Composite quantum gate calibration

Abstract

Systems and methods for calibrating composite quantum gates for quantum computing systems are provided. In some embodiments, one method includes accessing a unitary gate model describing the composite quantum gate. The unitary gate model includes a plurality of gate parameters. The method includes implementing the composite quantum gate on a quantum system up to a plurality of gate cycles to amplify the plurality of gate parameters. The method includes obtaining a measurement of the state of the quantum system after implementing the composite quantum gate up to a plurality of gate cycles. The method includes determining at least one of the plurality of gate parameters based at least in part on the measurement of the state of the quantum system. The method includes calibrating the composite quantum gate for a quantum computing system based at least in part on the plurality of gate parameters.

Description

[0001] Priority requirements

[0002] This application claims the benefit of priority to U.S. Provisional Application Serial No. 63 / 002,764 entitled “Composite Quantum Gate Calibration”, filed on March 31, 2020, which is incorporated herein by reference. Technical Field

[0003] This disclosure relates generally to quantum computing systems, and more specifically to calibrating composite quantum gates (e.g., two-qubit quantum gates) in quantum computing systems. Background Technology

[0004] Quantum computing is a computational method that utilizes quantum effects such as superposition and entanglement of ground states to perform certain calculations more efficiently than classical digital computers. In contrast to digital computers that store and manipulate information in the form of bits (e.g., "1" or "0"), quantum computing systems are able to manipulate information using qubits ("qubits"). A qubit can refer to a quantum device that realizes a superposition of multiple states (e.g., data in "0" and "1" states) and / or to a superposition of data itself in multiple states. In conventional terms, a superposition of "0" and "1" states in a quantum system can be represented, for example, as a|0> + b|1>. The "0" and "1" states of a digital computer are analogous to the |0> and |1> ground states of a qubit, respectively. Summary of the Invention

[0005] Aspects and advantages of embodiments of this disclosure will be set forth in part in the description which follows, or may be learned from the description or by practice of the embodiments.

[0006] One example aspect of this disclosure relates to a method for calibrating a quantum computing system for implementing quantum circuits on a quantum system having multiple qubits. The quantum circuits include composite quantum gates. The method includes accessing a unitary gate model describing the composite quantum gate by one or more computing devices. The unitary gate model includes multiple gate parameters. The method includes implementing the composite quantum gate on the quantum system by one or more computing devices up to multiple gate cycles to amplify the multiple gate parameters. The method includes obtaining a measurement of the state of the quantum system by one or more computing devices after implementing the composite quantum gate up to multiple gate cycles. The method includes determining at least one of the multiple gate parameters by one or more computing devices based at least partially on the measurement of the state of the quantum system. The method includes calibrating the composite quantum gate for the quantum computing system by one or more computing devices based at least partially on the multiple gate parameters.

[0007] Other aspects of this disclosure relate to various systems, methods, apparatuses, non-transitory computer-readable media, computer-readable instructions, and computing devices.

[0008] These and other features, aspects, and advantages of the various embodiments of this disclosure will become better understood with reference to the following description and the appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the disclosure and, together with the description, explain the relevant principles. Attached Figure Description

[0009] A detailed discussion of embodiments for those skilled in the art is set forth in the description with reference to the accompanying drawings, in which:

[0010] Figure 1 An example quantum computing system according to an exemplary embodiment of the present disclosure is depicted;

[0011] Figure 2 A flowchart depicting an example method according to an example embodiment of the present disclosure is shown;

[0012] Figure 3 An example circuit representation of a composite quantum gate model according to an exemplary embodiment of the present disclosure is depicted;

[0013] Figure 4 An overview of example scaled-up quantum gate parameters according to exemplary embodiments of the present disclosure is provided;

[0014] Figure 5 A flowchart depicting an example method according to an example embodiment of the present disclosure is shown;

[0015] Figure 6 An example quantum circuit for measuring the phase of a qubit according to an example embodiment of the present disclosure is depicted;

[0016] Figure 7 A representation of a summation function of the phases of the first and second qubits according to an exemplary embodiment of the present disclosure is depicted;

[0017] Figure 8 A flowchart depicting an example method according to an example embodiment of the present disclosure is shown;

[0018] Figure 9 An example quantum circuit for measuring conditional phase according to an example embodiment of the present disclosure is depicted;

[0019] Figure 10 A representation of a function that makes a conditionally phase-dependent condition according to an example embodiment of the present disclosure is described;

[0020] Figure 11 A flowchart depicting an example method according to an example embodiment of the present disclosure is shown;

[0021] Figure 12 An example quantum circuit for obtaining calibration data according to an example embodiment of the present disclosure is depicted;

[0022] Figure 13 A representation of example calibration data according to an example embodiment of the present disclosure is depicted;

[0023] Figure 14 An example oscillation frequency function according to an example embodiment of the present disclosure is described;

[0024] Figure 15 A flowchart depicting an example method according to an example embodiment of the present disclosure is shown;

[0025] Figure 16 An example quantum circuit for obtaining calibration data according to an example embodiment of the present disclosure is depicted;

[0026] Figure 17 An example quantum circuit for obtaining calibration data according to an example embodiment of the present disclosure is depicted;

[0027] Figure 18 A representation of a summation function of the phases of the first and second qubits according to an exemplary embodiment of the present disclosure is depicted;

[0028] Figure 19 A representation of a function that makes a conditionally phase-dependent condition according to an example embodiment of the present disclosure is described;

[0029] Figure 20 An example quantum gate for modeling parasitic interactions between qubits in a quantum circuit according to an exemplary embodiment of the present disclosure is depicted; and

[0030] Figure 21 An example computing system according to an example embodiment of the present disclosure is described. Detailed Implementation

[0031] An exemplary aspect of this disclosure relates to systems and methods for calibrating composite quantum gates (e.g., two-qubit quantum gates) in quantum computing systems. A quantum gate is a building block of quantum circuits implemented by a quantum computing system for quantum computing. Composite quantum gates operate on more than one qubit (e.g., two qubits, three qubits). The operation of a quantum computer requires the characterization and calibration of experimentally achievable quantum gates. Robust and efficient quantum gate characterization provides information about the implemented quantum gate, which can then be used for subsequent quantum control calibration in the quantum computing system. Quantum control calibration can include, for example, calibration of control pulses to implement the quantum gate on a quantum system with multiple qubits. Quantum gate characterization and calibration are useful for achieving high-fidelity quantum computing and large-scale deployment.

[0032] The robustness of a quantum gate calibration protocol can be measured by its ability to extract true quantum gate parameters with high accuracy against other compounding defects such as errors in quantum state preparation and measurement. The efficiency of a calibration protocol can be measured by the total physical runtime used to achieve a given level of accuracy. A criterion for improved efficiency of a calibration protocol is achieved when the variance of the characteristic parameters scales inversely with the amount of time required to implement the calibration protocol (e.g., physical runtime).

[0033] Existing methods and systems for efficient quantum gate characterization have been provided for single-qubit quantum gates. However, both single-qubit and composite quantum gates are desirable for realizing universal quantum computing. Furthermore, unwanted qubit-to-qubit interactions caused by control errors such as crosstalk and environmental defects can also take the form of composite gates. Therefore, robust and efficient composite gate characterization and calibration can be expected towards realizing universal quantum computing and towards learning and reducing errors.

[0034] An exemplary aspect of this disclosure provides a calibration protocol for characterizing and calibrating composite quantum gates (e.g., any two-qubit quantum gate). In some embodiments, the calibration protocol has access to a model capable of representing arbitrary unary operations. The parameters of this model can be learned using the techniques described in the calibration protocol according to an exemplary aspect of this disclosure. During the calibration protocol, quantum gates can be repeatedly applied in a cyclic manner up to multiple gate cycles before obtaining measurements of the state of the quantum system. This allows for coherent amplification of quantum gate parameters without requiring quantum entanglement. The amplification of quantum gate parameters according to an exemplary aspect of this disclosure allows for more efficient determination of quantum gate parameters for composite quantum gates (e.g., two-qubit quantum gates).

[0035] For example, in some embodiments, the example calibration method can include performing multiple measurement instances on the quantum system. Each measurement instance can be associated with implementing up to k gate cycles of the quantum gate. k can also be referred to as the "amplification factor". Measurement instances can be associated with different values ​​of k. For example, a first measurement instance can be associated with two cycles of implementing the quantum gate before obtaining a measurement result of the state of the quantum system. A second measurement instance can be associated with four cycles of implementing the quantum gate before obtaining a measurement result of the state of the quantum system. A third measurement instance can be associated with sixteen cycles of implementing the quantum gate before obtaining a measurement result of the state of the quantum system, and so on. In some embodiments, multiple measurement instances can be associated with the same amplification factor. For example, multiple measurement results can be associated with an amplification factor k. Each measurement result can be obtained after implementing up to k gate cycles of the quantum gate.

[0036] Implementing a repetitive gate loop in a quantum gate amplifies the gate parameters. Measurements of the state of the quantum system obtained for each measurement instance can be used to determine the parameters of a model describing a composite quantum gate according to an exemplary embodiment of this disclosure. Once the parameters are known, the composite quantum gate can be calibrated for use in quantum operations and / or to reduce errors.

[0037] The exemplary aspects of this disclosure provide numerous technical effects and benefits. For example, calibration protocols according to the exemplary aspects of this disclosure can determine composite quantum gate parameters with an accuracy of about 1% or better, suppressing control errors below those from other error sources (e.g., decoherence). In some embodiments, the calibration protocols can achieve improved efficiency in quantum parameter estimation. In some cases, the efficiency can approach the Heisenberg limit, where the accuracy of the estimation increases quadratically (e.g., variance decreases) faster than certain classical parameter estimation methods (e.g., using classical processing algorithms). The efficiency produced by the calibration protocols according to the exemplary aspects of this disclosure can approach the Heisenberg limit without using entanglement. Considering the difficulty of generating large-scale entanglement using noisy intermediate-scale quantum computers, the methods and systems for calibrating composite quantum gates according to the exemplary aspects of this disclosure offer unique advantages for characterizing and calibrating quantum computing systems.

[0038] Example embodiments of this disclosure will now be discussed in further detail with reference to the accompanying drawings. As used herein, the term "about" in conjunction with values ​​refers to values ​​within 20%.

[0039] Figure 1An example quantum computing system 100 is depicted. Example system 100 is an example of a system on one or more classical computers or quantum computing devices at one or more locations, wherein the systems, components, and techniques described below can be implemented. Those skilled in the art who use the disclosure provided herein will understand that other quantum computing structures or systems can be used without departing from the scope of this disclosure.

[0040] System 100 includes quantum hardware 102 that communicates data with one or more classical processors 104. Quantum hardware 102 includes components for performing quantum computing. For example, quantum hardware 102 includes a quantum system 110, a control device 112, and a readout device 114 (e.g., a readout resonator). Quantum system 110 can include one or more multi-level quantum subsystems, such as registers of qubits. In some embodiments, the multi-level quantum subsystem can include superconducting qubits, such as flux qubits, charge qubits, transmon qubits, gmon qubits, etc.

[0041] The type of multilevel quantum system utilized by system 100 can vary. For example, in some cases, it may be convenient to include one or more readout devices 114 attached to one or more superconducting qubits (e.g., transmon, flux, gmon, xmon, or other qubits). In other cases, ion traps, photonic devices, or superconducting cavities can be used (e.g., they can be used to prepare states without requiring qubits). Other examples of realizing multilevel quantum systems include fluxmon qubits, silicon quantum dots, or phosphorus-impurity qubits.

[0042] Quantum circuits can be constructed and applied to registers of qubits included in quantum system 110 via multiple control lines coupled to one or more control devices 112. Example control devices 112 operating on the qubit registers can be used to implement quantum gates or quantum circuits having multiple quantum gates (e.g., Pauli gates, Hadamard gates, controlled-NOT (CNOT) gates, controlled-phase gates, T-gates, multi-qubit quantum gates, coupler quantum gates, etc.). One or more control devices 112 can be configured to operate on quantum system 110 via one or more corresponding control parameters (e.g., one or more physical control parameters). For example, in some embodiments, the multi-level quantum subsystem may be superconducting qubits, and control devices 112 may be configured to provide control pulses to the control lines to generate magnetic fields to adjust the frequency of the qubits.

[0043] Quantum hardware 102 may further include a readout device 114 (e.g., a readout resonator). Measurement results 108 obtained via the measurement device can be provided to classical processor 104 for processing and analysis. In some embodiments, quantum hardware 102 may include quantum circuitry, and control device 112 and readout device 114 may implement one or more quantum logic gates operating on quantum system 102 via physical control parameters (e.g., microwave pulses), which are transmitted via lines included in quantum hardware 102. Other examples of control devices include arbitrary waveform generators, where a DAC (digital-to-analog converter) generates the signal.

[0044] Readout device 114 can be configured to perform quantum measurements on quantum system 110 and send the measurement result 108 to classical processor 104. Furthermore, quantum hardware 102 can be configured to receive data from classical processor 104 specifying physical control qubit parameter values ​​106. Quantum hardware 102 can use the received physical control qubit parameter values ​​106 to update the actions of control device 112 and readout device 114 on quantum system 110. For example, quantum hardware 102 can receive data specifying new values ​​representing the voltage strength of one or more DACs included in control device 112, and can update the actions of the DACs on quantum system 110 accordingly. Classical processor 104 can be configured, for example, to initialize quantum system 110 in an initial quantum state by sending data specifying an initial parameter set 106 to quantum hardware 102.

[0045] The readout device 114 can measure the state of an element (e.g., a qubit) by utilizing the impedance difference between the |0> and |1> states of an element (e.g., a qubit). For example, the resonant frequency of the readout resonator can take different values ​​when the qubit is in state |0> or state |1> due to the nonlinearity of the qubit. Therefore, the microwave pulse reflected from the readout device 114 carries a load that depends on the amplitude and phase shift of the qubit state. In some embodiments, a Purcell filter can be used in conjunction with the readout device 114 to block microwave propagation at the qubit frequency.

[0046] Figure 2 A flowchart depicts an example method (200) for calibrating parameters of a composite quantum gate (e.g., a two-qubit quantum gate) according to an example embodiment of this disclosure. The method (200) can be used with any suitable system (such as...). Figure 1 The system 100 shown in the figure or Figure 21 The system 1000 shown in the figure is used to implement this. Figure 2The steps are described in a specific order for illustrative and discussion purposes. Using the disclosure provided herein, those skilled in the art will understand that the individual steps of any method described herein can be adapted, extended, omitted, rearranged, included (including steps not shown), performed concurrently, and / or modified in various ways without departing from the scope of this disclosure.

[0047] In (202), the method includes accessing a unitary gate model. This unitary gate model is capable of describing composite quantum gates (e.g., two-qubit quantum gates). The unitary gate model can include multiple gate parameters. More specifically, in some embodiments, the model is capable of describing composite quantum gates as unitary fermion analog gates Ui. FSIM U FSIM A gate can include five gate parameters, including the first gate parameter ψ, the second gate parameter Φ, the third gate parameter φ, and so on. The fourth gate parameter θ and the fifth gate parameter χ. FSIM The definition of a door is explained below:

[0048]

[0049] Control parameter S A and S B This is achieved by implementing a single-qubit Z-gate (Pauli Z-gate) before the composite quantum gate. The Z-gate can have a matrix representation of the following form:

[0050]

[0051] This disclosure provides various aspects of calibration protocols for learning five parameters: χ, θ, and Φ and ψ enable any composite quantum gate to be learned precisely and derived from the corresponding U. FSIM It is represented by a door model.

[0052] In some embodiments, U represents a two-qubit quantum gate. FSIM Doors can be modeled as Figure 3 The set of quantum gates 220 is shown in the figure. More specifically, U FSIM The gates can be modeled as a first Z-rotation angle gate 222 for the first qubit q0, a second Z-rotation angle gate 224 for the second qubit q1, an iSWAP gate 226 for the first qubit q0 and the second qubit q1, and a controlled phase gate 228 for the first qubit q0 and the second qubit q1. The first Z-rotation angle gate 222 can be used for angle α0. The second Z-rotation angle gate 224 can be used for α1. In some embodiments, the third gate parameter... It can be defined as follows:

[0053]

[0054] iSWAP gate 226 can be used for angle θ. Controlled phase gate 228 can be used for angle Φ.

[0055] Return to reference Figure 2 The method (200) can include repeatedly composing quantum gates up to multiple gate cycles to amplify the gate parameters. More specifically, the method can include implementing multiple measurement instances. For each measurement instance, the method can include repeating the quantum gates up to k cycles. The number k can also be referred to as an amplification factor. The method can then obtain a measurement result of the state of the quantum system (e.g., multiple qubits in the quantum system). The data associated with this measurement result can be stored, for example as a record, in one or more memory devices for use in learning the gate parameters, as detailed below. The method can then implement other measurement instances. These measurement instances can include different numbers of gate cycles k (e.g., can be associated with different amplification factors) for repeating the quantum gates before obtaining the measurement result. The data associated with this measurement result can be stored, for example as a record, in one or more memory devices for use in learning the gate parameters, as detailed below.

[0056] This amplification of the gate parameters is expressed as Figure 2 (204), (206), and (208). More specifically, in (204), the method can include implementing a composite quantum gate up to a plurality of gate loops k. k can be any suitable number, such as 1, 2, 3, 4, 5, 6, 7, 16, 32, 64, etc. k can also be referred to as a magnification factor for the measurement instance. Example values ​​of k are provided for illustrative and discussion purposes. Using the disclosure provided herein, those skilled in the art will understand that any value of k can be used without departing from the scope of this disclosure.

[0057] In (206), the method is capable of including measurements of the state of a quantum system. More specifically, the method is capable of including obtaining the states of multiple qubits (e.g., a first qubit and a second qubit) after implementing a composite quantum gate for k gate cycles. The measurements can be stored as records in one or more storage devices for use in determining gate parameters according to examples of this disclosure. In some embodiments, the method is also capable of including performing multiple measurement instances for the same value of k. In this way, multiple measurements of the quantum state can be obtained for the same amplification factor.

[0058] In (208), the method can include determining whether to repeat (204) and (206) for different values ​​of k (e.g., to perform another measurement instance). If so, the method can return (204) to implement the composite quantum gate through multiple gate cycles k and obtain the measurement result (206) of the state of the quantum system. The process can continue until it is determined in (208) that no more measurement instances are needed.

[0059] Figure 4 An overview of implementing multiple measurement instances according to exemplary embodiments of the present disclosure is provided, wherein each measurement instance is associated with a different number of gate cycles k of amplification gate parameters. For example, a first measurement instance 230 may be associated with a gate cycle k value of 1. The first measurement instance 230 may include, for example, a preparation phase 232. The preparation phase 232 may include implementing one or more quantum gates and / or control pulses to prepare qubits in the quantum system for calibration. The first measurement instance 230 may include a gate cycle phase 234 implementing a composite quantum gate up to k gate cycles (such as a single gate cycle). The first measurement instance 230 includes a readout phase 236. The readout phase 236 may implement one or more quantum gates and / or control pulses to prepare qubits in the quantum system for measurement. The first measurement instance 230 may ultimately include a measurement result 238, wherein the state of the qubits in the quantum system is measured.

[0060] The second measurement instance 240 can be associated with a gate cycle value of 2k. The second measurement instance 240 can include, for example, a preparation phase 242. The preparation phase 242 can include implementing one or more quantum gates and / or control pulses to prepare the qubits in the quantum system for calibration. The second measurement instance 240 can include a gate cycle phase 244 that implements a composite quantum gate up to k gate cycles (such as two gate cycles). The second measurement instance 240 includes a readout phase 246. The readout phase 246 can implement one or more quantum gates and / or control pulses to prepare the qubits in the quantum system for measurement. The second measurement instance 240 can ultimately include a measurement result 248, in which the state of the qubits in the measured quantum system is determined.

[0061] The third measurement instance 250 can be associated with a gate cycle value of 3 k. The third measurement instance 250 can include, for example, a preparation phase 252. The preparation phase 252 can include implementing one or more quantum gates and / or control pulses to prepare the qubits in the quantum system for calibration. The third measurement instance 250 can include a gate cycle phase 254 implementing composite quantum gates up to k gate cycles (such as three gate cycles). The third measurement instance 250 includes a readout phase 256. The readout phase 256 can implement one or more quantum gates and / or control pulses to prepare the qubits in the quantum system for measurement. The third measurement instance 250 can ultimately include a measurement result 258, in which the state of the qubits in the quantum system is measured.

[0062] The fourth measurement instance 260 can be associated with a gate cycle value of 4 k. The fourth measurement instance 260 can include, for example, a preparation phase 262. The preparation phase 262 can include implementing one or more quantum gates and / or control pulses to prepare the qubits in the quantum system for calibration. The fourth measurement instance 260 can include a gate cycle phase 264 that implements composite quantum gates up to k gate cycles (such as four gate cycles). The fourth measurement instance 260 includes a readout phase 266. The readout phase 266 can implement one or more quantum gates and / or control pulses to prepare the qubits in the quantum system for measurement. The fourth measurement instance 260 can ultimately include a measurement result 268, in which the state of the qubits in the quantum system is measured.

[0063] Figure 4 Four measurement examples are depicted for illustrative and discussion purposes. Those skilled in the art will understand, using the disclosure provided herein, that any number of measurement examples can be included without departing from the scope of this disclosure. Furthermore, the value of k can be varied in any suitable manner for different measurement examples. As will be discussed in detail below, in some embodiments, the number of gate loops k used for the measurement example increases exponentially relative to the number of gate loops used for previous measurement examples.

[0064] Return to reference Figure 2 The method can then determine multiple gate parameters (210) based on the obtained measurement results, as will be described in detail below. In (212), the method can include calibrating composite quantum gates in a quantum computing system based on the gate parameters. For example, it is possible to adjust and / or control the control pulses and / or other control parameters used to implement composite quantum gates in a quantum computing system to achieve a more accurate implementation of the quantum gates and / or reduce errors.

[0065] Figure 5 A flowchart depicts an example method (300) for determining a first gate parameter ψ according to an example embodiment of this disclosure. The method (300) can be used with any suitable system (such as...). Figure 1 The system 100 shown in the figure or Figure 21 The system 1000 shown in the figure is used to implement this. Figure 5 The steps are described in a specific order for illustrative and discussion purposes. Using the disclosure provided herein, those skilled in the art will understand that the various steps of any method described herein can be adapted, extended, omitted, rearranged, included as steps not shown, performed concurrently, and / or modified in various ways without departing from the scope of this disclosure.

[0066] In (302), the method can include determining the first phase of the first qubit in the quantum system according to k, where k is the number of gate cycles used to amplify the first gate parameter ψ. Figure 6 A circuit diagram of an example quantum circuit 310, according to an exemplary embodiment of the present disclosure, for determining the first phase of a first qubit q0 based on a composite quantum gate with k gate cycles, is depicted. The quantum circuit 310 implements a Y / 2 Pauli gate 312 to apply a rotation to the first qubit q0. For each measurement instance, the quantum circuit 310 implements a composite quantum gate 314 up to k gate cycles (where k is different for each measurement instance). The quantum circuit 310 then implements a -Y / 2 or X / 2 Pauli gate 316 to apply a rotation to the first qubit q0. The quantum circuit 310 then obtains a measurement result 318 of the state of the first qubit q0. By applying rotations at the beginning and end of the sequence, the phase of the first qubit q0 can be determined by tomographic imaging. For example, a final rotation angle of -Y / 2 (or X / 2) allows... <x>(or in the case of X / 2 rotation) <y>The measurement results of complex numbers. <x> +i <y>This represents the projection of the qubit state onto the XY plane. <x> +i <y>The phase of q is the phase of the first quantum bit q0.

[0067] In (304), the method can include determining the second phase of the second qubit in the quantum system according to k, where k is the number of gate cycles used to amplify the first gate parameter ψ. Figure 6 A circuit diagram of an example quantum circuit 320, according to an exemplary embodiment of the present disclosure, for determining the second phase of a second qubit q0 based on a composite quantum gate with k gate cycles is depicted. The quantum circuit 320 implements a Y / 2 Pauli gate 322 to apply a rotation to the second qubit q1. For each measurement instance, the quantum circuit 320 implements a composite quantum gate 314 up to k gate cycles (where k is different for each measurement instance). The quantum circuit 320 then implements a -Y / 2 or X / 2 Pauli gate 326 to apply a rotation to the second qubit q1. The quantum circuit 320 then obtains a measurement result 328 of the state of the second qubit q1. By applying rotations at the beginning and end of the sequence, the phase of the second qubit q1 can be determined by tomographic imaging. For example, the final rotation angle of -Y / 2 (or X / 2) allows... <x>(or in the case of X / 2 rotation) <y>The measurement results of complex numbers. <x> +i <y>This represents the projection of the qubit state onto the XY plane. <x> +i <y>The phase of q1 is the phase of the second quantum bit q1.

[0068] exist Figure 5 In (306), the method can include determining a function that makes the sum of the first phase and the second phase related to k. For example, Figure 7 A graphical representation of an example function 330 is depicted that associates the sum of the first and second phases with k. Figure 7 Plot the number of gate loops along the horizontal axis and the sum of the first and second phases along the vertical axis. Each point 332 represents the sum of the first and second phases for a certain value of k. As shown, function 330 can be represented by (e.g., using any suitable fitting technique) a roughly linear function 334 fitted to point 332.

[0069] In (308), the method is capable of determining a first gate parameter ψ based at least in part on properties associated with a function that correlates the sum of the first and second phases with k. In some embodiments, the first gate parameter ψ is determined as the slope of the function. (See reference...) Figure 7 The first gate parameter ψ is determined to be the slope of a roughly linear function 334 336.

[0070] Figure 8 A flowchart depicts an example method (400) for determining a second gate parameter Φ according to an example embodiment of this disclosure. The method (400) can be used with any suitable system (such as...). Figure 1 The system 100 shown in the figure or Figure 21 The system 1000 shown in the figure is used to implement this. Figure 8 The steps are described in a specific order for illustrative and discussion purposes. Using the disclosure provided herein, those skilled in the art will understand that the various steps of any method described herein can be adapted, extended, omitted, rearranged, included as steps not shown, performed concurrently, and / or modified in various ways without departing from the scope of this disclosure.

[0071] In (402), the method can include setting a qubit to an excited state, such as the |1> state. For example, the method can include setting a first qubit q0 to an excited state, such as the |1> state. In (404), the method can include determining a conditional phase for each second qubit according to k, where k is the number of gate cycles used to amplify the second gate parameter Φ. Setting the first qubit q0 to an excited state changes the phase of the second qubit q1. The difference between the phases of the qubits when the first qubit is set between the |0> state and the |1> state is the conditional phase.

[0072] Figure 9 A circuit diagram of an example quantum circuit 410 for determining the conditions of a second qubit q0 based on a composite quantum gate with k gate cycles, according to an exemplary embodiment of the present disclosure, is depicted. As shown, a first qubit is set to an excited state |1>. Quantum circuit 410 implements a Y / 2 Pauli gate 412 to apply a rotation to the second qubit q1. For each measurement instance, quantum circuit 410 implements k gate cycles of a composite quantum gate 414 (where k is different for each measurement instance). Quantum circuit 410 then implements a -Y / 2 or X / 2 Pauli gate 416 to apply a rotation to the second qubit q1. Quantum circuit 320 then obtains a measurement result 418 of the state of the second qubit q1. By applying rotations at the beginning and end of the sequence, the phase of the second qubit q1 can be determined by tomographic imaging. The difference in phase when the first qubit q0 is set to an excited state is the conditional phase.

[0073] For illustrative and discussion purposes, the discussion will refer to setting the first qubit to an excited state and determining the conditional phase of the second qubit. Figure 8 and Figure 9 Using the disclosure provided herein, those skilled in the art will understand that the method can include setting the second qubit to an excited state and determining the conditional phase of the first qubit without departing from the scope of this disclosure.

[0074] exist Figure 8 In (406), the method can include determining a function that makes the conditional phase dependent on k. For example, Figure 10 A graphical representation of an example function 420 that makes the conditional phase dependent on k is depicted. Figure 10 Plot the number of gate loops along the horizontal axis and the conditional phase along the vertical axis. Each point 422 represents the conditional phase for a certain value of k. As shown, function 420 can be represented by (e.g., using any suitable fitting technique) a roughly linear function 4244 fitted to point 422.

[0075] In (408), the method can include determining a second gate parameter Φ based at least in part on properties associated with a function that makes the conditional phase related to k. In some embodiments, the second gate parameter Φ is determined as the slope of the function. (See reference...) Figure 10 The second gate parameter Φ is determined to be the slope of a roughly linear function 424 426.

[0076] Figure 11 An example embodiment of the present disclosure is described for determining a third gate parameter. A flowchart of the example method (500) with the fourth parameter θ. Method (500) can be used with any suitable system (such as... Figure 1 The system 100 shown in the figure or Figure 21 The system 1000 shown in the figure is used to implement this. Figure 11 The steps are described in a specific order for illustrative and discussion purposes. Using the disclosure provided herein, those skilled in the art will understand that the various steps of any method described herein can be adapted, extended, omitted, rearranged, included as steps not shown, performed concurrently, and / or modified in various ways without departing from the scope of this disclosure.

[0077] In (502), the method can include obtaining calibration data. The calibration data can be obtained by implementing... Figure 12 The quantum circuit 520 depicted is used to obtain this. More specifically, the quantum circuit 520 can realize the Z-rotation angle β in the first qubit q0 using a Z(β)Pauli gate 522. For each measurement instance, the quantum circuit 520 implements a composite quantum gate 524 up to k gate cycles (where k is different for each measurement instance). As shown, the composite quantum gate 524 can be written as a first Z-rotation angle gate for the first qubit q0, a second Z-rotation angle gate for the second qubit q1, an iSWAP gate for the first qubit q0 and the second qubit q1, and a controlled phase gate for the first qubit q0 and the second qubit q1. The first Z-rotation angle gate 222 can be used for angle α0. The second Z-rotation angle gate 224 can be used for α1. In some embodiments, the third gate parameter... It can be defined as follows:

[0078]

[0079] Then, the quantum circuit 520 obtains a measurement result 528 of the state of the first qubit q0. The calibration data can include data indicating the state of the qubit (e.g., a population of qubits) using measurements obtained for different values ​​of β and k.

[0080] Figure 13 Depicting the use Figure 12 Example calibration data 530 was obtained from the quantum circuit 520. Calibration data 530 represents the population of qubits as a function of both the rotation angle β and the number of gate cycles k. Calibration data 530 in... Figure 13 The data is represented as an image. This image includes pixel values ​​representing a group for each β / π and k. The calibration data 530 can be stored or accessed in any suitable format (e.g., table, function, record, list) without departing from the scope of this disclosure.

[0081] exist Figure 11 (504) This method includes fitting calibration data (e.g., calibration data 530) using an oscillation frequency function. More specifically, each column of data (e.g., for each β / π) can be fitted to an oscillation frequency function that correlates the oscillation frequency with the z-rotation angle β and k. An example oscillation frequency function is defined as:

[0082] βββ / π=IA*sin(ωk) 2

[0083] Where ω is the oscillation frequency.

[0084] Figure 14 A graphical representation of the example oscillation frequency function 540 generated from calibration data 530 is depicted. Figure 14 Plot the curves of the z-rotation angle (β / π) along the horizontal axis and the oscillation frequency ω along the vertical axis.

[0085] In (508), the method includes determining the third gate parameter based on a first characteristic of the oscillation frequency function. For example, the x-offset based on the local minimum of the oscillation frequency function (e.g., Figure 14 The third gate parameters are determined by the x-offset of 544 from the local minimum 542 in the local minimum. In some embodiments, It can be correlated with or equal to the x-offset of the local minimum of the oscillation frequency function.

[0086] exist Figure 11 (510) This method includes determining the fourth gate parameter θ based on a second characteristic of the oscillation frequency function. For example, it is possible to determine the y-offset based on the local minimum of the oscillation frequency function (e.g., Figure 14 The fourth gate parameter θ is determined by the y-offset 546 of the local minimum 542 in the oscillation frequency function. In some embodiments, θ / 2 can be associated with or equal to the y-offset of the local minimum of the oscillation frequency function.

[0087] Figure 15 A flowchart depicts an example method (600) for determining the fifth gate parameter χ according to an example embodiment of the present disclosure. This method (600) can be used with any suitable system (such as...). Figure 1 The system 100 shown in the figure or Figure 21 The system 1000 shown in the figure is used to implement this. Figure 11 The steps are described in a specific order for illustrative and discussion purposes. Those skilled in the art who use the disclosure provided herein will understand that the various steps of any method described herein can be adapted, extended, omitted, rearranged, included as steps not shown, performed concurrently, and / or modified in various ways without departing from the scope of this disclosure.

[0088] In (602), the method can include similar components as described above. Figure 11 The calibration data is obtained in (502), however, the z-rotation angle at the beginning of the quantum circuit can remain constant, making It is equal to a fixed value, such as π / 2, where β is a fixed rotation angle. This allows for the utilization of... Figure 16 The quantum circuit 610 shown in the figure is used to implement this. The quantum circuit 610 implements a fixed Z rotation Zφ, followed by k gate cycles of the composite quantum gate 612 (where k is different for each measurement instance). The rotation angle is determined such that... It is equal to a fixed value, such as π / 2, where β is a fixed rotation angle. The X Pauli gate 614 can be applied to the second qubit q1. The quantum circuit 610 obtains the measurement result 616 of the state of the first qubit q0.

[0089] In (604), the method is capable of including determining a first probability P based on the measurement results. 10 Second probability P 00 First probability P 10 The probability that the states of the first and second qubits in a quantum system are |1>|0> (e.g., in different states) is represented by the second probability P. 00 It can represent the probability that the states of the first and second qubits in a quantum system are |0> (e.g., in the same state).

[0090] In (606), the method can include determining the fifth gate parameter χ based on the first probability, the second probability, and the previously determined gate parameters. For example, the fifth gate parameter χ can be determined using the following relationship:

[0091] P 01 -P 00 ∝sin[dΨ-χ]

[0092] Given the previously determined first gate parameter ψ and third gate parameter Given the value of the fourth parameter θ, this method can use the above relationship to invert and obtain the fifth parameter χ.

[0093] Figure 17 Another example quantum circuit 620 capable of determining the fifth gate parameter χ is depicted. Quantum circuit 620 achieves a fixed Z-rotation Z-axis. f This is followed by k gate cycles of a composite quantum gate 622 (where k is different for each measurement instance). The rotation angle f is determined as... A fixed rotation angle. An X Pauli gate 614 can be applied to the second qubit q1 in each gate cycle. A Y / 2 Pauli gate 626 can be applied to the first qubit q0 in each gate cycle. The quantum circuit 620 obtains a measurement result 628 of the state of the first qubit q0. It can be based on... Figure 15 (604) and (606) are used to process the calibration data obtained using circuit 620 to determine the fifth gate parameter χ.

[0094] Variations and modifications can be made to the exemplary embodiments of this disclosure. For example, in some embodiments, modifications are made to improve the efficiency of the calibration protocol. In some embodiments, modifications can produce efficiencies close to the Heisenberg limit (as defined above).

[0095] For example, when the number of measurements repeated in each iteration is much smaller than the maximum number of repetitions, efficiency close to the Heisenberg limit can be achieved. However, within this limit, aliasing in periodic calibration can also pose a challenge. This is because the measurements can be periodic functions of the gate parameters. If the amplification factor (e.g., the number of gate loops) increases exponentially, the number of possible solutions also increases exponentially. A next-step estimation process, explicitly dependent on the estimation of previous steps, as outlined below, can resolve this aliasing problem, improving the efficiency of the calibration protocol and allowing it to approach the Heisenberg limit.

[0096] In some embodiments, the calibration protocol can increase the number of gate loops k for each measurement instance exponentially. For example, the number of gate loops k for a measurement instance can increase exponentially relative to the number of gate loops used for previous measurement instances. As an example, the value of k can be increased to 2, 4, 8, 16, 32, 64, etc.

[0097] For example, Figure 18 A graphical representation of an example function 710 is depicted, which relates the sum of the first phase of the first qubit and the second phase of the second qubit to an exponentially increasing k. Figure 18 Plot the number of gate loops along the horizontal axis and the sum of the first and second phases along the vertical axis. Each point 712 represents the sum of the first and second phases for a given value of k, which increases exponentially. See the above for reference. Figure 5-7 The first gate parameter ψ is determined from point 712.

[0098] As another example, Figure 19 A graphical representation of an example function 720 is depicted that associates the conditional phase of a qubit with an exponentially increasing k. Figure 19 Plot the number of gate loops along the horizontal axis and the conditional phase along the vertical axis. Each point 722 represents the conditional phase for a certain value of k, which increases exponentially. This can be seen from the reference above. Figure 8-10 The point 722 discussed determines the second gate parameter Φ.

[0099] In some embodiments, to improve efficiency, the calibration protocol can apply recursive updates to infer the parameters for each measurement instance, reducing aliasing in the periodic functional dependencies of the gate parameters and measurement results. For example, at each new measurement instance, the parameter estimate for the measurement instance can be chosen to be within the uncertainty range given by the periodicity of previous measurement instances. For trigonometric functions, since the periodicity is typically n*π / k for the gate cycle k and integer n, the uncertainty range can be scaled to O(1 / k).

[0100] As an example, the following method demonstrates how to determine the third gate parameter. And this technique with the fourth parameter θ. First, according to k=2 for i={0,1,...d} i A gated loop is set for the exponentially increasing amplification factor k, where d is the number of different amplification factors. Estimates are obtained for α0-α1 and θ. For each amplification factor, repeated measurement instances M are performed. i Next, of which:

[0101] M i =a(2 k -i)+b

[0102] Where a and b are constants.

[0103] The probability of the quantum state of the first and second qubits changing from 0>|0> to 0>|1> depends on the third gate parameter. And the fourth parameter θ, as follows:

[0104]

[0105] use The inversion is performed using a rough estimate of θ to update Ω, which in turn depends on the following parameters:

[0106]

[0107] This allows for repetition with different β' to obtain new estimates of Ω(β'). Third and fourth gate parameters And θ can be updated using the following formula:

[0108]

[0109]

[0110] The dataset of measurement instances associated with previous iterations can be used to estimate Ω(β) and Ω(β') to the highest accuracy. Similar calculations can be performed with respect to θ, except for the final estimation using Ω(β) and Ω(β'). The final estimate.

[0111] In some embodiments, calibration protocols according to exemplary aspects of this disclosure can be used to estimate gate parameters of parasitic interactions among multiple qubits in a quantum system. For example, Figure 20 An example quantum circuit 800 implemented on four qubits q0, q1, q2, and q3 is depicted. In this example, the quantum circuit 800 can include a Z-rotation gate 802 on the first qubit q0 and a Z-rotation gate 804 on the second qubit q1. The quantum circuit 800 can include iSWAP gates on the first qubit q0 and the second qubit q1. The quantum circuit 800 can include iSWAP gates on the third qubit q2 and the fourth qubit q3. The quantum circuit 800 can generate, for example, parasitic qubit-to-qubit interactions between the second qubit q1 and the third qubit q2. This parasitic interaction can be modeled as a unitary gate U. FSIM 820. The parameters of this gate can be determined according to the exemplary aspects of this disclosure. In this way, the calibration protocol according to the exemplary aspects of this disclosure can be used to determine the characteristics of parasitic interactions in qubits and / or reduce errors attributable to such parasitic interactions during the implementation of quantum circuits.

[0112] For purposes of illustration and discussion, aspects of this disclosure have been discussed with reference to the calibration of two-qubit composite gates. As shown below, the calibration protocol according to exemplary embodiments of this disclosure can be used to calibrate any higher-order composite gate (e.g., three-qubit composite gates, etc.).

[0113] Number-conserving two-qubit gates (generalized fSim gates) take the following form in the basis |00>, |01>, |10>, |11>:

[0114]

[0115] Where 0 ≤ θ ≤ π / 2 is the iSWAP angle, φ is the controlled phase angle, and δ, χ, γ are single-qubit phase factors. Single-qubit rotation on two qubits can be expressed as...

[0116]

[0117] Where ~ indicates equivalence up to the overall phase, And η = (ζ0 - ζ1) / 2.

[0118] The generalized fSim gate (1) can be decomposed into

[0119] G fSim (θ, δ, χ, γ, φ)~R z (-γ,-γ)R z (β,-β)fSim(θ,φ)R z (α,-α), (3)

[0120] Among them, α=(δ+χ) / 2, β=(δ+χ) / 2 and fSim(θ,φ)=G fSim (θ, 0, 0, φ) is a standard fSim gate. It is formed by a G... fSim The loop consisting of two single-qubit Z-rotations added to the gate is written as:

[0121]

[0122] This leads to the following transformation rules for the parameters,

[0123]

[0124] In this context, the capped Greek letters represent the parameters of the gate.

[0125] As described herein, one example method for robustly and accurately calibrating quantum gates according to exemplary embodiments of this disclosure is by repeating them multiple times (e.g., up to multiple gate cycles). The coherent amplification of the gate's eigenvalues ​​allows one to measure them up to the Heisenberg limit. Because the eigenvalues ​​are amplified, it is also more robust to state preparation and measurement errors.

[0126] The nth product of the generalized fSim gate is written as

[0127] G fSim (θ, δ, χ, γ, φ) n =diag(1,e) -inγ u(θ, δ, χ) n e -in(2γ+φ) (6)

[0128] Where u is a 2×2 matrix

[0129]

[0130] It is possible to analytically solve for the nth power of u using Pauli representation.

[0131]

[0132] in

[0133] cosΩ=cosθcosδ,λ n =sin(nΩ) / sinΩ, (11)

[0134] Furthermore, the floquet frequency Ω ∈ [θ, π-θ]. The floquet frequency Ω can be measured with extremely high precision using phase amplification. To estimate both θ and δ, the loop in equation (4) should be considered for at least two distinct values ​​of η = (ζ0 - ζ1) / 2. To simplify the notation, the loop is represented as...

[0135]

[0136] Corresponding to The frequency of floquet is

[0137]

[0138] For η≠η′, the parameter δ can be estimated using the following formula:

[0139]

[0140] Knowing δ, θ can be estimated by simply putting its value into equation (14). The hidden assumption here is: 1. Gate G fSim (θ, δ, χ, γ, φ) are independent of ζ0 and ζ1, i.e., pulse leakage is negligible; 2. Single-qubit rotation can be perfectly realized. Both are quite reasonable assumptions for current-superconducting qubits.

[0141] To calibrate the fSim gate, loop (4)n is repeated for k = 0, 1, ..., κ-1. k Number of repetitions n k An exponential function approximately equal to k, i.e.,

[0142] logn k =hk, (16)

[0143] Here, λ is a constant. The advantage of this choice is that fewer quantum circuits can be implemented to achieve the desired accuracy, while maintaining the tracking of how many times the phase accumulates within a 2π interval. The three setup examples are different parameters calibrated in the generalized fSim gate. These setup examples can be intentionally implemented in a specific order to obtain improved results.

[0144] The first instance (Example 0) considers the following matrix elements:

[0145]

[0146] in, yes The abbreviation. For n=1, And for n=2, Capable of including floquet frequencies The information can be used to infer the values ​​of θ and δ using equation (14). This example has the advantage of being able to select the output state in the subspaces of the two ground states |00> and |11>, which is robust to single-bit flip errors. However, in some cases, it can only be used to estimate θ and δ.

[0147] For improved sensitivity, η can be chosen such that small changes in θ and δ cause a change in the measurement probability. The significant change. For large n, and... compared to, It is a slowly changing function, and equation (17) is approximated by the following equation.

[0148]

[0149] in To better estimate θ, η can be chosen such that... Maximize or nearly maximize η. To better estimate δ, the optimal choice of η satisfies...

[0150] δ + η = π / 4 (mod π / 2). (19)

[0151] This option can be used because it is more robust in practice (e.g., it provides a larger margin of error when errors are present). This is achieved by utilizing intervals of 2π. The four possible values ​​of δ are separated to the maximum extent possible by using the same value.

[0152] The Floquet frequency can be estimated for a certain value of η by running the circuit at different values ​​of n and then estimating θ and δ. In some cases, this can present challenges. First, The value of η can be very small and prone to error. Secondly, for some values ​​of k, the sensitivity of the estimator can be very low. These challenges can be addressed by using an adaptive method, where the value of η is chosen based on the current estimates of θ and δ. To improve robustness, the estimates of θ and δ are updated using data from the current step and previous steps. The process can be as follows: (1) For step k, the value of η is obtained using equation (19) based on the estimates of θ and δ obtained in step k-1; (2) These values ​​of η are used to run the calibration circuit and collect data; and (3) The estimates of θ and δ are updated using the data obtained in step k and several previous steps (e.g., k-2, k-1, and k).

[0153] The second example (Example 1) can be used to estimate θ, δ, and γ with high accuracy. It can also be used to estimate χ. Consider two matrix elements.

[0154]

[0155]

[0156] The value can be estimated directly from the measurement results using equation (21), and The value can be obtained using simple algebra To obtain. To know. Equation (20) can be used to estimate the relative phase.

[0157]

[0158] Use specific matrix elements Its advantage lies in the fact that its phase is relatively stable.

[0159]

[0160] Where χ is fixed, and η can be controlled with high precision. The phase of the matrix elements is...

[0161]

[0162] And therefore

[0163]

[0164] Knowing μ, we can provide different values ​​of n to estimate the values ​​of χ and γ using linear fitting. The relative phase μ can be solved using the following relationship.

[0165]

[0166] In this instance, and

[0167] The value of η can be chosen such that It is maximized or nearly maximized. Can be selected as These choices can improve the robustness and accuracy of the estimator.

[0168] Third example (Example 2). In Example 2, consider matrix elements.

[0169]

[0170]

[0171] This example provides a high-precision estimate of the parameter φ by first estimating the relative phase.

[0172]

[0173] Figure 21 An example computing system 1000 (such as reference 1) capable of implementing systems and methods according to exemplary embodiments of the present disclosure is described. Figure 1 A block diagram of the system under discussion. System 1000 includes a calibration system 1010 and a quantum computing system 1030 communicatively coupled via a network 1050. One or more aspects of any of the methods described herein can be implemented on the calibration system 1010 and / or the quantum computing system 1030.

[0174] The calibration system 1010 can include any type of computing device (e.g., a classical computing device). The calibration system 1010 includes one or more processors 1012 and a memory 1014. The one or more processors 1012 can include any suitable processing device (e.g., a processor core, microprocessor, ASIC, FPGA, controller, microcontroller, etc.) and can be a single processor or multiple processors operatively connected. The memory 1014 can include one or more non-transitory computer-readable storage media, such as RAM, ROM, EEPROM, EPROM, flash memory devices, disks, etc., and combinations thereof. The memory 1014 can store data 1016 (e.g., qubit parameters, measurement results, etc.) and instructions 1018 that are executed by the processor 1012 to cause the calibration computing device 1010 to perform operations, such as one or more aspects of any of the methods disclosed herein. The calibration system 1010 can be configured to process calibration data 1020 obtained by measuring the state of a quantum system (e.g., quantum system 1040) to determine gate parameters of a model of a composite gate according to an example embodiment of this disclosure.

[0175] The quantum computing system 1030 includes one or more processors 1032 and a memory 1034. The one or more processors 1032 can include suitable processing devices (e.g., processor cores, microprocessors, ASICs, FPGAs, controllers, microcontrollers, etc.) and can be a single processor or multiple processors operatively connected. The memory 1034 can include one or more non-transitory computer-readable storage media, such as RAM, ROM, EEPROM, EPROM, flash memory devices, disks, etc., and combinations thereof. The memory 1034 can store data 1036 and instructions 1038, which are executed by the processors 1032 to cause the quantum computing system 1030 to perform operations, such as implementing a quantum circuit with one or more quantum gates on a quantum system 1040 having multiple qubits and obtaining associated measurement results. The quantum computing system 1030 can be similar to a reference... Figure 1 The quantum computing system discussed and described is also available. Other suitable quantum computing systems can be used without departing from the scope of this disclosure.

[0176] Network 1050 can be any type of communication network, such as a local area network (e.g., intranet), a wide area network (e.g., the Internet), or some combination thereof, and can include any number of wired or wireless links. Typically, communication through Network 1050 can be carried via any type of wired and / or wireless connection, using various communication protocols (e.g., TCP / IP, HTTP, SMTP, FTP), encoding or format (e.g., HTML, XML), and / or protection schemes (e.g., VPN, Secure HTTP, SSL).

[0177] The digital, classical, and / or quantum themes and implementations of digital functional operations and quantum operations described in this specification can be implemented in digital electronic circuits, suitable quantum circuits, or more generally in quantum computing systems, in physically implemented digital and / or quantum computer software or firmware, in digital and / or quantum computer hardware including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. The term "quantum computing system" may include, but is not limited to, quantum computers / computing systems, quantum information processing systems, quantum cryptography systems, or quantum simulators.

[0178] The embodiments of the digital and / or quantum themes described in this specification can be implemented as one or more digital and / or quantum computer programs, i.e., one or more modules of digital and / or quantum computer program instructions encoded on a tangible, non-transitory storage medium for execution by a data processing device or for controlling the operation of a data processing device. The digital and / or quantum computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, one or more qubit / qubit structures, or a combination thereof. Alternatively or additionally, the program instructions can be encoded on an artificially generated propagation signal (e.g., a machine-generated electrical, optical, or electromagnetic signal) capable of encoding digital and / or quantum information, which is generated to encode digital and / or quantum information for transmission to a suitable receiver device for execution by a data processing device.

[0179] The terms quantum information and quantum data refer to information or data carried, stored, or preserved in quantum systems, the smallest nontrivial system being the qubit, i.e., the system that defines the unit of quantum information. It should be understood that the term "qubit" encompasses all quantum systems that can be appropriately approximated as a two-level system in the corresponding context. Such quantum systems can include multi-level systems, for example, having two or more levels. For instance, such systems can include atomic, electron, photon, ion, or superconducting qubits. In many implementations, the computational ground state is identified by ground and the first excited state; however, it should be understood that other arrangements are possible, identifying computational states by higher-level excited states (e.g., qubits).

[0180] The term "data processing device" refers to digital and / or quantum data processing hardware and encompasses various devices, apparatuses, and machines for processing digital and / or quantum data, including, for example, programmable digital processors, programmable quantum processors, digital computers, quantum computers, or multiple digital and quantum processors or computers, and combinations thereof. The device may also be or further include special-purpose logic circuitry, such as FPGAs (Field-Programmable Gate Arrays) or ASICs (Application-Specific Integrated Circuits), or quantum simulators—that is, quantum data processing devices designed to simulate or generate information about a particular quantum system. Specifically, a quantum simulator is a special-purpose quantum computer that does not have the capability to perform general-purpose quantum computing. In addition to hardware, the device may optionally include code that creates an execution environment for digital and / or quantum computer programs, such as code constituting processor firmware, protocol stacks, database management systems, operating systems, or combinations thereof.

[0181] Digital or classical computer programs, which can also be referred to or described as programs, software, software applications, modules, software modules, scripts, or code, can be written in any form of programming language, including compiled or interpreted languages ​​or descriptive or procedural languages, and can be deployed in any form, including as standalone programs or as modules, components, subroutines, or other units suitable for use in digital computing environments. Quantum computer programs, which can also be referred to or described as programs, software, software applications, modules, software modules, scripts, or code, can be written in any form of programming language, including compiled or interpreted languages ​​or descriptive or procedural languages, and can be translated into a suitable quantum programming language, or can be written in quantum programming languages ​​such as QCL, Quipper, Cirq, etc.

[0182] Digital and / or quantum computer programs can, but do not necessarily, correspond to files in a file system. Programs can be stored as a portion of a file containing other programs or data (e.g., one or more scripts stored in a markup language document), a single file dedicated to the program under discussion, or multiple collaborative files, such as a file storing portions of one or more modules, subroutines, or code. Digital and / or quantum computer programs can be deployed to execute on a single digital or quantum computer, or on multiple digital and / or quantum computers located at one site or distributed across multiple sites and interconnected by digital and / or quantum data communication networks. A quantum data communication network is understood as a network that can transmit quantum data using quantum systems (e.g., qubits). Generally, digital data communication networks cannot transmit quantum data; however, quantum data communication networks can transmit both quantum data and digital data.

[0183] The processes and logic flows described in this specification can be executed, where appropriate, by one or more programmable digital and / or quantum computers operating with one or more digital and / or quantum processors, which execute one or more digital and / or quantum computer programs to perform functions by manipulating input digital and quantum data and generating outputs. The processes and logic flows can also be executed by dedicated logic circuits such as FPGAs or ASICs, or quantum simulators, or by a combination of dedicated logic circuits or quantum simulators with one or more programmable digital and / or quantum computers, and the apparatus can also be implemented as dedicated logic circuits such as FPGAs or ASICs, or quantum simulators, or by a combination of dedicated logic circuits or quantum simulators with one or more programmable digital and / or quantum computers.

[0184] For a system of one or more digital and / or quantum computers or processors to be "configured" or "operable for" performing a specific operation or action, it means that the system has software, firmware, hardware, or a combination thereof installed thereon that causes the system to perform the operation or action in operation. For one or more digital and / or quantum computer programs to be configured to perform a specific operation or action, it means that one or more programs include instructions that cause the device to perform the operation or action when executed by a digital and / or quantum data processing device. A quantum computer can receive instructions from a digital computer that cause the device to perform the operation or action when executed by a quantum computing device.

[0185] A digital and / or quantum computer suitable for executing digital and / or quantum computer programs can be based on a general-purpose or special-purpose digital and / or quantum microprocessor or both, or any other kind of central digital and / or quantum processing unit. Generally, the central digital and / or quantum processing unit receives instructions and digital and / or quantum data from read-only memory, or random access memory, or a quantum system suitable for transmitting quantum data (e.g., photons), or a combination thereof.

[0186] Some example elements of a digital and / or quantum computer are a central processing unit (CPU) for executing or running instructions and one or more memory devices for storing instructions and digital and / or quantum data. The CPU can be supplemented or incorporated into dedicated logic circuitry or a quantum simulator. Generally, a digital and / or quantum computer will also include, or be operatively coupled to, receiving digital and / or quantum data from or transferring digital and / or quantum data to one or more mass storage devices, or both, for storing digital and / or quantum data, such as magnetic disks, magneto-optical disks, or optical disks, or quantum systems suitable for storing quantum information. However, a digital and / or quantum computer does not need to have such devices.

[0187] Digital and / or quantum computer-readable media suitable for storing digital and / or quantum computer program instructions and digital and / or quantum data include all forms of non-volatile digital and / or quantum memories, media, and memory devices, including, for example, semiconductor memory devices such as EPROM, EEPROM, and flash memory devices; disks, such as internal hard disks or removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks; and quantum systems such as trapped atoms or electrons. It should be understood that quantum memory is a device capable of storing quantum data with high fidelity and efficiency for extended periods, for example, a light-matter interface in which light is used for transmission and matter for storing and preserving quantum data, such as quantum characteristics like superposition or quantum coherence.

[0188] Control of the various systems or portions thereof described in this specification can be implemented in a digital and / or quantum computer program product comprising instructions stored on one or more tangible, non-transitory, machine-readable storage media and executable on one or more digital and / or quantum processing devices. The systems or portions thereof described in this specification can each be implemented as means, methods, or electronic systems that may include one or more digital and / or quantum processing devices and memories for storing executable instructions for performing the operations described in this specification.

[0189] While this specification includes many specific implementation details, this should not be construed as a limitation on the scope of what may be claimed, but rather as a description of features that may be specific to particular embodiments. Some features described herein in the context of individual implementations can also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation can also be implemented separately or in any suitable sub-combination in multiple implementations. Furthermore, although features may be described above as acting in certain combinations and even initially claimed in this way, one or more features from a claimed combination can be excluded from that combination in some cases, and the claimed combination may involve sub-combinations or variations thereof.

[0190] Similarly, although operations are depicted in a specific order in the accompanying drawings, this should not be construed as requiring these operations to be performed in the specific order shown or in sequential order, or requiring the execution of all illustrated operations to achieve the desired result. In some cases, multitasking and parallel processing can be advantageous. Furthermore, the separation of various system modules and components in the embodiments described above should not be construed as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0191] Specific embodiments of this subject matter have been described. Other embodiments are within the scope of the following claims. For example, the actions described in the claims can be performed in a different order and still achieve the desired result. As an example, the processes depicted in the drawings do not necessarily require a specific order or sequence to achieve the desired result. In some cases, multitasking and parallel processing can be advantageous.< / y> < / x> < / y> < / x> < / y> < / x> < / y> < / x> < / y> < / x> < / y> < / x>

Claims

1. A method for calibrating a quantum computing system for implementing quantum circuits on a quantum system having multiple qubits, the quantum circuits including composite quantum gates, the method comprising: The unitary gate model describing the composite quantum gate is accessed by one or more computing devices, the unitary gate model including multiple gate parameters; By implementing the composite quantum gate through one or more computing devices to achieve multiple gate loops, the multiple gate parameters are amplified using an amplification factor; After amplifying the plurality of gate parameters, the state of the quantum system is measured by the one or more computing devices; The value of at least one of the plurality of gate parameters is determined by the one or more computing devices based on measurements of the state of the quantum system; as well as The composite quantum gates used in the quantum computing system are calibrated by the one or more computing devices based on the values ​​of the plurality of gate parameters.

2. The method according to claim 1, wherein, The measurement results of the state of the quantum system obtained by the one or more computing devices include: For each of the multiple measurement instances, the measurement result of the state of the quantum system is obtained; Each measurement instance is associated with a different number of gate loops.

3. The method according to claim 2, wherein, The number of gate loops used for at least one measurement instance increases exponentially relative to the number of gate loops used for previous measurement instances.

4. The method according to claim 1, wherein, The composite quantum gate represents the parasitic interaction between multiple qubits in the quantum system.

5. The method according to claim 1, wherein, The unitary gate model is modeled as a first Z-rotation angle gate for the first qubit, a second Z-rotation angle gate for the second qubit, an iswap gate for the first and second qubits, and a controlled phase gate for the first and second qubits.

6. The method according to claim 1, wherein, The gate model includes a first parameter, a second parameter, a third parameter, a fourth parameter, and a fifth parameter, wherein determining the plurality of gate parameters includes determining each of the first parameter, the second parameter, the third parameter, the fourth parameter, and the fifth parameter.

7. The method according to claim 6, wherein, Determining the first parameter includes: The first phase of the first qubit is determined as a function of k, where k is the number of gate loops; The second phase of the second qubit is determined as a function of k; Determine a function that makes the sum of the first phase and the second phase dependent on k; and The first parameter is determined at least in part based on the properties associated with the function that makes the sum of the first phase and the second phase related to k.

8. The method according to claim 7, wherein, The first parameter is determined based on the slope of the function associated with the sum of the first phase and the second phase and k.

9. The method according to claim 6, wherein, Determining the second parameter includes: When the first quantum bit is in When the state is reached, the conditional phase for the second qubit is determined; Determine a function that relates the conditional phase to k, where k is the number of gate loops; The second parameter is determined at least in part based on parameters associated with the function that makes the conditional phase related to k.

10. The method according to claim 9, wherein, The second parameter is determined based on the slope of the function associated with the conditional phase and k.

11. The method according to claim 6, wherein, Determining the third parameter and determining the fourth parameter include: Calibration data indicating the state of the first and second qubits is obtained as a function of both the z-rotation angle applied to the first qubit and k, where k is the number of gate loops; The calibration data is fitted using an oscillation frequency function based on the oscillation frequency and k. Determine a function that relates the oscillation frequency to the z-rotation angle; and The third parameter is determined based on a first characteristic of the function that relates the oscillation frequency to the z-rotation angle; and The fourth parameter is determined based on a second characteristic of the function that relates the oscillation frequency to the z-rotation angle.

12. The method according to claim 6, wherein, The method includes: At a fixed rotation angle applied to the first qubit, calibration data indicating the state of the first and second qubits is obtained according to k, where k is the number of gate loops. The calibration data includes a first probability associated with the first and second qubits being in the same state and a second probability associated with the first and second qubits being in different states. The fifth parameter is determined at least in part based on the first probability and the second probability.

13. The method according to claim 1, wherein, For at least one measurement instance, the parameter estimate for said measurement instance can be selected to be within an uncertainty range determined at least in part based on the periodicity associated with previous measurement instances.

14. The method according to claim 1, wherein, Determining at least one gate parameter among the plurality of gate parameters by the one or more computing devices includes determining at least one gate parameter among the plurality of gate parameters as being within variance by the one or more computing devices.

15. The method according to claim 14, wherein, The variance is inversely proportional to the amount of time required to determine at least one of the plurality of gate parameters by the one or more computing devices.

16. The method of claim 14, wherein, The variance decreases approximately quadratically faster than the estimation process performed using classical processing algorithms.

17. The method according to claim 1, wherein, The composite quantum gate is a two-qubit quantum gate.

18. A computing system, comprising: A quantum computing system with multiple qubits; One or more processors; One or more memory devices storing computer-readable instructions that, when executed by the one or more processors, cause the one or more processors to perform operations including one or more aspects of any one of the methods according to any one of claims 1 to 17.

19. A computer program product configured to perform one or more aspects of any one of the methods according to any one of claims 1 to 17.

Images