computer can be a coherent link containing two MZMs, a tetron containing four MZMs, or a hexon containing six MZMs. Classical bits can be encoded with coherent links, and qubits can be encoded with tetrons or hexons. The ground state of a Majorana island containing 2n MZMs is 2 n-1 It exhibits a 2x degeneracy, which allows quantum information to be stored in the ground state of Majorana islands. To perform quantum computations, measurement-based operations can be performed on instantiated qubits in a Majorana-based quantum computing device. Measurement-based operations can be performed by using quantum dots (QDs) adjacent to Majorana islands and coupling pairs of MZMs contained within the same or different Majorana islands. When coupled, pairs of MZMs form a non-self-crossing loop, which allows for coherent single-electron transport between the pair. The total energy of the linked system of MZMs depends on the collective fermion parity of the MZMs. This parity can be measured by connecting the MZMs or QDs to a readout circuit.

[0007]

[0031] Topological protection is a property of Majorana-based qubits that has fueled interest in using Majorana-based qubits in quantum computing platforms. Topological protection refers to the exponential suppression of errors as a function of the macroscopic energy ratio of a Majorana-based qubit system. This exponential suppression applies to three potential error sources in a Majorana island: residual energy splitting between MZMs, intrinsic quasiparticle poisoning of a Majorana island, and the addition or removal of electrons between a Majorana island tuned to a Coulomb valley. The suppression of residual energy splitting is e -L / ξ The factor is given by L, where L is the distance separating MZM and ξ is the topological correlation length. Intrinsic quasiparticle poisoning occurs when quasiparticles are excited beyond the superconducting gap Δ of a superconductor. The suppression of intrinsic quasiparticle poisoning is

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[0008]

[0032] Quasiparticle poisoning (QPP) will be discussed in more detail below. QPP is a type of error that alters the fermion parity of the MZM used to encode information within Majorana islands, and can thereby cause errors in quantum computing. There are three types of QPP that occur in Majorana-based quantum computing systems: intrinsic QPP, extrinsic QPP, and intercomponent QPP.

[0009]

[0033] Intrinsic QPPs occur when the fermion number of a Majorana island remains constant, but the state of the Majorana island is thermally excited across the superconducting gap. In hardgap superconductors, intrinsic QPPs occur when a quasiparticle on the gap is excited from the MZM. This quasiparticle is typically absorbed by the MZM, relaxing the Majorana island and returning it to a subspace of its ground state. The emitting and absorbing MZMs can be different MZMs. Therefore, the ground state of the Majorana island can change during quasiparticle emission and absorption. This change in the ground state can lead to quantum computation errors due to fermion transfer between the emitting and absorbing MZMs.

[0010]

[0034] Extrinsic QPP (Quasi-Particle Diffusion) is a QPP that occurs when a Majorana island exchanges fermions with a fermion source located outside the Majorana qubit and qubit measurement component (QD and coherent link) system. Extrinsic QPP can occur, for example, as a result of quasiparticle leakage from adjacent electrostatic gates or transport leads contained in the quantum computing device. The lowest energy process that changes the number of fermions on a Majorana island is the absorption or emission of fermions at the island by the MZM (Multiple Zodiac Machine). Therefore, quasiparticle leakage from components outside the Majorana qubit and measurement component system typically affects the information encoded within the qubit, thereby leading to errors in quantum computing.

[0011]

[0035] Intercomponent QPPs occur when a Majorana island exchanges one or more fermions with another component of the qubit system, which may be another Majorana island or QD. Similar to extrinsic QPPs, intercomponent QPPs typically occur when fermions enter and leave a Majorana island via a multi-zone mechanism (MZM). Therefore, intercomponent QPPs are also typically errors. Intercomponent QPPs can occur, for example, during a decoupling step of a measurement where a Majorana island is disconnected from one or more other components of the qubit system.

[0012]

[0036] As discussed above, the intercomponent QPP is equal to the charge energy E of Majorana Island. c It can be suppressed by increasing or decreasing temperature T. However, E c It can be difficult to increase the ratio of / T. In addition, after an intercomponent QPP occurs, the probability of the poisoned quasiparticle moving to other Majorana islands during subsequent measurements increases, which can lead to correlation errors. This probability approaches (n-1) / n for measurements performed on n Majorana islands of the same size. In such n island measurements, the same energy cost is incurred by the additional fermions to move to each of the linked Majorana islands during the measurement. If the distribution of fermions across the linked Majorana islands is unbalanced, the fermions move with a high probability to a state that equalizes the number of fermions on the Majorana islands. The charge energy of the QDs contained in the qubit system is typically much higher than the charge energy of the Majorana islands. Therefore, intercomponent QPPs between Majorana islands are typically the highest probability form of intercomponent QPPs.

[0013]

[0037] The apparatus and methods described below can be used to correct inter-component QPP in a Majorana-based quantum computer. Figure 1 schematically shows a computing system 1 including a quantum computer 10 and a controller 20. The quantum computer 10 and the controller 20 are communicatively coupled so that the controller 20 receives input from the quantum computer 10 and transmits output instructions to the quantum computer 10. The controller 20 may be a classical computer including a processor 22 and memory 24, for example, as shown in the example in Figure 1.

[0014]

[0038] The quantum computing device 10 includes one or more island dot systems 11. Each of the island dot systems 11 includes a Majorana island 12 in which a plurality of Majorana zero modes (MZMs) 14 are instantiated. The Majorana island 12 can be a coherent link, a Majorana tetron, or a Majorana hexon. The island dot system 11 further includes a measurement circuit 15 that includes a quantum dot 16 that is electrically connectable to one of the plurality of MZMs 14. Additionally, QD 16 is configured to be electrically connectable to another MZM 14 located in the same Majorana island 12 or another Majorana island 12. The Majorana island 12 and the QD 16 located in proximity to the Majorana island 12 form the island dot system 11. The quantum dot 16 can be coupled to and decoupled from the MZM 14 by opening and closing a switch 17 included in the measurement circuit 15.

[0015]

[0039] The measurement circuit 15 further includes a capacitance sensor 18 capacitively coupled to the quantum dot 16. In the island dot system 11, a Majorana island gate voltage N g and a quantum dot gate voltage n g are applied to the Majorana island 12 and the quantum dot 16, respectively. Depending on the values of the Majorana island gate voltage N g and the quantum dot gate voltage n g , the capacitance sensor 18 measures different capacitance values of the island dot system 11. The values obtained during the capacitance measurement are used to detect QPP in the Majorana island 12 as discussed below. Additionally, as discussed in further detail below, the capacitance sensor 18 is used to perform a joint parity measurement when the corresponding QD 16 is electrically coupled to the plurality of MZMs 14. [[ID=​​As used herein, the term “island dot system” refers to a system of one or more Majorana islands 12 and one or more QD16 on which a joint parity measurement 32 or QPP detection 36 is performed, as will be discussed in more detail below. An island dot system 11 is formed by electrically coupling one or more QD16 to one or more Majorana islands 12. In some examples, one or more QD16 included in an island dot system 11 may differ from one or more QD16 used to perform a joint fermion parity measurement. Depending on the specific measurement that the controller 20 instructs the quantum computer 10 to perform between different joint parity measurements 32 and QPP detections 36, different combinations of Majorana islands 12 and QD16 selected from the sets of Majorana islands 12 and QD16 included in the quantum computer 10 may be used to form different island dot systems 11.

[0017]

[0041] Figure 2 shows an exemplary island-dot system 11A in which the Majorana island 12 is a coherent link. The coherent link includes a first MZM14A and a second MZM14B that form individual ends of the topological superconducting nanowire 50. In the example of Figure 2, QD16 is electrically connectable to the second MZM14B. QD16 is located within the semiconductor 51. The capacitance sensor 18 in the example of Figure 2 is configured to measure the quantum capacitance between QD16 and a cutter gate 19 coupled to an alternating current (AC) voltage source 52. When QD16 is electrically coupled to the Majorana island 12, the quantum capacitance changes.

[0018]

[0042] In the example in Figure 2, the Majorana island gate voltage N g and quantum dot gate voltage n gHowever, this can be configured via individual plunger gates 53A and 53B. The plunger gates 53A and 53B may be located above the surface of the island dot system 11, close to the Majorana island 12 and QD16 in the thickness direction. In other examples, the plunger gates 53A and 53B may be located below the Majorana island 12 and QD16 or within the plane of the island dot system 11. The plunger gates 53A and 53B may be electrostatic gates.

[0019]

[0043] In the example in Figure 2, the capacitance sensor 18 includes a microwave reading circuit 56 that is electrically coupled to an AC voltage source 52 and capacitively coupled to the QD 16. The microwave reading circuit 56 is configured to generate a microwave response signal 57 based at least partially on the quantum capacitance of the island dot system 11A. For example, the microwave reading circuit 56 may be an LC circuit in which the quantum capacitances of the QD 16 and the Majorana island 12 influence the resonance frequency of the microwave reading circuit 56. Thus, the value of the quantum capacitance can be determined from the microwave response signal 57. In the example in Figure 2, the microwave response signal 57 is output to the controller 20 as a quantum capacitance measurement.

[0020]

[0044] In the example in Figure 2, the quantum dot 16 used to perform the QPP detection measurement is also used to perform the joint parity measurement 32 included in the quantum computation. The quantum dot 16 allows the quantum computing device 10 to be further configured to perform joint parity measurements 32 of multiple MZM14s, including the MZM14B to which the quantum dot 16 is electrically coupled. Since each joint parity measurement 32 is for an even number of MZM14s, the joint parity measurement 32 is also performed for at least one other MZM14. Thus, the QD16 can serve a dual purpose, thereby enabling QPP detection without increasing the number of QD16s used in the island dot system 11. The increase in size and manufacturing complexity of the quantum computing device 10 can be avoided by using the same QD16 for both QPP detection 36 and joint parity measurement 32.

[0021]

[0045] Figure 2 further shows a fermion reservoir 58 that can be electrically connected to the Majorana island 12 and QD 16. The Majorana island 12 or QD 16 may be electrically coupled to the fermion reservoir 58 to set the fermion number of the Majorana island 12 or QD 16, for example, to reset the fermion number to zero. As depicted in the example in Figure 2, the fermion reservoir 58 may be an additional QD. The fermion reservoir 58 may be coupled to the MZM 14B as shown in Figure 2, or in addition to or instead to the MZM 14A.

[0022]

[0046] Returning to the example in Figure 1, the controller 20 is configured to transmit a joint parity measurement instruction 30 to the quantum computer 10. The joint parity measurement instruction 30 includes one or more joint parity measurements 32 that encode a quantum computation that the controller 20 instructs the quantum computer 10 to perform. Each joint parity measurement 32 indicated within the joint parity measurement instruction 30 is an instruction to measure the parity operator of an even number of MZM14s. The MZM14s may be contained in the same Majorana island 12 or in different Majorana islands 12. For example, a single-qubit Pauli measurement of Majorana-based qubits may correspond to measuring the fermion parity associated with a pair of MZM14s. The map between the MZM14s and the Pauli operators depends on the choice of encoding.

[0023]

[0047] As shown in the example in Figure 1, the controller 20 is further configured to transmit QPP detection commands 34 to the quantum computing device 10. The QPP detection commands 34 specify one or more QPP detections 36 that are configured to be executed in each island dot system 11.

[0024]

[0048] The controller 20 is configured to transmit a joint parity measurement command 30 and a QPP detection command 34 to the quantum computing device 10, and then to receive a plurality of quantum capacitance measurements 38 from the capacitance sensor 18. When the controller 20 performs the quantum capacitance measurements 38, the controller 20 receives a microwave response signal 57 measured in the island dot system 11. The controller 20 is further configured to determine the joint parity values ​​39 of two or more MZMs 14, at least in part, based on the microwave response signals 57. The joint parity values ​​39 are indications of positive parity, negative parity, or ambiguous parity values.

[0025]

[0049] As will be discussed in more detail below, when performing a joint parity measurement 32, the controller 20 controls the Majorana island gate voltage N g and quantum dot gate voltage n g The controller 20 is configured to perform quantum capacitance measurements 38 for different values ​​of N. g and quantum dot gate voltage n g To improve the visibility of the measurement for different values, one or more cutter gate voltages n are applied to one or more of the cutter gates 19. cg It can be further configured to adjust. The difference in response signals for positive and negative parity is nearly maximum when the island dot system 11 is tuned to resonance. Away from the resonance region, the visibility of the measurement signal that distinguishes parity decreases significantly, which can lead to ambiguous or erroneous measurement results. The quantum capacitance measurement 38 is also used when performing both the joint parity measurement 32 and the QPP detection 36.

[0026]

[0050] The quantum computing device 10 is configured to perform a 2-qubit joint parity measurement in addition to a 1-qubit joint parity measurement. As shown in the example in Figure 3, the 2-qubit measurement is configured to be performed in an island-dot system 11B including a first Majorana island 12A and a second Majorana island 12B. In the example of the island-dot system 11B in Figure 3, the first Majorana island 12A and the second Majorana island 12B are Majorana tetrons. In each Majorana tetron, four MZM14 are instantiated. The four MZM14 instantiated in each Majorana tetron are formed at the individual ends of a pair of topological superconducting nanowires 50. The topological superconducting nanowires 50 contained in each Majorana tetron are coupled by trivial superconducting nanowires 54. The measurement circuit 15 and fermion reservoir 58 of the Majorana tetron are omitted from Figure 3 for clarity.

[0027]

[0051] The island dot system 11B in Figure 3 further includes a first QD16A and a second QD16B positioned between the individual ends of the topological superconducting nanowires 50 contained in the first Majorana island 12A and the second Majorana island 12B. Thus, two of the MZM14 contained in the first Majorana island 12A are electrically coupled to two of the MZM14 contained in the second Majorana island 12B via the first QD16A and the second QD16B. This electrical coupling is between QD16A and 16B, the trivial superconducting nanowires 54 of the Majorana islands 12A and 12B, and

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[0028]

[0052] Figures 4A and 4B show the island-dot system 11B of Figure 3 when the controller controls the quantum computing device 10 to perform a joint parity measurement 32 and a quasiparticle poisoning detection 36. In the example of Figures 4A and 4B, the first Majorana island 12A and the second Majorana island 12B are Majorana tetrons. The first Majorana island 12A includes the first MZM14A, the second MZM14B, the third MZM14C, and the fourth MZM14D. The second Majorana island 12B includes the fifth MZM14E, the sixth MZM14F, the seventh MZM14G, and the eighth MZM14H. The first step shown in Figure 4A can be sampled across multiple candidate resonance regions during the joint parity measurement 32. The first step shown in Figure 4B can be sampled across multiple candidate resonance regions. The first step shown in Figure 4B allows sampling across multiple candidate resonance regions for QPP detection.

[0029]

[0053] The joint parity measurement 32 is performed on two or more of the multiple MZM14s. As shown in the example in Figure 4A, when the controller 20 controls the quantum computer 10 to perform the joint parity measurement 32, the quantum computer 10 is configured to electrically couple two or more MZM14s via one or more of the multiple quantum dots 16. In the example in Figure 4A, the joint parity measurement 32 is a 4MZM measurement in which two MZM14s contained in each of the first Majorana island 12A and the second Majorana island 12B are coupled via the first quantum dot 16A and the second quantum dot 16B. In this example, the second MZM14B is coupled to the fifth MZM14E via the first quantum dot 16A, and the fourth MZM14D is coupled to the seventh MZM14G via the second quantum dot 16B. Therefore, an interference loop 55 is formed between the first Majorana island 12A, the first QD16A, the second Majorana island 12B, and the second QD16B.

[0030]

[0054] When the joint parity measurement 32 is performed in the example shown in Figure 4A, the controller 20 adjusts the voltages of the plunger gates 53A and 53B to set the Majorana island gate voltage N g and quantum dot gate voltage n g It can be configured to set the Majorana island gate voltage N g and quantum dot gate voltage n g This can be configured to iteratively set to a value within the range of each of multiple candidate resonance regions.

[0031]

[0055] After performing the joint parity measurement 32, the controller 20 is further configured to control the quantum computing device 10 to isolate two or more MZMs 14 from one or more quantum dots 16. Isolating the MZMs 14 from the quantum dots 16 electrically isolates the Majorana islands 12 from the quantum dots 16 and from each other.

[0032]

[0056] After separating two or more MZMs 14 from one or more quantum dots 16, the controller 20 is further configured to control the quantum computing device 10 to perform quasiparticle poisoning detection 36 in each of the Majorana islands 12 where the two or more MZMs 14 are located. The quasiparticle poisoning detection is performed by individual capacitance sensors 18 of a plurality of capacitance sensors 18 located in close proximity to the MZMs 14. When performing quasiparticle poisoning detection, each capacitance sensor 18 of the plurality of capacitance sensors 18 measures the quantum capacitance of an individual island-dot system 11, which includes the Majorana islands 12 of the plurality of Majorana islands 12 and the quantum dots 16 of the plurality of quantum dots 16.

[0033]

[0057] In the examples of Figures 4A and 4B, the first quantum dot 16A and the second quantum dot 16B are included in the first capacitance sensor 18A and the second capacitance sensor 18B, respectively. The first capacitance sensor 18A and the second capacitance sensor 18B can be configured as shown in Figure 2, respectively. In this example, each QD16 used in the QPP detection 36 is also included in one or more QD16 through which two or more MZM14 are electrically coupled during the joint parity measurement 32. Thus, the same QD16 is used for both the joint parity measurement 32 and the quasiparticle poisoning detection 36, thereby reducing the size and complexity of the quantum computing device 10. In other examples, separate QD16 may be used to perform the joint parity measurement 32 and the QPP detection 36.

[0034]

[0058] In the example of Figure 4B, when the QPP detection 36 is performed, the controller 20 controls the quantum computing device 10 to electrically couple the first QD16A to the second MZM14B and the second QD16B to the seventh MZM14G. The first Majorana island 12A and the first QD16A form the first island dot pair 59A, and the second Majorana island 12B and the second QD16B form the second island dot pair 59B. Thus, the quantum capacitance is measured for each of the Majorana islands 12. In other examples, the first QD16A may instead be electrically coupled to the fifth MZM14E, and the second QD16B may instead be electrically coupled to the fourth MZM14D.

[0035]

[0059] The controller 20 may be further configured to control the quantum computing device 10 to electrically disconnect QD16 from the Majorana island 12 after measuring the quantum capacitance. Thus, the island dot system 11B can be prepared for a subsequent joint parity measurement 32.

[0036]

[0060] Figure 5 schematically shows the island dot system 11 and controller 20 when the joint parity measurement 32 is performed. For each of the multiple candidate resonance regions 40, the Majorana island gate voltage N g and quantum dot gate voltage n g These are set to the candidate resonance Majorana island gate voltage 42A and the candidate resonance quantum dot gate voltage 42B, respectively, located within the candidate resonance region 40. In some examples, the cutter gate voltage n on one or more cutter gates 19 is set. cg The candidate resonance cutter gate voltage 42C can also be set. Each candidate resonance region 40 is the Majorana island gate voltage N g and quantum dot gate voltage n g This is the parameter space region of the value. The controller 20 controls the Majorana island gate voltage N of one or more Majorana islands 12 included in the island dot system 11. g Each of these is set to a candidate resonance Majorana island gate voltage of 42A, and the quantum dot gate voltage n of one or more quantum dots 16 included in the island dot system 11 g Each of these can be configured to set the candidate resonant quantum dot gate voltage 42B. The individual cutter gate voltages n of each cutter gate 19 included in the island dot system 11 cg The candidate resonant cutter gate voltage can also be set to 42C.

[0037]

[0061] As discussed above, the controller 20 is further configured to receive quantum capacitance measurements 38 from a capacitance sensor 18 located in close proximity to the Majorana Island 12. The quantum capacitance measurements 38 include individual microwave response signals 57 measured in the candidate resonance region 40. When the controller 20 controls the quantum computing device 10, the capacitance sensor 18, which performs the quantum capacitance measurements 38 in the candidate resonance region 40, is located within the candidate resonance region 40 and is close to the Majorana Island gate voltage N of the candidate resonance Majorana Island gate voltage 42A, the candidate resonance quantum dot gate voltage 42B, and the candidate resonance cutter gate voltage 42C. g and quantum dot gate voltage ng The quantum capacitance is measured within each individual range of the value.

[0038]

[0062] The candidate resonance region 40 corresponds to the total fermion number N of the island dot system 11. tot Each of these corresponds to an individual value. Total number of fermions N tot This is the number of fermions located in the island dot system 11 relative to the reference value. N is the number of fermions of a single Majorana island 12 coupled to a single quantum dot 16. tot The change is given by N+n, where N is the change in the fermion number of the Majorana island 12 and n is the change in the fermion number of the QD16. By measuring the capacitance in several different candidate resonance regions 40, the capacitance sensor 18 is configured to measure the joint parity of several MZM14 even under conditions where QPP occurs in one or more Majorana islands 12. In some examples, one or more candidate resonance regions 40 are given by the fermion number N of the island dot system 11, given by {-3, -2, -1, 0, 1, 2, 3}. tot This can correspond to a set of values ​​of change. In another example, the candidate resonance region 40 is given by the fermion number N given by {-2, -1, 0, 1, 2} or {-1, 0, 1}. tot It can correspond to the value of change.

[0039]

[0063] When the controller 20 performs a joint parity measurement 32, the controller 20 is further configured to at least partially determine the joint parity values ​​39 of two or more MZM14 by classifying the microwave response signal 57 as a positive parity response signal 41A, a negative parity response signal 41B, or an ambiguous measurement result 41C. The difference between the positive parity response signal 41A and the negative parity response signal 41B is the Majorana island gate voltage N g , quantum dot gate voltage n g , and the fermion number N tot It depends on the change in . When the island dot system exhibits resonance, the visibility of the measurement increases. Some candidate resonance regions 40 have fermion number N totThe visibility of the measurement is low for a constant value of the change, which can lead to ambiguous measurement results41C.

[0040]

[0064] The controller 20 controls the quantum computing device 10 to determine the Majorana island gate voltage N in the candidate resonance region 40. g and quantum dot gate voltage n g The controller 20 may be configured to measure the microwave response signal 57 within the range of values ​​of . The controller 20 may take the measured microwave response signal 57 and convert it to a positive parity response signal 41A, a negative parity response signal 41B, or its N during the calibration step. tot The value is classified as an ambiguous measurement result 41C and can be further configured to distinguish between positive and negative joint parity values ​​39 for two or more MZM14s. The controller 20 is further configured to output the joint parity values ​​39 for two or more MZM14s.

[0041]

[0065] As shown in the example in Figure 1, the controller 20 is further configured to control the quantum computing device 10 to perform a QPP detection 36 after a joint parity measurement 32. The QPP detection 36, like the joint parity measurement 32, may be performed using the capacitance sensor 18 by performing a number of quantum capacitance measurements 38.

[0042]

[0066] The mathematical form describing the one-qubit joint parity measurement 32 following the QPP detection 36 is shown below. Single island measurements of MZM j and k contained in the same Majorana island 12 can be modeled using the following Hamiltonian:

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[0043]

[0067] E C ≠ε C When the Majorana island gate voltage N is given by the following Hamiltonian, the low-energy sector can be described by any fixed-charge sector (value of change in the fermion number of the island dot system 11). g and quantum dot gate voltage n g The value exists:

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[0044]

[0068] The energy and capacitance measured in quantum dot 16 are:

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[0045]

[0069] Measurement visibility ΔC Q teeth,

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[0046]

[0070] The position of the resonance point depends on the charge sector of the island dot system 11. In the N tot = N + n = 0 sector, the lowest energy states are |0,0〉 and |-1,;1〉, and the resonance occurs at

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[0047]

[0071] If the measurement circuit 15 achieves a signal-to-noise ratio sufficient to distinguish between the two parity states of a non-poisoned qubit, measuring the quantum capacitance of a poisoned qubit results in an ambiguous quantum capacitance measurement 38. The ambiguity of the measurement in the poisoned state is related to the quantum capacitance relationship.

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[0048]

[0072] Quasiparticle poisoning during two-qubit measurements is discussed below. The two-qubit measurements performed on the first Majorana island 12A and the second Majorana island 12B in Figure 3 can be modeled using the following Hamiltonian:

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[0049]

[0073] The point N in the parameter space g,A = N g,B = 1 / 2, n g,1 = n g,2 = -1 / 2 for the degeneracy of the ground state of the charge energy Hamiltonian will be discussed below. The total charge sector in this example is N tot = N A + N B + n1 + n2, and the charge configuration state is written as |N A , N B ; n1, n2〉. For values of N tot ∈ {-2, -1, 0, 1, 2}, the two qubits have the following ground states.

[0050]

[0074] N tot = -2: The eigen ground state |0, 0; -1, -1〉.

[0051]

[0075] N tot = -1: Four degenerate ground states |0, 0; -1, 0〉, |0, 0; 0, -1〉, |1, 0; -1, -1〉, and |0, 1; -1, -1〉.​​​​​​​​​​​​​​​​

[0078] N tot =2: Intrinsic ground state |1,1;0,0〉.

[0055]

[0079] N g,A , N g,B , n g,1 , and n g,2 The curvature of the ground state energy with respect to varies between different charge sectors. However, the charge sector N tot ∈{-1,0,1} is a point N in the state space of the gate voltage. g,A =N g,B = 1 / 2, n g,1 =n g,2 Since they still exhibit degeneracy at -1 / 2, these charge sectors may also exhibit resonance during quantum capacitance measurements. This resonance can provide visibility and distinguishability between positive and negative joint parity values ​​39.

[0056]

[0080] Charge sector N tot At =0, the effective Hamiltonian in the low-energy state space (where the ground states are ordered as shown above) can be written as follows:

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[0057]

[0081] E C,A = E C,B = E C 、ε C,1 = ε C,2 = ε C 、N g,A = N g,B = N g 、and n g,1 = n g,2 = n g By setting them as such, the analytical formula of the energy band in the example of two - qubit measurement can be written. The detuning energy of the island dot system 11 <00�0904>

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[0058]

[0082] FIG. 6A shows a plot of the energy E of the island dot system 11 of FIG. 3 as a function of the detuning energy δ0 for different values of θ when N tot =0. In the plot shown in FIG. 6A

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[0059]

[0083] The value of the detuning energy δ0 is the Majorana island gate voltage N g and quantum dot gate voltage n g Since it is determined by the Majorana Island Gate Voltage N, the controller 20 controls the Majorana Island Gate Voltage N g and quantum dot gate voltage n g The measurement position on the curve can be changed by modifying the value of . When a quantum capacitance measurement 38 is performed, the microwave response signal 57 is obtained from a thermally averaged combination of different energy levels associated with positive or negative parity.

[0060]

[0084] N g,A =N g,B = 1 / 2, n g,1 =n g,2 = -1 / 2, and N tot In the example where = 1, the first Majorana island 12A and the second Majorana island 12B have the following effective Hamiltonian:

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[0061]

[0085] Figure 6B shows N tot Figure 3 shows a plot of the energy E of the island-dot system 11B as a function of the detuning energy δ0 for different values ​​of θ when = 1. In the plot shown in Figure 6B,

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[0062]

[0086] Figure 7A schematically shows the computing system 1 when QPP detection 36 is performed in the quantum computing device 10. The quantum computing device 10 is configured to perform QPP detection 36 on one or more Majorana islands 12, thereby generating error data 80. The controller 20 is further configured to receive the error data 80 from the quantum computing device 10. The error data 80 includes one or more QPP indications 82 related to one or more Majorana islands 12 on which joint parity measurements 32 are performed. As shown in the example in Figure 7A, the controller 20 may be configured to calculate one or more QPP indications 82 based at least in part on a plurality of quantum capacitance measurements 38 received from the capacitance sensor 18 when QPP detection 36 is performed. In such an example, one or more QPP indications 82 are the fermion number N of the island dot system 11. tot This may include one or more indications of changes. The QPP indication 82, in some examples, has a fermion number N of multiple island-dot systems 11. tot This may include an indication of the change. In an example where the capacitance sensor 18 detects that no QPP is occurring in the island dot system 11, the error data 80 indicates that the inter-component QPP error is not related to the joint parity measurement 32.

[0063]

[0087] In addition to one or more QPP indications 82, the error data 80 may further include one or more indications of one or more joint parity measurements 32 performed prior to the QPP detection 36. The error data 80 may further include an indication of which MZM 14 was used in one or more joint parity measurements 32. In some examples, the QPP indications 82 may be expressed with respect to the individual fermion numbers of one or more Majorana islands 12 before and after each joint parity measurement 32.

[0064]

[0088] Based at least in part on the error data 80, the controller 20 is further configured to calculate Pauli operator error data 83. The Pauli operator error data 83 may specify a Pauli operator 84 to be applied to one or more qubits encoded in one or more Majorana islands 12 by a QPP event indicated in the QPP indication 82. In cases where no intercomponent QPP error has occurred in the island-dot system 11, as detected by the capacitance sensor 18, the Pauli operator error data 83 may indicate the identity operator associated with the corresponding joint parity measurement 32. The calculation of the Pauli operator error data 83 will be discussed in more detail below.

[0065]

[0089] Based at least in part on the error data 80, the controller 20 is further configured to update the cumulative error state 86 for one or more Majorana islands 12 where joint parity measurements 32 are performed. The cumulative error state 86 is configured to store information for multiple joint parity measurements 32, either by the individual error data 80 or by further processing the error data 80. Thus, the cumulative error state 86 tracks intercomponent QPP errors across multiple joint parity measurements 32 included in the quantum computation or error correction code.

[0066]

[0090] As shown in the example in Figure 7B, the controller 20 is further configured to perform an update operation 90 based at least partially on the cumulative error state 86. In the example in Figure 7B, the controller 20 is further configured to receive the quantum computation output 92 from the quantum computing device 10. The update operation 90 shown in this example includes correcting the quantum computation output 92 in the controller 20 based at least partially on the cumulative error state 86, thereby generating a corrected quantum computation output 94. The controller 20 is configured to apply a Pauli correction 96 to the quantum computation output 92 that acts as the inverse of the Pauli operator sequence 88 encoded in the cumulative error state 86. Thus, the controller 20 is configured to correct the quantum computation output 92 for the inter-component QPP.

[0067]

[0091] Figure 7C shows another example of an update operation 90. In the example of Figure 7C, the update operation 90 includes transmitting an instruction 98 to the quantum computer 10 to perform quantum error correction. The controller 20 is configured to generate the instruction 98 based at least partially on the accumulated error state 86. In the example of Figure 7C as shown, the quantum computer 10 is configured to implement a quantum code 100 that maps a set of physical level operations 102 performed on physical qubits to individual logic level operations 104 performed on logic qubits. The controller 20 may be configured to generate the instruction 98 based at least partially on the quantum code 100 so that the quantum error correction precisely maps the modification of the physical qubit state to the correction performed on the logic qubits.

[0068]

[0092] Figure 8 schematically shows a plurality of logical computation timesteps 106 and a plurality of physical computation timesteps 108 that can be executed in the computing system 1 in the examples of Figures 7A to 7C. Each of the logical computation timesteps 106 is a timestep in which a logic-level operation 104 specified by the quantum code 100 is performed. During each logical computation timestep 106, the controller 20 is configured to control the quantum computing device 10 to execute a plurality of physical computation timesteps 108. The physical computation timesteps 108 include individual joint parity measurements 32 and quasiparticle poisoning detection 36. Each of the physical computation timesteps 108 is executed in one or more ensembles of physical qubits, each encoding a logic qubit. In each of the logical computation timesteps 106, a logic operation of one or more logic qubits is constructed using a plurality of joint parity measurements 32 performed at the physical level.

[0069]

[0093] During each of the physical computation timesteps 108, the controller 20 may be further configured to control the quantum computing device 10 to perform multiple joint parity measurements 32 in parallel. In addition, the controller 20 may be further configured to control the quantum computing device 10 to perform multiple corresponding QPP detections 36 in parallel. Thus, the joint parity measurements 32 and QPP detections 36 can be performed in a time-efficient manner in an ensemble of physical qubits forming one or more logical qubits.

[0070]

[0094] During the logical computation time step 106, the controller 20 is further configured to perform update operations 90 after a number of physical computation time steps 108. As shown in Figure 7C, in some examples where quantum error correction is performed in the quantum computing device 10, the controller 20 may be configured to perform update operations 90 after the physical computation time step 108 immediately preceding the non-Clifford logic operation among the number of physical computation time steps 108. The non-Clifford logic operation is performed in the second logical computation time step 106, as shown in the example in Figure 8. Since the order of Pauli gates and other Clifford gates can be swapped up to possible updates of Pauli gates, quantum error correction can be delayed until any step of the quantum computation prior to the non-Clifford logic operation. In some examples, the correction may include performing a Clifford logic operation after the non-Clifford logic operation. In an example where a T-gate non-Clifford logic operation is performed, the correction may include applying a logical Clifford S-gate after the T-gate non-Clifford logic operation. By delaying quantum error correction, the computing system 1 can avoid the need to perform an update operation 90 to correct additional QPP events that occur after quantum error correction is performed in the logical computation time step 106.

[0071]

[0095] The following mathematical form explains the effect of QPP on the quantum state of Majorana Island 12 and further describes the calculation of the Pauli operator sequence 88. This mathematical form is provided according to the example where Majorana Island 12 is a Majorana tetron, but can also be applied to Majorana Island 12 containing other numbers of MZM14. As shown in the example in Figure 3, in the following example, a two-qubit measurement is performed on two MZM14 from the first Majorana tetron and the second Majorana tetron, respectively. The Majorana tetrons are labeled A and B. The corresponding MZM is j A , k A , j B , and k B Labeled as, j A , k A , j B , k B∈{1,2,3,4}, and none of these MZM numbers are repeated on a given Majorana tetron.

[0072]

[0096] MZM j A , k A , j B , and k B The joint parity measurement 32 is the joint fermion parity operator associated with MZM14.

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[0073]

[0097] The eigenstates of the two-tetron system discussed above are the joint fermion parity operators.

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[0074]

[0098] As discussed above, the joint fermion parity operator

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[0075]

[0099] As shown in Figure 4A, after separating Majorana Island 12A and Majorana Island 12B, the fermion numbers of the separated system components (e.g., Tetron, QD, and / or coherent link) exhibit a thermal distribution with respect to the corresponding energy of the component. Fermions moving into or out of the Majorana Tetron may enter or exit the Majorana Tetron via one of the Tetron's MZM14s coupled to QD16. Alternatively, fermions may enter Majorana Island 12 as quasiparticles on the gap, with approximately equal probability of relaxing into any of the MZM14s. Such relaxations are associated with the pre-measurement energy Δ and the post-measurement energy E. c It is required.

[0076]

[0100] If the fermion number of the Majorana tetron changes by an odd integer as a result of QPP, this change in the fermion number has the effect of applying a Pauli operator 84 to the qubit encoded in the tetron. The specific Pauli operator 84 applied by QPP is determined by the specific MZM 14 in which the fermion movement occurs. The Pauli operator 84 also correlates with one or more other operations applied to one or more other corresponding components of the quantum computing device 10, which may be one or more tetrons, QDs, and / or coherent links.

[0077]

[0101] Hereinafter, we assume that the charge energy of QD16 and the coherent link is much greater than the charge energy of the tetron island. Therefore, the change in the fermion number n of QD16 and the coherent link is treated as fixed, while the fermion number N of the tetron island can change. Under this assumption, a QPP event moves fermions from one tetron to the other, and such a movement occurs between any pair of coupled MZMs. The above explanation of the effect of QPP can be generalized to cases where, given corresponding sensors configured to measure the fermion number of components, the fermion number of any of the components may change. For example, in a coherent link, a QPP detection measurement may be performed to determine whether the fermion number of the coherent link changes as a result of a joint parity measurement 32 or other process performed in the coherent link.

[0078]

[0102] When a fermion enters or leaves a Tetron Island via the j-th MZM, the corresponding Majorana operator Y j This is applied to the 2-Tetron state. This Majorana operator Y j This reverses the total parity of Tetron Islands.

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[0079]

[0103] The above equation for ρ'' can be rewritten to include a term corresponding to the movement of fermions through any of the bonding pathways. In addition, the rewritten equation for ρ'' can include a term that takes into account the coherence between fermion movement processes. Therefore, the state after measurement and decoupling is given by the following equation:

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[0080]

[0104] In the above equations for λ0 and λ1,

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[0081]

[0105] The rewriting formula for ρ'' can be simplified by taking advantage of the fact that ρ' is the state after measurement. Therefore, the following characteristics are satisfied:

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[0082]

[0106] As can be seen from the above equation for ρ'', when measuring the fermion parity of a tetron island after performing a 2-tetron measurement, the QPP error does not decoheren the encoded computation state. Because the QPP error does not decoheren the qubit state, errors in the qubit state can be tracked and corrected. Specifically, measuring the fermion parity of a tetron island after a 2-tetron measurement has potential results corresponding to even and odd changes in the fermion number, respectively. When the change in the fermion number is even, the tetron island has the following states:

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[0083]

[0107] Even if the parity of the tetron island does not change, the above mathematical form describing the state after measurement and separation can be further modified to distinguish the change in the number of fermions of the tetron island. In the following explanation, v represents the total number of fermions that move from tetron B to tetron A. Thus, the state after measurement and separation is given by the following equation:

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[0084]

[0108] In the example where fermion parity does not change when a Tetron island is detached, the resulting state is

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[0085]

[0109] As described above with respect to Figure 8, in some examples the cumulative error state 86 is tracked over multiple physical calculation time steps 108 and an update operation 90 is applied after multiple joint parity measurements 32. In such examples, as shown in Figure 8, the controller 20 is further configured to control the quantum computing device 10 to perform a QPP detection 36 after each of the multiple joint parity measurements 32. The controller 20 then checks the number of fermions N measured during the QPP detection 36. tot The controller 20 is further configured to generate a Pauli operator sequence 88 based at least partially on the individual values ​​of the changes. Thus, the controller 20 is configured to iteratively construct the Pauli operator sequence 88 over multiple physical calculation time steps 108.

[0086]

[0110] Multiple QPP detections 36 can be performed without the controller 20 transmitting active feedback commands to the quantum computing device 10 after each joint parity measurement 32. By not requiring active feedback to track and correct QPP errors, the computing system 1 can utilize a simpler control architecture to control the quantum computing device 10.

[0087]

[0111] When performing Pauli operator tracking in an example where the update operation 90 is delayed until after multiple physical calculation time steps 108, the controller 20 uses the Pauli operator P as a Pauli projection operator.

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[0088]

[0112] The above explanation of 2-Tetron measurements is generalized below to measurements of N-Majorana island systems. N-Majorana island measurements are performed on two MZM14 from each of the Majorana islands 12 being measured. In this specification, N Majorana islands 12 are used

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[0089]

[0113] Figure 10A shows an exemplary island-dot system 111 including Majorana Tetron 112A, Majorana Hexon 112B, and Coherent Link 112C. Operator

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[0090]

[0114] In this example of an N-Majorana island measurement, the projection operator is given by the following equation:

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[0091]

[0115] Figures 10B to 10C show the island dot system 111 in Figure 10A in an example where QPP occurs. In the example in Figure 10B, MZM

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[0092]

[0116] The state of the N Majorana island system after measurement and subsequent separation is given by the following equation:

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[0093]

[0117] The following explanation extends the above description of the effect of QPP to an example where QD poisoning occurs. In such an example, the Majorana operator corresponding to the intercomponent QPP is no longer guaranteed to contain an even number of MZM14s. Fermion movement can occur between Majorana island 12 and QD16, or between pairs of QD16s. In an example where fermion movement occurs between Majorana island J and QD k forming the k-th junction between Majorana island K and Majorana island K+1, the fermion movement is the following operator, i.e.

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[0094]

[0118] QPP can also result in fermion transfers between QD k and QD k+V, forming the k-th and k+V-th joints between Majorana island K and Majorana island K+V. In such an example, the corresponding operators applied by the fermion transfer are the following operators:

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[0095]

[0119] Figures 11A and 11B show examples of QPPs between QD16 in the island dot system 111 of Figure 10A. In these examples, the fermion moves from the first QD116A to the second QD116B. In the example of Figure 11A, the QPP moves from the first QD116A to the second QD116B.

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[0096]

[0120] Figures 11C to 11D show examples of QPP between Majorana Island 12 and QD16 in the island-dot system 111 of Figure 10A. In the examples of Figures 11C to 11D, the fermion moves from Majorana Tetron 112A to the second QD116B. In the example of Figure 11C, the QPP is

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[0097]

[0121] The mapping between Majorana operator 14 and Pauli operator 84 related to the MZM of the Majorana tetron is shown below. These mappings are as follows when the fermion parity of Majorana island 12 is the degree of freedom of the qubit: Y1 = -X q X p Y2=Y q X p Y3 = -Z q X p Y4=I q Y p In the above equation, label q corresponds to an encoded topological qubit, and label p corresponds to the island fermion parity.

[0098]

[0122] When Majorana Island 12 is in an idle configuration, the interaction between Majorana Island 12 and its environment is defined by the even and odd fermion parity subspace (Z p The eigenspaces of +1 and -1 are rapidly decohered. Therefore, Majorana island 12 does not typically exhibit a coherent superposition of states with different island parities. Thus, Z p The eigenvalues ​​of X can be treated as classical variables. p and Y p The operators can be treated as island parity inversion operators, where there is no significant distinction between them.

[0099]

[0123] The joint fermion parity operator -Y1Y2Y3Y4 can be expressed in terms of the Pauli operator 84 as follows: -Y1Y2Y3Y4=-(-X q X p )(Y q X p )(-Z q X p )(I q Y p )=I q Z p A pair of Majorana operators maps to the Pauli operator 84 of the encoded qubit according to the following: iY1Y2=i(-X q X p )(Y q X p )=Z q I p iY1Y3=i(-X q X p )(-Z q X p )=Y q I p iY1Y4=i(-X q X p )(I q X p )=X q Z p iY2Y3=i(-Y q X p )(-Z q X p )=X q I p iY2Y4=i(-Y q X p )(I q X p )=-Y q Z p iY3Y4=i(-Z q X p )(I q Y p )=Z q Z p Therefore, if the fermion parity of Majorana Island 12 is even, the following equation holds: X q =iY2Y3=iY1Y4 Y q =iY1Y3=iY2Y4 Z q =iY1Y2=iY3Y4 If the fermion parity of Majorana Island 12 is odd, then the following equation holds: X q =iY2Y3=-iY1Y4 Y q =iY1Y3=iY2Y4 Z q =iY1Y2=-iY3Y4

[0100]

[0124] In the example where the Majorana operators of a multi-Tetron system are mapped to the Pauli operator 84, the Jordan-Wigner string can be used to ensure that the Majorana operators are anticommutative with each other. If the Majorana Tetrons are arbitrarily labeled with integers n=1,...,N, the Majorana operator of the nth Tetron can be written as follows:

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[0101]

[0125] Using the above-described relationships between QPP events and joint parity measurements 32, and between joint parity measurements 32 and Pauli operators 84, the controller 20 is configured to calculate a Pauli operator sequence 88. Thus, the controller 20 is configured to determine an update operation 90 based at least in part on any change in the number of fermions detected as having occurred after each joint parity measurement 32.

[0102]

[0126] Figure 12A shows the fermion number N. tot A schematic representation of the calculation system 1 in an example where the controller 20 is further configured to calculate multiple estimated fermion number probabilities 120 corresponding to multiple candidate values ​​of the change. In addition, the controller 20 is further configured to receive probability thresholds 122 for ambiguous or failed measurements. An ambiguous measurement is one in which the joint parity values ​​39 of two or more MZM 14 are ambiguous in each of the candidate resonance regions 40. For example, the controller 20 may be configured to determine that a joint parity measurement 32 is ambiguous if the value of the microwave response signal 57 received in each of the candidate resonance regions 40 falls within a predetermined confidence interval related to both the positive parity response curve 41A and the negative parity response curve 41B. A failed measurement is one in which the measurement is either ambiguous or a measurement of the island dot system 11 in which QD poisoning occurred. The probability thresholds 122 can be parameters set, for example, by user input.

[0103]

[0127] In the example shown in Figure 12A, the controller 20 is further configured to select a number of candidate resonance regions 40 based at least in part on the estimated fermion number probability 120 and the probability threshold 122. For example, the controller 20 is configured to select a number of candidate resonance regions 40 based on the fermion number sampling range endpoint N maxIt may be configured to select the set {-N max ,-N max +1,...N max It can be further configured to test changes in the number of fermions contained in}. Thus the number of candidate resonance regions 40 is 2N max It could be equal to +1.

[0104]

[0128] In some examples, as shown in Figure 12B, the controller 20 selects a number of candidate resonance regions 40 corresponding to individual multiple joint parity measurement types 130. max It can be further configured to calculate +1. Thus, different joint parity measurement types 130 have different N max It may have a value of . For example, multiple joint parity measurement types 130 may include a 1-qubit measurement without using a coherent link, a 1-qubit measurement using a coherent link, a 2-qubit measurement without using a coherent link, a 2-qubit measurement using a coherent link, a 2-qubit measurement using two coherent links, a 3-qubit measurement without using a coherent link, a 3-qubit measurement using a coherent link, and a 4-qubit measurement without using a coherent link. max Each of these values ​​can be calculated based at least in part on an estimated fermion number probability of 120 and a probability threshold of ambiguity for failed measurements of 122.

[0105]

[0129] N for different joint parity measurement types 130 max If the joint parity measurement 32 is performed after the value of is calculated, the controller 20 may be further configured to select the number of candidate resonance regions 40 to be explored during the joint parity measurement 32. The controller 20 selects a number of multiple numbers 2N calculated for different joint parity measurement types 130, specified by the joint parity measurement type 130 of the joint parity measurement 32. max From the +1, select the number of candidate resonance regions (40).

[0106]

[0130] The calculation of the estimated fermion number probability 120 and the probability of an ambiguous or failed measurement will be discussed in more detail below. Using these probabilities, processor 22 calculates N such that the probability of an ambiguous or failed measurement falls below the probability threshold 122. max It can be configured to select a value. The probability of an ambiguous measurement is given by the following formula:

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[0107]

[0131] In an example where the joint parity measurement 32 is a 2MZM measurement utilizing one Majorana island 12 and one QD 16, ε C >>E C We first consider the following regime. In this regime, the probability of QD poisoning is treated as negligible. The probability p that Majorana Island 12 has a given value for the change in the fermion number N. N This can be modeled as a Gibbs distribution:

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[0108]

[0132] The joint parity measurement 32 can be modeled to begin with Majorana islands 12 in a non-poisoned state. In such an example, each two-qubit measurement ends with the two Majorana islands 12 used in the measurement having N poisoned states. The probability that the two Majorana islands 12 end up in an N poisoned state can be approximated as follows:

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[0109]

[0133] The following table shows N g In the case of a single qubit where = 0, N max and βE C p calculated for various values amb This shows the value.

[0110] [Table 1]

[0111]

[0134] In cases where the probability of QD poisoning cannot be ignored, the probability of a failed measurement is examined below. In this example, the following Hamiltonian can be used to model Majorana Island 12 and QD16: H(N,n)=E C (NN g ) 2 +ε C (nn g ) 2 Fermion number N tot The probability of measuring the change

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[0112]

[0135] The probability p of a failed measurement, which may be either an ambiguous measurement or a measurement resulting in QD poisoning. fail To calculate this, an additional constraint n=0 can be used. Therefore, if QD poisoning occurs and n≠0, the measurement is treated as a failed measurement. Accordingly,

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[0113]

[0136] In an example where the probability of QD poisoning is negligible, we examine the probability of ambiguous measurements in a two-Majorana island system. In this example, the Majorana islands labeled A and B can be modeled by the following Hamiltonian: H=E C,A (N A -N g,A ) 2 +E C,B (N B -N g,B ) 2 When Majorana Island 12 is separated, the Gibbs distribution can be used to approximate the probability of having different fermion numbers for the composition of Majorana Island 12. When Majorana Island 12 is separated, N g,A and Ng,B It has an idle value of almost zero. tot The partition function for a fixed value of is given by the following equation:

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[0114]

[0137] From the Gibbs distribution above, the estimated probability

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[0115] [Table 2]

[0116]

[0138] The following table shows

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[0117] [Table 3]

[0118]

[0139] In cases where the probability of QD poisoning cannot be ignored, the probability of a failed measurement is examined below for a two-Majorana island system. In this example, the two-Majorana island system can be modeled by the following Hamiltonian: H=E C,A (N A -N g,A ) 2 +E C,B (N B -N g,B ) 2 +ε C,1 (n1-n g,1 ) 2 +ε C,2 (n2-n g,2 ) 2 N tot The partition function for a fixed value of is given by the following equation:

number

number

number

number

[0119]

[0140] More general measurement failure probability p fail To calculate this, we can introduce an additional constraint n1=n2=0, which corresponds to the fact that the number of fermions in QD16 does not change. The resulting N tot The partition function for a fixed value of is given by the following equation:

number

number

number

number

number

[0120]

[0141] Figure 13A schematically shows the computational system 1 during the calibration phase for a given joint parity measurement 32, in which the controller 20 is configured to estimate multiple candidate resonance regions 40 and calibrate the classifier 150 to classify the parity response signals. The calibration phase may include a first phase and a second phase. In the first phase, the controller 20 calculates the quantum dot gate voltages n of one or more QDs 16 and one or more Majorana islands 12 used in the joint parity measurement 32. g and Majorana Island Gate Voltage N g By adjusting N tot The controller 20 can be configured to determine each candidate resonance region 40 for ∈{-N_max,...,N_max}. g , quantum dot gate voltage n g , and cutter gate voltage n cg The voltage can be adjusted to a value that falls within the Majorana island gate voltage range 140A, the quantum dot gate voltage range 140B, and the cutter gate voltage range 140C, which are the voltage ranges over which the controller 20 searches for candidate resonance regions 40.

[0121]

[0142] The second stage is the total number of fermions N tot ∈{-N max ,N max For each of the values ​​of}, this may include extracting a positive parity response curve 41A and a negative parity response curve 41B in each candidate resonance region 40. The positive parity response curve 41A and the negative parity response curve 41B can then be used as expected response signals to calibrate the classifier of the joint parity measurement 32. Extracting these response signals may further include adjusting the cutter gate voltage to improve the visibility of the measurement.

[0122]

[0143] Figures 13B to 13D show in more detail the island-dot system 11 during a calibration step in one example. The calibration steps shown in Figures 13B to 13D are configured such that the classifier 150 determines the positive parity response signal 41A and the negative parity response signal 41B in each candidate resonance region 40, with a fermion number N tot ∈{-N max ,N max This can be performed for each of the multiple values ​​of the change in}. As shown in Figure 13B, the controller 20 controls the quantum computing device 10 to control one or more Majorana island gate voltages N g and one or more quantum dot gate voltages n g It can be configured to initialize with individual Coulomb valley voltages. One or more Majorana island gate voltages N g These are set to Coulomb Valley Majorana Island gate voltages of 144A respectively, and one or more quantum dot gate voltages n g These are set to a Coulomb Valley quantum dot gate voltage of 144B respectively.

[0123]

[0144] The calibration step involves the controller 20 setting the fermion number N of the island dot system 11 to the currently configured value so as to identify the candidate resonance region 40. tot This may further include setting the change in the fermion number N. tot The change can be set by moving fermions onto or from the Majorana Island 12 via the fermion reservoir 58. The controller 20 may be further configured to electrically couple two or more MZMs 14 and one or more QDs 16. In the example in Figure 13B, two or more MZMs 14 and one or more QDs 16 are electrically coupled by closing the switch 17.

[0124]

[0145] As shown in Figure 13C, the controller 20 may be further configured to control the quantum computing device 10 to search across the Majorana island gate voltage range 140A, the quantum dot gate voltage range 140B, and the cutter gate voltage range 140C. The search is at least partially based on quantum capacitance measurements 38, and involves the Majorana island gate voltage N of one or more Majorana islands 12. g , one or more QD16 quantum dot gate voltage n g , and the cutter gate voltage n of one or more cutter gates 19 cg This can be done using the capacitance sensor 18 by iteratively adjusting the Majorana island gate voltage N. g , quantum dot gate voltage n g , and cutter gate voltage n cg It can be configured to use a hill climb search algorithm with respect to the following: During the search, one or more Majorana Islands 12 have the same Majorana Island gate voltage N g Each can be set to the same quantum dot gate voltage n, and one or more QD16s can have the same quantum dot gate voltage n g Each can be set to the same cutter gate voltage n, and one or more cutter gates 19 can have the same cutter gate voltage n cg These can be set accordingly. The controller 20 may be further configured to control the quantum computing device 10 to output multiple quantum capacitance measurements 38 of the island dot system 11 within a range including candidate resonant gate voltages 42A, 42B, and 42C. The controller 20 may be further configured to calculate a positive parity response signal 41A, a negative parity response signal 41B, and an ambiguous measurement result 41C from the multiple quantum capacitance measurements 38, thereby calibrating the classifier 150.

[0125]

[0146] As shown in Figure 13D, after the identification of the candidate resonance region 40 and the output of the quantum capacitance measurement 38 in the candidate resonance region 40, the controller 20 controls the quantum computing device 10 to obtain one or more Majorana island gate voltages Ng and one or more quantum dot gate voltages n g The controller 20 may be further configured to reset the individual Coulomb valley voltages 144A and 144B. In addition, the controller 20 may be further configured to control the quantum computing device 10 to electrically isolate two or more MZMs 14 and one or more QDs 16. Thus, the controller 20 can prepare the island dot system 11 to identify one or more additional candidate resonance regions 40.

[0126]

[0147] As discussed above, the calibration stage involves multiple N tot This may include identifying individual candidate resonance regions 40 for each value. Fermion number N tot For each of the values ​​of the change in N, the controller 20 controls the quantum computing device 10 to control the gate voltage N corresponding to the other candidate resonance region 40. g and n g The value of Majorana Island Gate Voltage N g , quantum dot gate voltage n g , and cutter gate voltage n cg The controller 20 may be further configured to output individual quantum capacitance measurements 38 of the island dot system 11 at each of the candidate resonance values ​​42A, 42B, and 42C. Thus the controller 20 can output (parity, N tot Each pair can be configured to identify multiple non-resonant values ​​of quantum capacitance.

[0127]

[0148] Figure 14A shows a flowchart of Method 200 for use with a computing system including a quantum computer and a controller. The quantum computer is a topological quantum computer including multiple Majorana islands on which multiple MZMs are instantiated. Each Majorana island may be a coherent link, a Majorana tetron, or a Majorana hexon. The quantum computer further includes multiple quantum dots located in close proximity to the multiple Majorana islands, as well as multiple capacitance sensors configured to perform quantum capacitance measurements of the Majorana islands and quantum dots. The controller is a classical computing device including a processor and memory. Using Method 200 in Figure 14A, joint parity measurements of MZMs can be performed even when a QPP is present.

[0128]

[0149] In step 202, method 200 includes controlling a quantum computing device to perform joint parity measurements on two or more MZMs of a plurality of MZMs located within one or more Majorana Islands. Step 202 is performed in an island-dot system controller comprising one or more Majorana Islands and one or more quantum dots.

[0129]

[0150] The flowchart in Figure 14A further illustrates additional steps performed in the controller when a joint parity measurement is performed. In step 204, step 202 includes electrically coupling two or more MZMs via one or more quantum dots. Thus, a measurement loop can be formed that includes two or more MZMs and one or more quantum dots.

[0130]

[0151] Steps 206 and 208 are performed in each of several candidate resonance regions corresponding to several values ​​of the fermion number change in the island-dot system. A candidate resonance region is a region in the parameter space defined in terms of Majorana island gate voltages and QD gate voltages. The candidate resonance regions may further include adjusting one or more cutter gate voltages identified during calibration to enhance the visibility of the measurement. The fermion number change is the total number of fermions (e.g., electrons) moving between the Majorana islands and / or QDs in the island-dot system during a QPP event. For example, one or more candidate resonance regions may correspond to a set of values ​​of the fermion number change in the island-dot system selected from the groups {-3, -2, -1, 0, 1, 2, 3}, {-2, -1, 0, 1, 2}, and {-1, 0, 1}.

[0131]

[0152] In step 206, step 202 further includes setting the corresponding Majorana island gate voltages of one or more Majorana islands and the corresponding quantum dot gate voltages of one or more QDs to individual candidate resonance values. The candidate resonance values ​​are the values ​​of the Majorana island gate voltages and QD gate voltages that lie within the candidate resonance region.

[0132]

[0153] In step 208, step 202 further includes detecting the microwave response signal measured in the island dot system by capacitance sensors of a plurality of capacitance sensors. The response signal is measured in step 208 by collecting one or more quantum capacitance measurements of the island dot system by capacitance sensors of a plurality of capacitance sensors located in close proximity to the island dot system. In some examples, the quantum capacitance may be measured within a range of Majorana island gate voltage and quantum dot gate voltage values ​​located within a candidate resonance region.

[0133]

[0154] In step 210, step 202 further includes detecting whether resonance occurs and then separating two or more MZMs from one or more quantum dots. After the microwave response signals have been measured in each of several candidate resonance regions, step 202 further includes, in step 212, outputting joint parity values ​​of two or more MZMs based at least partially on the microwave response signals. The joint parity values ​​are positive parity values, negative parity values, or ambiguous measurement results. Step 212 may include, in step 214, classifying the microwave response signals as positive parity response signals, negative parity response signals, or ambiguous measurement results. Positive and negative parity response signals can be estimated during the calibration step for different values ​​of the change in fermion number. By measuring the joint fermion parity of one or more Majorana islands, the quantum computing device performs steps of quantum computation or error correction code.

[0134]

[0155] Figure 14B shows additional steps that may be performed in some examples in which method 200 of Figure 14A is performed. The steps in Figure 14B may be performed before step 202. In step 216, method 200 may further include receiving a probability threshold for ambiguous or failed measurements. For example, a controller may receive the probability threshold via user input. In step 218, method 200 may further include selecting a number of candidate resonance regions. The number of candidate resonance regions may be selected such that, when a joint parity measurement is performed in each of the candidate resonance regions, the probability of an ambiguous or failed measurement is below the probability threshold for the joint parity measurement.

[0135]

[0156] When performing step 218, method 200 may further include, in step 220, calculating the number of candidate resonance regions corresponding to individual multiple joint parity measurement types. In step 222, step 218 may further include selecting the number of candidate resonance regions from a plurality of numbers according to the joint parity measurement type of the joint parity measurement. Multiple joint parity measurement types may include, for example, a 1-qubit measurement without a coherent link, a 1-qubit measurement with a coherent link, a 2-qubit measurement without a coherent link, a 2-qubit measurement with a coherent link, a 2-qubit measurement with two coherent links, a 3-qubit measurement without a coherent link, a 3-qubit measurement with a coherent link, and a 4-qubit measurement without a coherent link. The individual number of candidate resonance regions may also be calculated for other measurement types in some examples.

[0136]

[0157] Figure 14C shows additional steps of Method 200 that may be performed in some examples during the calibration step. The calibration step may be performed before step 202. As shown in Figure 14C, in step 224, Method 200 may further include estimating multiple candidate resonance regions for each of multiple values ​​of the change in the fermion number of the island-dot system. In addition, the calibration step may further include identifying positive parity response signals and negative parity response signals corresponding to positive fermion parity and negative fermion parity, respectively.

[0137]

[0158] In step 226, step 224 may include initializing the Majorana island gate voltages of one or more Majorana islands and the QD gate voltages of one or more QDs with their respective Coulomb valley voltages. After setting the Majorana island gate voltages and the QD gate voltages to their Coulomb valley voltages, step 224 may further include in step 228 setting the fermion number change of the island dot system to the value of the fermion number change at which the controller identifies a candidate resonance region. In step 230, step 224 may further include electrically coupling two or more MZMs and one or more QDs.

[0138]

[0159] In step 232, method 200 may further include approximating individual values ​​of one or more Majorana island gate voltages and one or more quantum dot gate voltages at which resonance occurs as candidate resonance values ​​corresponding to the value of the change in the fermion number. Candidate resonant Majorana island gate voltages and candidate resonant QD gate voltages can be at least partially approximated by exploring individual ranges of gate voltage values ​​using capacitance sensors.

[0139]

[0160] In step 234, step 224 may further include outputting a quantum capacitance measurement of the island dot system at a candidate resonance value. In some examples, step 234 may include outputting a number of quantum capacitance measurements within a range of Majorana island gate voltages and quantum dot gate voltages located within the candidate resonance region.

[0140]

[0161] In step 236, step 224 may further include resetting one or more Majorana island gate voltages and one or more QD gate voltages to individual Coulomb valley voltages. In step 238, step 224 may further include electrically disconnecting two or more MZMs and one or more QDs. In this way, the island dot system can be prepared for calibration with a different combination of changes in parity value and fermion number.

[0141]

[0162] In step 240, step 224 may further include calibrating a classifier that distinguishes between positive parity response signals, negative parity response signals, and ambiguous measurement results. The classifier may be calibrated at least in part on quantum capacitance measurements obtained for individual candidate resonance regions. Thus, the classifier may be calibrated to identify joint fermion parity in each of the candidate resonance regions.

[0142]

[0163] Figure 15A shows a flowchart of another method 300 that may be used with a computing system including a quantum computer and a controller. As shown in the example in Figure 15A, steps 302 and 304 are performed in the quantum computer. In step 302, method 300 includes performing joint parity measurements on two or more MZMs among a plurality of MZMs instantiated in a plurality of Majorana Islands included in the quantum computer. The two or more MZMs are located in one or more of the plurality of Majorana Islands. In some examples, the steps of method 200 in Figure 14A may be performed when step 302 is performed.

[0143]

[0164] In step 304, method 300 may further include performing QPP detection on one or more Majorana islands to generate error data. Similar to joint parity measurement, QPP detection may be performed using a capacitance sensor located in close proximity to the QD and the Majorana island. The error data includes one or more QPP indications associated with one or more Majorana islands, each QPP indication specifying whether a QPP occurred on that Majorana island during the joint parity measurement. Each QPP indication may further include changes in the individual fermion parity of one or more Majorana islands on which the joint parity measurement is performed.

[0144]

[0165] Steps 306, 308, 310, and 312 are performed in the controller. In step 306, method 300 further includes receiving error data from the quantum computing device. In step 308, method 300 further includes updating the cumulative error state of one or more Majorana Islands based at least in part on the error data. The cumulative error state may track QPP errors over a plurality of physical time steps.

[0145]

[0166] In some examples, step 308 may include calculating Pauli operator error data in step 310 based at least in part on the error data. The Pauli operator error data may specify the Pauli operators applied to the qubits encoded in one or more Majorana islands by the QPP events indicated within the QPP indication. In such examples, the cumulative error state may include a sequence of Pauli operators of multiple Pauli operators, each associated with multiple joint parity measurements.

[0146]

[0167] In step 312, method 300 further includes performing an update operation based at least in part on the accumulated error state. As will be discussed below, the update operation may be a controller-side update operation, a quantum computing device-side update operation, or an error state tracking operation. In this way, the computing system is configured to adjust the influence of QPP on quantum computation or error correction code.

[0147]

[0168] Figure 15B shows additional steps of Method 300 that may be performed in some examples. In step 314, Method 300 may further include performing multiple physical computation timesteps in the quantum computer during a logical computation timestep. A logical computation timestep may be specified by a quantum code that maps a set of physical-level operations performed on physical qubits to corresponding logical operations performed on logical qubits. A physical computation timestep may include individual joint parity measurements and individual quasiparticle poisoning detections, respectively. By performing multiple physical computation timesteps, the quantum computer can implement logical qubit-level gates using multiple physical qubit-level operations.

[0148]

[0169] In step 316, method 300 may further include performing an update operation in the controller during a logical computation time step after a number of physical computation time steps. Thus, in the example of Figure 15B, the update operation is a controller-side update operation. In step 318, step 316 may include the controller receiving the quantum computation output from the quantum computing device after a number of physical computation time steps. In an example in which step 318 is performed, step 316 may further include correcting the quantum computation output in step 320, at least partially based on the accumulated error state, when performing the update operation. Thus, the update operation may be performed at the end of a logical computation time step.

[0149]

[0170] Figure 15C shows additional steps of method 300 that may be performed in an example where the update operation is a quantum computing device-side update operation. In step 322, method 300 may further include generating an instruction in the controller to perform quantum error correction based at least partially on the accumulated error state. In step 324, method 300 may further include transmitting the instruction to the quantum computing device.

[0150]

[0171] In step 326, method 300 may further include receiving an instruction in the quantum computing device. The method may further include, in step 328, performing quantum error correction on one or more Majorana islands based at least partially on the instruction. In some examples, quantum error correction may be performed after the physical computation time step immediately preceding the non-Clifford logic operation among a group of physical computation time steps. In such examples, the quantum computing device can avoid the need to perform multiple Pauli error correction operations in examples where multiple QPP events occur during a logic computation time step.

[0151]

[0172] In some embodiments, the methods and processes described herein can be linked to a computing system of one or more computing devices. Specifically, such methods and processes can be implemented as computer application programs or services, application programming interfaces (APIs), libraries, and / or other computer program products.

[0152]

[0173] Figure 16 schematically illustrates a non-limiting embodiment of a computing system 400 capable of performing one or more of the above methods and processes. The computing system 400 is shown in a simplified form. The computing system 400 can embody the computing system 1 described above and shown in Figure 1. The components of the computing system 400 may be contained within one or more personal computers, server computers, tablet computers, home entertainment computers, network computing devices, game consoles, mobile computing devices, mobile communication devices (e.g., smartphones), and / or other computing devices, as well as wearable computing devices such as smartwatches and head-mounted augmented reality devices.

[0153]

[0174] The computing system 400 includes a logical processor 402, a volatile memory 404, and a non-volatile storage device 406. The computing system 400 may optionally include a display subsystem 408, an input subsystem 410, a communication subsystem 412, and / or other components not shown in Figure 16.

[0154]

[0175] The logical processor 402 includes one or more physical devices configured to execute instructions. For example, the logical processor may be configured to execute instructions that are part of one or more applications, programs, routines, libraries, objects, components, data constructs, or other logical constructs. Such instructions may be implemented to perform a task, to implement a data type, to change the state of one or more components, to achieve a technical effect, or to reach a desired result.

[0155]

[0176] A logic processor may include one or more physical processors (hardware) configured to execute software instructions. In addition, or separately, a logic processor may include one or more hardware logic circuits or firmware devices configured to execute logic or firmware instructions implemented by hardware. The processor of the logic processor 402 may be single-core or multi-core, and the instructions executed therein may be configured with respect to sequential processing, parallel processing, and / or distributed processing. Individual components of the logic processor may be optionally distributed between two or more separate devices located separately and / or configured for cooperative processing. Aspects of the logic processor may be virtualized and executed by remotely accessible networked computing devices configured within a cloud computing configuration.

[0156]

[0177] The non-volatile memory device 406 includes one or more physical devices configured to hold instructions executable by a logic processor for implementing the methods and processes described herein. When such methods and processes are implemented, the state of the non-volatile memory device 406 can be changed, for example, to hold various types of data.

[0157]

[0178] The non-volatile storage device 406 may include removable and / or embedded physical devices. The non-volatile storage device 406 may include optical memory, semiconductor memory, and / or magnetic memory, or other mass storage technology. The non-volatile storage device 406 may include non-volatile, dynamic, static, read / write, read-only, sequential access, position-addressable, file-addressable, and / or content-addressable devices. It will be understood that the non-volatile storage device 406 is configured to retain instructions even when power to the non-volatile storage device 406 is cut off.

[0158]

[0179] The volatile memory 404 may include a physical device containing random access memory. The volatile memory 404 is typically used by the logical processor 402 to temporarily store information during the processing of software instructions. It will be understood that the volatile memory 404 typically does not retain instructions when power to the volatile memory 404 is cut off.

[0159]

[0180] The aspects of the logic processor 402, volatile memory 404, and non-volatile storage device 406 can be integrated into one or more hardware logic components. Such hardware logic components may include, for example, rewritable gate arrays (FPGAs), program-specific integrated circuits and application-specific integrated circuits (PASICs / ASICs), program-specific standards and application-specific standards (PSSPs / ASSPs), systems on a chip (SOCs), and composite programmable logic devices (CPLDs).

[0160]

[0181] The terms “module,” “program,” and “engine” may be used to describe aspects of a computing system 400 that are implemented in software by a processor to perform specific functions, typically using a portion of volatile memory, and which include transformations that specifically configure the processor to perform those functions. Thus, a module, program, or engine may be instantiated by a logical processor 402 that executes instructions held by a non-volatile storage device 406 using a portion of volatile memory 404. 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. Similarly, the same module, program, and / or engine may be instantiated by different applications, services, code block, object, routine, API, function, etc. The terms “module,” “program,” and “engine” may encompass each or a group of executable files, data files, libraries, drivers, scripts, database records, etc.

[0161]

[0182] If included, the display subsystem 408 may be used to present a visual representation of the data held by the non-volatile memory 406. This visual representation may take the form of a graphical user interface (GUI). Since the methods and processes described herein modify the data held by the non-volatile memory and thus change the state of the non-volatile memory, the state of the display subsystem 408 can also be changed to visually represent the changes in the underlying data. The display subsystem 408 may include one or more display devices utilizing virtually any kind of technology. Such display devices can be combined with the logical processor 402, volatile memory 404, and / or non-volatile memory 406 within a shared enclosure, or they can be peripheral display devices.

[0162]

[0183] If included, the input subsystem 610 may include or interface with one or more user input devices such as a keyboard, mouse, touchscreen, or game controller. In some embodiments, the input subsystem may include or interface with selected natural user input (NUI) components. Such components may be integrated or peripheral devices, and the conversion and / or processing of input actions may be handled onboard or offboard. Examples of NUI components may include microphones for conversation and / or speech recognition, infrared, color, stereoscopic, and / or depth cameras for machine vision and / or gesture recognition, head trackers, eye trackers, accelerometers, and / or gyroscopes for motion detection and / or intent recognition, and electric field sensing components and / or other suitable sensors for evaluating brain activity.

[0163]

[0184] Where included, the communication subsystem 412 may be configured to connect the various computing devices described herein to each other and to other devices in a communicative manner. The communication subsystem 412 may include wired and / or wireless communication devices compliant with one or more different communication protocols. In non-limiting examples, the communication subsystem may be configured for communication over a wireless telephone network or a wired or wireless local or wide-area network. In some embodiments, the communication subsystem may enable the computing system 400 to send and receive messages with other devices over a network such as the Internet.

[0164]

[0185] The following paragraphs discuss several aspects of the present disclosure. According to one aspect of the present disclosure, a computing system is provided which includes a quantum computing device including a plurality of Majorana islands in which a plurality of Majorana zero-modes (MZMs) are instantiated. The quantum computing device further includes a plurality of quantum dots located in close proximity to the plurality of Majorana islands. The quantum computing device further includes a plurality of capacitance sensors. The computing system further includes a controller configured to control the quantum computing device to perform joint parity measurements of two or more MZMs located within one or more Majorana islands for an island-dot system including one or more Majorana islands and one or more quantum dots. Performing joint parity measurements includes setting the corresponding Majorana island gate voltages of one or more Majorana islands and the corresponding quantum dot gate voltages of one or more quantum dots to the respective candidate resonance values ​​located within the candidate resonance region, for each of a plurality of candidate resonance regions corresponding to a plurality of values ​​of the change in the fermion number of the island-dot system. Performing a joint parity measurement further includes detecting the microwave response signal measured in the island-dot system by capacitance sensors of multiple capacitance sensors in each of the candidate resonance regions. Performing a joint parity measurement further includes outputting two or more MZM joint parity values ​​based at least partially on the microwave response signal. The above features may have the technical effect of performing joint parity measurements with sufficient measurement visibility even in the presence of quasiparticle poisoning.

[0165]

[0186] According to this embodiment, each Majorana Island can be a coherent link, a Majorana tetron, or a Majorana hexon. The above features may have the technical effect of enabling the instantiation of classical bits or qubits in each Majorana Island.

[0166]

[0187] According to this embodiment, performing a joint parity measurement may further include electrically coupling two or more MZMs via one or more quantum dots in each of a plurality of candidate resonance regions. After detecting the microwave response signal, performing a joint parity measurement may further include decoupling two or more MZMs from one or more quantum dots. The above features may have the technical effect of electrically isolating the MZMs from the quantum dots after the joint parity measurement.

[0167]

[0188] According to this embodiment, the controller may be configured to determine the joint parity values ​​of at least two or more MZMs by classifying the microwave response signal into a positive parity response signal, a negative parity response, a signal, or an ambiguous response signal. The above feature may have the technical effect of indicating in the output whether the joint parity value and sufficient measurement visibility have been achieved.

[0168]

[0189] According to this embodiment, one or more candidate resonance regions may correspond to a set of values ​​representing the change in the fermion number of an island dot system selected from the groups {-3, -2, -1, 0, 1, 2, 3}, {-2, -1, 0, 1, 2}, and {-1, 0, 1}. The above feature may have the technical effect of confirming a distinguishable parity value in the candidate resonance region corresponding to the most probable fermion number.

[0169]

[0190] According to this embodiment, the controller is further configured to receive a probability threshold for ambiguous or failed measurements. The controller may be further configured to select a number of candidate resonance regions in which the joint parity measurement has a probability of being an ambiguous or failed measurement below a probability threshold, when a joint parity measurement is performed in each of a plurality of candidate resonance regions. The above features may have the technical effect of allowing the user to set the number of candidate resonance regions according to a target rate of ambiguous or failed measurements.

[0170]

[0191] According to this embodiment, the controller may be further configured to calculate a number of candidate resonance regions corresponding to individual multiple joint parity measurement types. The controller may be further configured to select a number of candidate resonance regions from a plurality of numbers according to the joint parity measurement type of the joint parity measurement. The above features may have the technical effect of allowing the quantum computer to confirm sufficient measurement visibility in a different number of candidate resonance regions for different types of joint parity measurements where the probability of failure or ambiguity of measurement differs.

[0171]

[0192] According to this embodiment, the multiple joint parity measurement types may include a 1-qubit measurement without using a coherent link, a 1-qubit measurement using a coherent link, a 2-qubit measurement without using a coherent link, a 2-qubit measurement using a coherent link, a 2-qubit measurement using two coherent links, a 3-qubit measurement without using a coherent link, a 3-qubit measurement using a coherent link, and a 4-qubit measurement without using a coherent link. The above features may have the technical effect of allowing the quantum computer to confirm sufficient measurement visibility in a different number of candidate resonance regions for different types of joint parity measurements with different probabilities of failure or ambiguity.

[0172]

[0193] According to this embodiment, the controller may be further configured to estimate, at least partially, multiple candidate resonance regions during the calibration step by setting the change in the fermion number of the island-dot system for each of a plurality of values ​​of the change in the fermion number of the island-dot system and controlling the quantum computing device to electrically couple two or more MZMs and one or more quantum dots. For each of the values ​​of the change in the fermion number, the controller may be further configured to control the quantum computing device to approximate each of the values ​​of one or more Majorana island gate voltages and one or more quantum dot gate voltages that at least partially resonate, by searching for each range of gate voltage values ​​using a capacitance sensor as candidate resonance values ​​corresponding to the value of the change in the fermion number. For each of the values ​​of the change in the fermion number, the controller may be further configured to control the quantum computing device to output the quantum capacitance measurement of the island-dot system at the candidate resonance value. The above features may have the technical effect of calibrating the quantum capacitance measurement by identifying candidate resonance regions.

[0173]

[0194] According to this embodiment, for each of several values ​​of the fermion number change, the controller may be further configured to estimate several candidate resonance regions by controlling the quantum computing device to initialize one or more Majorana island gate voltages and one or more quantum dot gate voltages to individual Coulomb valley voltages before setting the fermion number change to a value. After outputting the quantum capacitance measurement, the controller may be further configured to control the quantum computing device to reset one or more Majorana island gate voltages and one or more quantum dot gate voltages to individual Coulomb valley voltages. The controller may be further configured to control the quantum computing device to electrically disconnect two or more MZMs and one or more quantum dots. The above features may have the technical effect of preparing the quantum computing device for calibration in another candidate resonance region.

[0174]

[0195] According to this embodiment, for each value of the fermion number change, the controller may be further configured to control the quantum computing device to output individual quantum capacitance measurements of the island-dot system for each of the candidate resonance values ​​of the Majorana island gate voltage and the quantum dot gate voltage. The above feature may have the technical effect of obtaining quantum capacitance measurements in each candidate resonance region for each value of the fermion number change during the calibration step.

[0175]

[0196] Another aspect of this disclosure provides a method for use with a computing system including a quantum computing device and a controller. The quantum computing device includes a plurality of Majorana islands. A plurality of Majorana zero modes (MZMs) are instantiated in each of the Majorana islands. The quantum computing device further includes a plurality of quantum dots located in close proximity to the plurality of Majorana islands, and further includes a plurality of capacitance sensors. The method includes, in the controller, controlling the quantum computing device for one of the plurality of Majorana islands or an island-dot system including one of the plurality of Majorana islands and one of the plurality of quantum dots to perform joint parity measurements of two or more MZMs of a plurality of MZMs located within one or more Majorana islands. Performing a joint parity measurement involves setting the corresponding Majorana island gate voltages of one or more Majorana islands and the corresponding quantum dot gate voltages of one or more quantum dots to the respective candidate resonance values ​​located within the candidate resonance region, for each of several candidate resonance regions corresponding to several values ​​of the change in the fermion number of the island-dot system. Performing a joint parity measurement in each of the several candidate resonance regions further involves detecting the microwave response signal measured in the island-dot system using capacitance sensors of several capacitance sensors. Performing a joint parity measurement further involves outputting two or more MZM joint parity values ​​based at least partially on the microwave response signal. The above features may have the technical effect of performing joint parity measurements with sufficient measurement visibility even in the presence of quasiparticle poisoning.

[0176]

[0197] According to this embodiment, each Majorana Island can be a coherent link, a Majorana tetron, or a Majorana hexon. The above features may have the technical effect of enabling the instantiation of classical bits or qubits in each Majorana Island.

[0177]

[0198] According to this embodiment, performing a joint parity measurement may further include electrically coupling two or more MZMs via one or more quantum dots in each of a plurality of candidate resonance regions. After detecting the microwave response signal, performing a joint parity measurement may further include decoupling two or more MZMs from one or more quantum dots. The above features may have the technical effect of electrically isolating the MZMs from the quantum dots after the joint parity measurement.

[0178]

[0199] In this embodiment, performing a joint parity measurement may further include classifying the microwave response signal into a positive parity response signal, a negative parity response signal, or an ambiguous response signal. The above features may have the technical effect of indicating in the output whether the joint parity value and sufficient measurement visibility have been achieved.

[0179]

[0200] According to this embodiment, one or more candidate resonance regions correspond to a set of values ​​representing the change in the fermion number of an island dot system selected from the groups {-3, -2, -1, 0, 1, 2, 3}, {-2, -1, 0, 1, 2}, and {-1, 0, 1}. The above feature may have the technical effect of confirming a distinguishable parity value in the candidate resonance region corresponding to the most probable fermion number.

[0180]

[0201] According to this embodiment, the method may further include receiving a probability threshold for ambiguous or failed measurements. The method may further include selecting a number of candidate resonance regions in which joint parity measurements have a probability of being ambiguous or failed measurements below a probability threshold, when joint parity measurements are performed in each of a plurality of candidate resonance regions. The above features may have the technical effect of allowing the user to set the number of candidate resonance regions according to a target rate of ambiguous or failed measurements.

[0181]

[0202] According to this embodiment, the method may further include calculating in the controller the number of candidate resonance regions corresponding to each of the multiple joint parity measurement types. The method may further include selecting the number of candidate resonance regions from a plurality of numbers according to the joint parity measurement type of the joint parity measurement. The multiple joint parity measurement types may include a 1-qubit measurement without a coherent link, a 1-qubit measurement with a coherent link, a 2-qubit measurement without a coherent link, a 2-qubit measurement with a coherent link, a 2-qubit measurement with two coherent links, a 3-qubit measurement without a coherent link, a 3-qubit measurement with a coherent link, and a 4-qubit measurement without a coherent link.

[0182]

[0203] In this embodiment, the method may further include estimating a plurality of candidate resonance regions during the calibration step by setting the change in the fermion number of the island dot system for each of a plurality of values ​​of the change in the fermion number of the island dot system. The calibration step may further include electrically coupling two or more MZMs and one or more quantum dots for each of the values ​​of the change in the fermion number. The calibration step may further include approximating the values ​​of one or more Majorana island gate voltages and one or more quantum dot gate voltages that at least partially resonate by exploring each range of gate voltage values ​​using a capacitance sensor as candidate resonance values ​​corresponding to the values ​​of the change in the fermion number. The calibration step may further include outputting the quantum capacitance measurement of the island dot system at the candidate resonance value for each of the values ​​of the change in the fermion number.

[0183]

[0204] In another aspect of the present disclosure, a computing system is provided which includes a quantum computing device. The quantum computing device includes a plurality of Majorana islands in which a plurality of Majorana zero modes (MZMs) are instantiated. The quantum computing device further includes a plurality of quantum dots located in close proximity to the plurality of Majorana islands, and further includes a plurality of capacitance sensors. The computing system further includes a controller configured to control the quantum computing device to perform joint parity measurements of two or more MZMs located within one or more Majorana islands for an island-dot system comprising one or more Majorana islands and one or more quantum dots. Performing joint parity measurements involves electrically coupling two or more MZMs via one or more quantum dots in each of a plurality of candidate resonance regions corresponding to a plurality of values ​​of the change in the fermion number of the island-dot system, and further corresponding to individual plurality of joint parity measurement types. Performing a joint parity measurement further includes setting the corresponding Majorana island gate voltages of one or more Majorana islands and the corresponding quantum dot gate voltages of one or more quantum dots to their respective candidate resonance values ​​located within the candidate resonance region. Performing a joint parity measurement using capacitance sensors of multiple capacitance sensors further includes detecting the microwave response signal measured in the island-dot system. Performing a joint parity measurement after detecting the microwave response signal further includes decoupling two or more MZMs from one or more quantum dots. Performing a joint parity measurement at least partially based on the microwave response signal further includes outputting the joint parity values ​​of two or more MZMs. The above features may have the technical effect of performing a joint parity measurement with sufficient measurement visibility even in the presence of quasiparticle poisoning.

[0184]

[0205] According to another aspect of this disclosure, a computing system is provided which includes a quantum computing device. The quantum computing device includes a plurality of Majorana islands in which a plurality of Majorana zero modes (MZMs) are instantiated. The computing system further includes a controller configured to control the quantum computing device to perform joint parity measurements in two or more of the plurality of MZMs. The two or more MZMs are located in one or more of the plurality of Majorana islands. The controller is further configured to control the quantum computing device to perform quasiparticle poisoning (QPP) detection in one or more Majorana islands, thereby generating error data. The error data includes one or more QPP indications associated with one or more Majorana islands. The controller is further configured to receive the error data from the quantum computing device and to update the cumulative error state of one or more Majorana islands based at least in part on the error data. The controller is further configured to perform the update operation based at least in part on the cumulative error state. The above features may have the technical effect of tracking and / or correcting QPP errors that occur during joint parity measurement.

[0185]

[0206] According to this embodiment, during the logical computation timestep of the quantum code, the controller may be configured to control the quantum computing device to perform a plurality of physical computation timesteps, including individual joint parity measurements and quasiparticle poisoning detection. The above feature may have the technical effect of constructing a logical qubit from a plurality of physical qubits controlled using joint parity measurements.

[0186]

[0207] According to this embodiment, during a logical computation time step, the controller may be further configured to perform an update operation after a plurality of physical computation time steps. The above feature may have the technical effect of reducing the number of update operations by delaying the update operation until the error condition accumulates over a plurality of physical computation time steps.

[0187]

[0208] According to this embodiment, the controller may be further configured to receive the quantum computation output from the quantum computing device after a number of physical computation time steps. The update operation may include correcting the quantum computation output in the controller based at least in part on the accumulated error state. The above features may have the technical effect of allowing errors by QPP to be corrected by classical computation rather than in the quantum computing device.

[0188]

[0209] According to this embodiment, the update operation may include transmitting instructions to the quantum computer for performing quantum error correction. The controller may be configured to generate instructions based at least partially on the accumulated error state. The above features may have a technical effect of correcting QPP errors in the quantum computer.

[0189]

[0210] According to this embodiment, the instructions may include instructions for performing quantum error correction after the physical calculation time step immediately preceding a non-Clifford logic operation among a plurality of physical calculation time steps. The above feature may have the technical effect of performing quantum error correction immediately before logic operations that do not commute with operations applied to the quantum state by QPP.

[0190]

[0211] According to this embodiment, during each physical computation time step, the controller may be further configured to control the quantum computing device to perform multiple joint parity measurements and corresponding multiple quasiparticle poisoning detections in parallel. The above features may have the technical effect of improving the speed of quantum computation by simultaneously performing joint parity measurements in multiple island-dot systems and further performing multiple QPP detections in those island-dot systems.

[0191]

[0212] According to this embodiment, the controller may be further configured to compute Pauli operator error data, at least in part, based on the error data. The Pauli operator error data may specify the Pauli operator applied to one or more qubits encoded in Majorana islands by a QPP event indicated within the QPP indication. The above features may have the technical effect of tracking Pauli operator errors applied to qubits by QPP events.

[0192]

[0213] According to this embodiment, the cumulative error state may include a sequence of Pauli operators, each associated with a multiple joint parity measurement. The above feature may have the technical effect of tracking Pauli operator errors applied to qubits by QPP events.

[0193]

[0214] According to this embodiment, the QPP indication is an indication of the change in the individual fermion parity of one or more Majorana islands on which joint parity measurements are performed. The above features may have a technical effect of tracking the change in fermion parity.

[0194]

[0215] Another aspect of this disclosure provides a method for use with a computing system including a quantum computer and a controller. The method includes, in the quantum computer, performing a joint parity measurement on two or more Majorana zero modes (MZMs) instantiated in a plurality of Majorana islands contained within the quantum computer. The two or more MZMs are located in one or more Majorana islands. The method further includes performing quasiparticle poisoning (QPP) detection on one or more Majorana islands to generate error data. The error data includes one or more QPP indications associated with one or more Majorana islands. The method further includes, in the controller, receiving the error data from the quantum computer and updating the cumulative error state of one or more Majorana islands based at least in part on the error data. The method further includes performing an update operation based at least in part on the cumulative error state. The above features may have the technical effect of tracking and / or correcting QPP errors occurring during joint parity measurements.

[0195]

[0216] According to this embodiment, the method may further include performing a plurality of physical computation timesteps during a logical computation timestep of a quantum code in a quantum computing device. The physical computation timesteps may include individual joint parity measurements and individual quasiparticle poisoning detections, respectively. The above features may have the technical effect of constructing a logical qubit from a plurality of physical qubits controlled using joint parity measurements.

[0196]

[0217] According to this embodiment, the method may further include, in the controller, performing an update operation during a logical calculation time step after a plurality of physical calculation time steps. The above feature may have the technical effect of reducing the number of update operations by delaying the update operation until the error condition accumulates over a plurality of physical calculation time steps.

[0197]

[0218] In this embodiment, the method may further include, in the controller, receiving the quantum computation output from the quantum computing device after a number of physical computation time steps. When performing an update operation, the method may further include correcting the quantum computation output based at least in part on the accumulated error state. The above features may have the technical effect of enabling the correction of errors by QPP in classical computation rather than in the quantum computing device.

[0198]

[0219] In this embodiment, the method may further include, in a controller, generating instructions for performing quantum error correction based at least partially on the accumulated error state. The method may further include transmitting the instructions to a quantum computing device. In the quantum computing device, the method may further include receiving the instructions. The method may further include performing quantum error correction on one or more Majorana islands based at least partially on the instructions. The above features may have a technical effect of correcting QPP errors in a quantum computing device.

[0199]

[0220] According to this embodiment, quantum error correction may be performed after a physical computation timestep among several physical computation timesteps immediately preceding a non-Clifford logic operation. The above feature may have the technical effect of performing quantum error correction immediately before a logic operation that does not commute with the operation applied to the quantum state by QPP.

[0200]

[0221] In this embodiment, the method may further include calculating Pauli operator error data based at least in part on error data. The Pauli operator error data may specify the Pauli operator applied to one or more qubits encoded in Majorana islands by a QPP event indicated within the QPP indication. The above feature may have the technical effect of tracking Pauli operator errors applied to qubits by QPP events.

[0201]

[0222] According to this embodiment, the cumulative error state may include a sequence of Pauli operators, each associated with a multiple joint parity measurement. The above feature may have the technical effect of tracking Pauli operator errors applied to qubits by QPP events.

[0202]

[0223] According to this embodiment, the QPP indication may be an indication of the change in the individual fermion parity of one or more Majorana islands on which joint parity measurements are performed. The above features may have a technical effect of tracking the change in fermion parity.

[0203]

[0224] In another aspect of this disclosure, a computing system is provided which includes a controller configured to receive error data from a quantum computing device in each of a plurality of physical computation timesteps included in a logical computation timestep of a quantum code. The error data includes a plurality of quasiparticle poisoning (QPP) indications associated with a plurality of individual physical qubits instantiated in the quantum computing device. In each of the physical computation timesteps, the controller is further configured to update the cumulative error state of the plurality of physical qubits based at least in part on the error data. After the plurality of physical computation timesteps, the controller is further configured to perform an update operation based at least in part on the cumulative error state. The above features may have the technical effect of tracking and / or correcting QPP errors occurring during joint parity measurements.

[0204]

[0225] As is clearly stated in the following truth table, when used herein, "and / or" is defined as inclusive or ∨.

[0205] [Table 4]

[0206]

[0226] The configurations and / or methods described herein are essentially illustrative, and numerous modifications are possible; therefore, it should be understood that these particular embodiments or examples should not be considered in an restrictive sense. The specific routines or methods described herein may represent one or more of any number of processing strategies. Thus, the various actions illustrated and / or described may be performed in the order illustrated and / or described, in other orders, simultaneously, or omitted. Similarly, the order of the processes described above can be changed.

[0207]

[0227] The contents of this disclosure include all novel and non-trivial combinations and subcombinations of the various processes, systems, and configurations disclosed herein, as well as other features, functions, actions, and / or characteristics, and any and all equivalents thereof.

Claims

1. A quantum computing device including multiple Majorana islands in which multiple Majorana zero modes (MZMs) are instantiated, It is a controller, Controlling the aforementioned quantum computing device Performing joint parity measurements in two or more of the aforementioned multiple MZMs, wherein the two or more MZMs are located within one or more of the aforementioned multiple Majorana Islands, and Performing quasi-particle poisoning (QPP) detection on one or more Majorana islands and thereby generating error data, wherein the error data includes one or more QPP indications related to one or more Majorana islands. Perform The quantum computing device receives the error data, The cumulative error status of one or more Majorana Islands is updated based at least partially on the aforementioned error data. Perform an update operation based at least partially on the aforementioned cumulative error state. A controller configured in such a way A computing system that includes this.

2. The computing system according to claim 1, wherein during a logical computation timestep of the quantum code, the controller is configured to control the quantum computing device to perform a plurality of physical computation timesteps, including individual joint parity measurements and quasiparticle poisoning detection.

3. The computing system according to claim 2, wherein during the logical computing time step, the controller is further configured to perform the update operation after the plurality of physical computing time steps.

4. The controller is further configured to receive the quantum computation output from the quantum computing device after a plurality of physical computation time steps, The update operation includes correcting the quantum computation output in the controller based at least partially on the accumulated error state. The calculation system according to claim 1.

5. The update operation includes transmitting instructions to the quantum computing device for performing quantum error correction, The controller is configured to generate the instruction based at least partially on the accumulated error state. The calculation system according to claim 3.

6. The computing system according to claim 5, wherein the instruction includes an instruction for performing the quantum error correction after the physical calculation time step immediately preceding the non-Clifford logic operation among the plurality of physical calculation time steps.

7. The computing system according to claim 2, wherein during each of the physical calculation time steps, the controller is further configured to control the quantum computing device to perform a plurality of joint parity measurements and a corresponding plurality of quasiparticle poisoning detections in parallel.

8. Based at least partially on the error data, the controller is further configured to calculate Pauli operator error data. The Pauli operator error data specifies the Pauli operator to be applied to the one or more qubits encoded in the Majorana islands by the QPP event shown in the QPP indication. The calculation system according to claim 1.

9. The calculation system according to claim 8, wherein the cumulative error state includes a sequence of Pauli operators of a plurality of Pauli operators each associated with a plurality of joint parity measurements.

10. The calculation system according to claim 1, wherein the QPP indication is an indication of the change in the individual fermion parity of one or more of the one or more Majorana islands on which the joint parity measurement is performed.

11. A method for use with a computing system including a quantum computing device and controller, In the aforementioned quantum computing device, Performing joint parity measurements in two or more Majorana zero modes (MZMs) instantiated in a plurality of Majorana islands contained within the quantum computing device, wherein the two or more MZMs are located within one or more of the plurality of Majorana islands, and Performing quasi-particle poisoning (QPP) detection on one or more Majorana islands and thereby generating error data, wherein the error data includes one or more QPP indications related to one or more Majorana islands, and In the aforementioned controller, Receiving the error data from the quantum computing device, Updating the cumulative error status of one or more Majorana Islands based at least partially on the aforementioned error data, and Performing an update operation based at least partially on the aforementioned cumulative error state. Methods that include...

12. The method according to claim 11, further comprising, in the quantum computing apparatus, executing a plurality of physical computation time steps during a logical computation time step of a quantum code, wherein each physical computation time step includes individual joint parity measurements and individual quasiparticle poisoning detections, respectively.

13. The method according to claim 12, further comprising, in the controller, performing the update operation during the logical calculation time step after the plurality of physical calculation time steps.

14. In the aforementioned controller, Receiving the quantum computation output from the quantum computing device after multiple physical computation time steps, and When performing the update operation, correct the quantum computation output based at least partially on the accumulated error state. The method according to claim 11, further comprising:

15. In the aforementioned controller, To generate instructions for performing quantum error correction based at least partially on the cumulative error state, and Transmitting the aforementioned instructions to the quantum computing device, In the aforementioned quantum computing device, Receiving the aforementioned command, and Performing quantum error correction on one or more Majorana islands based at least in part on the aforementioned instructions. The method according to claim 13, further comprising:

16. The method according to claim 15, wherein the quantum error correction is performed after the physical calculation time step immediately preceding the non-Clifford logic operation among the plurality of physical calculation time steps.

17. The method according to claim 11, further comprising calculating Pauli operator error data based at least in part on the error data, wherein the Pauli operator error data specifies a Pauli operator to be applied to the one or more qubits encoded in the Majorana islands by a QPP event indicated in the QPP indication.

18. The method according to claim 17, wherein the cumulative error state includes a sequence of Pauli operators of a plurality of Pauli operators each associated with a plurality of joint parity measurements.

19. The method according to claim 11, wherein the QPP indication is an indication of a change in the individual fermion parity of one or more of the one or more Majorana islands on which the joint parity measurement is performed.

20. In each of the multiple physical computation timesteps included in the logical computation timestep of the quantum code, Receiving error data from a quantum computing device, wherein the error data includes a plurality of quasiparticle poisoning (QPP) indications associated with a plurality of individual physical qubits instantiated in the quantum computing device, and Updating the cumulative error state of the plurality of physical qubits based at least partially on the error data, and After the aforementioned multiple physical calculation time steps, perform an update operation based at least partially on the accumulated error state. A controller configured to perform the following actions A computing system that includes this.

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