Method for evaluating quantum gate fidelity
Patent Information
- Application Number
- KR1020267028763
- Authority / Receiving Office
- KR · KR
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2024-03-05
- Filing Date
- 2025-03-04
- Publication Date
- 2026-09-17
Smart Images
Figure PCT00381_ABST
Abstract
Description
Technology Field
[0001] Reference by reference
[0002] This application incorporates by reference the entire contents of application EP24305337.8 filed on March 5, 2024.
[0003] Technology field
[0004] The present invention relates to a method for evaluating quantum gate fidelity. Background Technology
[0005] A. General Background
[0006] A1. General Considerations Regarding Quantum System Error Correction
[0007] Quantum gates are fundamental logical components essential for realizing quantum computing devices. They typically involve one or more qubits. Some quantum gates involve two qubits—a control qubit and a target qubit whose state changes according to the state of the control qubit.
[0008] To extract common information from multiple data qubits, conventional quantum circuits perform a series of 2-qubit gates (typically CNOT gates) between an auxiliary qubit (acting as a control qubit) and multiple data qubits (each acting as a target qubit) before measuring the auxiliary qubit. When this operation is used to detect errors, it is included in a syndrome extraction round (or "SER").
[0009] The realization of these quantum gates is critical for detecting errors and consequently executing quantum error correction codes (or "QECC"), which is currently considered the only way to construct reliable and usable quantum chips. The general concept behind QECC is to encode logic qubits using multiple (at least three) physical qubits and to establish an error detection mechanism to verify that the information in the multiple physical qubits does not change over time. When an error is detected, error correction is performed either by changing the qubit states themselves or by post-processing the results of quantum algorithms involving these qubits. The circuits used to implement QECC are called quantum error correction circuits or QEC circuits.
[0010] A2. Fidelity of the CNOT quantum gate of the prior art
[0011] The characteristics used to evaluate the quality of a quantum gate are its execution time (i.e., the time the gate operates) and the associated error probability. Knowing the error probability in terms of bit flips and phase flips is of the utmost importance, as it enables better prediction of the reliability of the SER and, consequently, the reliability of the QECC.
[0012] In the case of a phase-flip QECC performing SER relying on a CNOT gate, the most important errors to be measured are the bit flip probability during the CNOT on the target qubit. , phase flip probability during CNOT on the control qubit , and phase flip probability during CNOT on the target qubit am.
[0013] Conventional techniques regarding the measurement of these probabilities currently rely on two approaches.
[0014] The main approach is to perform a full quantum process tomography (or "QPT") of the CNOT to derive measurements. The measurements of the QPT itself are affected by types of errors different from those associated with the QEC circuit, such as state preparation and measurement (or "SPAM") errors.
[0015] In practice, deconvolving SPAM errors from bit-flip and phase-flip errors can be difficult and requires an ad-hoc approach based on independent measurements to characterize SPAM errors. Furthermore, measuring the entire QPT requires the preparation of 16 different initial states and the measurement of 16 different sets of observations, followed by fitting the measured QPT matrix to a theoretical quantum process map. Consequently, this is a burdensome task that hinders testing many variations of CNOT. Overall, while it provides reliable results, this method is impractical to perform. Additionally, due to its cumbersome nature, this process is particularly unsuitable for optimizing the parameters of CNOT gates and even more unsuitable for use in an automated manner.
[0016] Recently, in the specific field of noise-biased qubits, a theoretical approach was outlined in the paper "Estimating the Bias of CX Gates via Character Randomized Benchmarking" by Claes et al., PRX Quantum 4, 010307, doi 10.1103 / PRXQuantum.4.010307. In this theoretical method, CNOT gates are repeated multiple times, and random single-qubit Clifford gates are inserted in between. In particular, this discloses estimating the fidelity of a gate by using standard or insertion-biased random benchmarking, which inserts the gate of interest with random elements from an insertion group designed to simplify the error channel.
[0017] This approach is bit flip probability It appears to be efficient for deriving the noise-biasing characteristics of CNOT gates that are directly related to it. However, this has not only not been experimentally verified, but also requires excellent single-qubit gates that do not exist. As a result, there is a possibility that the quality of the results in the experiment will be degraded due to the fact that single-qubit gates will not be perfect.
[0018] The present invention aims to improve the situation. To this end, the applicant proposes a method for measuring the probability of a bit flip and / or phase flip while performing a CNOT gate between a control qubit having a control qubit resonant frequency and a target qubit having a target qubit resonant frequency, wherein the CNOT gate is performed by a sequence of the following operations:
[0019] S1) An operation of applying dissipation stabilization to the target qubit and the control qubit,
[0020] S2) An operation of applying radiation having the control qubit resonant frequency such that the Hamiltonian generated from the radiation having the control qubit resonant frequency acts substantially simultaneously on the target qubit and the control qubit,
[0021] S3) After a selected gate duration, turn off the radiation having the control qubit resonant frequency, and apply the dissipation stabilization to the target qubit for a selected re-stabilization duration. This method includes the following operations:
[0022] a) operation providing a superconducting quantum circuit comprising a control qubit and a target qubit that are all noise-biased qubits stabilized in a dissipative manner and are non-linearly coupled to each other,
[0023] b) an operation to determine a set of phase flip CNOT iterations comprising multiple different integers included between 0 and a phase flip upper limit, and / or a set of bit flip CNOT iterations comprising multiple different integers included between 0 and a bit flip upper limit,
[0024] c) performing steps c1) to c5) for each integer npf in the set of phase flip CNOT iterations and / or performing steps c6) to c10) for each integer nbf in the set of bit flip CNOT iterations:
[0025] c1) Measurement control qubit logic state , phase included in the range [0;2π] , logical state of target qubit for measurement , and the phase included in the set of values {0;π} Steps to set up,
[0026] c2) Control qubit state Prepare as, and set the target qubit state The preparation stage,
[0027] c3) A step of performing the CNOT gate npf times between the control qubit and the target qubit of operation c2),
[0028] c4) A step of measuring the target qubit's Pauli operator X, the target qubit's Pauli operator Y, the control qubit's Pauli operator X, and the control qubit's Pauli operator Y,
[0029] c5) A step of repeating operations c2) to c4) to obtain an average value for each measurement of operation c4),
[0030] c6) Measurement control qubit logic state and measurement target qubit logic state Steps to set up,
[0031] c7) Control qubit state or Prepare as, and set the target qubit state or The preparation stage,
[0032] c8) A step of performing the CNOT gate nbf times between the control qubit and the target qubit of operation c7),
[0033] c9) Step of measuring the Pauli operator Z of the target qubit,
[0034] c10) A step of repeating operations c7) to c9) to obtain an average value for the measurement of operation c9),
[0035] d) If available, the measurements of operation c5) and By fitting the phase flip probability value for the control qubit to each curve based on the exponential function of the number of CNOT iterations and phase flip probability value for the target qubit Derive and the measurements of operation c10) By fitting it to a curve based on an exponential function of the number of CNOT iterations, the bit flip probability value for the target qubit An action that derives.
[0036] This method is advantageous because it has been proven to work experimentally and allows for the measurement of all three relevant probabilities in a simpler manner to perform. As discussed above, the paper by Claes et al. is interesting but does not offer sufficient potential. When compared to the QPT approach, this method represents nearly a tenfold gain in terms of the number of samples required.
[0037] In various embodiments, the method may exhibit one or more of the following features:
[0038] - Action d) is the measurements curve It includes fitting to, where n is the number of CNOT iterations, and is attributed to state preparation and measurement errors for the target qubit, and thereby the phase flip probability value for the target qubit Deriving,
[0039] - Action d) is the measurements curve It includes fitting to, where n is the number of CNOT iterations, and It is attributed to state preparation and measurement errors for the control qubit, and thereby the phase flip probability value for the control qubit Deriving,
[0040] - Operation d) is the measurements curve As a fitting to, where n is the number of CNOT iterations, and It is attributed to state preparation and measurement errors for the control qubit, and is due to errors occurring in the control qubit during step S2), and is due to errors occurring in the control qubit during step S3), and is the fitting above, which is due to state readiness errors of the target qubit, and the phase flip probability value for the control qubit Includes calculating,
[0041] - Operation d) is the measurements curve As a fitting to, where n is the number of CNOT iterations, and It is attributed to state preparation and measurement errors regarding the target qubit, and is due to errors occurring in the target qubit during step S2), and is the fitting, and the phase flip probability value for the target qubit, which is attributed to errors occurring in the target qubit during step S3). Includes calculating,
[0042] - Operation d) uses the measurements of operation c5) on each of the respective curves and As fitting simultaneously to, where n is the number of CNOT iterations, and It is attributed to state preparation and measurement errors for the control qubit, and is due to errors occurring in the control qubit during step S2), and is caused by errors occurring in the control qubit during step S3), and It is due to state readiness errors of the target qubit, and It is attributed to state preparation and measurement errors regarding the target qubit, and is due to errors occurring in the target qubit during step S2), and is the simultaneous fitting, and the phase flip probability value for the target qubit, which is attributed to errors occurring in the target qubit during step S3). and phase flip probability values for control qubits Includes calculating,
[0043] - Operation d) is the measurements from operation c10) curve It includes fitting to, where n is the number of CNOT iterations, and It is attributed to state preparation and measurement errors regarding the target qubit, and thereby the bit flip probability value for the target qubit Deriving,
[0044] - Operation c9) further includes measuring the Pauli operator Z of the control qubit, and operation d) takes the measurements of operation c10) and each curve and As fitting simultaneously to, where n is the number of CNOT iterations, and It is attributed to state preparation and measurement errors regarding the target qubit, and is due to errors occurring in the target qubit during step S2), and is due to errors occurring in the target qubit during step S3), and It is attributed to state preparation and measurement errors for the control qubit, and is due to errors occurring in the control qubit during step S2), and is due to errors occurring in the control qubit during step S3), and is due to state readiness errors of the control qubit, the simultaneously fitting, and the bit flip probability value for the target qubit Includes calculating,
[0045] - Step S2) includes turning off the dissipation stabilization for the target qubit, or applying another stabilization conditional to the control qubit for the target qubit.
[0046] The present invention also relates to a computer program product comprising instructions that cause a processing circuit to perform the above method when executed by a processing circuit, a carrier comprising one of electronic signals, optical signals, radio signals, or a computer-readable storage medium comprising such computer program, and a non-transient computer-readable medium on which such computer program is stored. Brief explanation of the drawing
[0047] Other features and advantages of the present invention will be easily apparent from the following description of the drawings illustrating exemplary embodiments of the present invention, in which: - FIG. 1 shows a general diagram of a computer device for performing a method according to an embodiment, and - FIG. 2 shows a general view of a computer program used in the embodiment of FIG. 1, and - FIG. 3 shows a block diagram of a method according to an embodiment, and - FIG. 4 illustrates an exemplary fitting using the first type of method used in the operation of FIG. 3, and - Fig. 5 shows an exemplary fitting using the second type of method used in the operation of Fig. 3. The drawings and the following description consist mostly of active and clearly defined features. As a result, they are not only useful for understanding the invention but may also be used to contribute to its definition when necessary. Specific details for implementing the invention
[0048] B. Noise-biased qubits
[0049] The present invention relates to the realization of high-performance quantum gates in the context of noise-biased qubits and the determination of their fidelity.
[0050] Stabilized CAT qubits are known to have the advantage of noise bias. More precisely, effective error channels (e.g., bit errors or "bit flips") are suppressed exponentially according to the "size" of the Schrödinger CAT states of the CAT qubits—i.e., the average number of photons. Other qubits, such as 2-photon exchange qubits, are also known to have the advantage of noise bias (as disclosed in Pop et al.'s "Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles", Nature 508, 369-372, 2014, doi 10.1038 / nature13017). While CAT qubits will be the main examples discussed below, it should be noted that this method applies to any noise-biased qubit with a dissipation stabilization scheme.
[0051] According to current knowledge, this suppression should be applied to a wide range of physical noise processes that have a local effect in the phase space of the harmonic oscillator. This includes, but is not limited to, photon losses, thermal excitations, photon dephasing, and various nonlinearities induced by coupling to Josephson junctions.
[0052] Recent experiments in the context of quantum superconducting circuits have observed this exponential suppression of bit-flip errors depending on the average number of photons in cat states. Due to this noise structure, the use of a single iterative code is considered sufficient to correct residual error channels. In fact, if one intends to correct only phase jumps, it is sufficient to use only a phase jump error correction code. This can be, for example, an iterative code defined in a dual basis or any other classical error correction code.
[0053] The cat qubit iteration code is constructed using d cat qubits (called data cat qubits) in which logical information is encoded. This is accomplished by repeatedly measuring quantum operators indicating whether some errors have occurred in the data cat qubits. This is accomplished by using d-1 additional cat qubits (called auxiliary cat qubits or auxiliary cat qubits). The quantum circuit of the iteration code requires preparing the auxiliary qubit to the state "+"—which is the Schrödinger cat state for the cat qubit—two CNOT gates between the auxiliary cat qubits and the data cat qubits, and measuring the Pauli X operator of the auxiliary qubit—which is the photon number parity for the cat qubit.
[0054] The challenge in implementing this iterative code is to execute the code on hardware that operates below a fault tolerance error threshold. This means that the fidelity of the quantum operations in this circuit must be very high so that the code has a positive effect.
[0055] More precisely, when the iterative code operates beyond a threshold, that is, when the fidelity of the physical operations constituting the iterative code is insufficient, the lifespan of the logical information decreases as the number of physical data qubits d increases: new errors introduced by the addition of quantum systems are not compensated by error correction strategies.
[0056] On the other hand, when the iteration code operates below the error correction threshold, that is, when the fidelity of the physical operations is sufficient, the lifetime of the logical information increases exponentially with the number of data qubits d (also called the distance d of the iteration code).
[0057] More recently, the applicant also proposed a classical LDPC code using quantum CAT qubits to encode logic qubits. These quantum systems provide a promising platform for realizing practical fault-tolerant quantum computing (FTQC). Consequently, the optimization of CNOT quantum gates used in SERs is becoming increasingly important.
[0058] The field of quantum computing is very young. This is even more so in the field of cat qubits. In many ways, it functions as a research field. Consequently, the desirable path of progress involves making changes that may appear very gradual at first glance but actually require significant physics work to be verified and industrialized. In other words, what is considered the current level of technology generally remains unchanged until a critical obstacle is discovered. This means that solutions known to work are not easily replaced.
[0059] C. Cat Cubits
[0060] Some of the applicant's research over the past few years has been on the stabilization of cat qubits. In "Exponential suppression of bit-flips in a qubit encoded in an oscillator", Nature Physics, 2020, R. Lescanne et al. demonstrated that cat qubits can be stabilized by using a nonlinear transformation between two photons in the first mode a—memory mode or cat qubit mode—and one photon in the second mode b—buffer mode.
[0061] The cat cubit has two coherent states and The so-called cat states, which are nests of It is defined as a 2-dimensional manifold spanned by:
[0062]
[0063] Here:
[0064]
[0065] Stabilized cat qubits are known to have the advantage of high noise bias, which means that the bit-flip probability is exponentially smaller than the phase-flip probability. More precisely, the effective error channel (e.g., bit errors or "bit-flips") is the "size" of the Schrödinger cat states of the cat qubits—i.e., the average number of photons. - is suppressed exponentially according to. As previously mentioned, this exponential suppression of bit-flip errors comes at the cost of a linear increase in phase-flip errors.
[0066] D. Stabilization methods
[0067] Cat qubits can be stabilized or restrained by the following exemplary methods:
[0068] a) Jump operator As a parametric dissipation stabilization having, where is the 2-photon extinction rate, and is a photon annihilation operator, and is a complex number defining a cat qubit. This jump operator has a extinction rate A lossy buffer mode b and a 4-wave mixed device having—typically a Josephson junction, ATS, or DC bias coupled to Josephson junctions—couples to cat qubit mode a and Hamiltonian It can be realized by engineering, and here is the photon extinction operator of buffer mode b, and is the 2-photon coupling rate, and for a 4-wave mixed device, the frequency |2f a -f b Pump and frequency of | The drive in buffer mode, Authorize under the condition.
[0069] b) Kerr Hamiltonian As, here is the amplitude of the Kerr Hamiltonian, and is the photon annihilation operator, and |α| 2 is the average number of photons.
[0070] c) Detuned Kerr Hamiltonian As, here is the amplitude of the Kerr Hamiltonian, and a is the photon annihilation operator, and is a complex number defining a cat qubit, and is a detuning factor.
[0071] d) 2-Photon Exchange (TPE) Hamiltonian As, here is the complex 2-photon coupling rate, and is the photon annihilation operator, and is a complex number defining a cat qubit, and are the descent and rise operators of a 2-level system. This Hamiltonian can be engineered in the same way as the parametric dissipation stabilization a).
[0072] e) Jump operator As a dissipative squeezing stabilization having, where is the squeezed 2-photon extinction rate, and is the photon annihilation operator, and is a complex number defining a cat qubit, and and is the complex squeezing parameter It is the modulus and argument of. This jump operator is the extinction rate A lossy buffer mode b and 4-wave mixed device—typically a Josephson junction or ATS—couples a cat qubit mode a and Hamiltonian It can be realized by engineering, and here is the photon annihilation operator of mode b, and is the squeezed 2-photon coupling rate, and the frequencies |2f a -f b |, and Various pumps of, and frequency The drive of buffer mode b, Use under normal conditions.
[0073] f) As a variation of the previous stabilization method e), the applicant filed European patent application EP 23175147.0 regarding this, where the bosonic qubit—called a "mooncat qubit" because the two blobs of the Wigner function have a crescent shape—is the Hamiltonian It is stabilized by engineering, and here is the frequency |2f a -f b It is the amplitude of the pump, and is the destruction operator for cat qubit mode a, and is frequency It is a complex number in which the phase and amplitude arise from the amplitude of the longitudinal coupling generated by the pump, and is frequency It is a complex number arising from the drive in buffer mode b, and is the destruction operator for buffer mode b; the comparison between the cat qubit and the squeezed cat qubit is complex squeezing parameter It can be established as a function of as follows: .
[0074] g) Jump operator As a resonance dissipation stabilization having, where is the 2-photon extinction rate, and is a photon annihilation operator, and is a complex number defining a cat qubit. This jump operator has a extinction rate A Hamiltonian with lossy buffer mode b and a 3-wave mixed device coupled to cat qubit mode a It can be realized by engineering, and here is the photon extinction operator for buffer mode b, and the mode frequencies are substantially satisfies is, and accordingly, the frequency A drive in buffer mode is added.
[0075] The present invention relates to a stabilization scheme or a combination thereof comprising at least dissipation stabilization schemes (e.g., a), e), f) and g)) above for generating data cat qubits and auxiliary qubits used in QECC.
[0076] E. Implementation of CNOT Gates
[0077] In application EP23305297.6, the applicant described in detail implementations of CNOT quantum gates and components used to enable them.
[0078] The theoretical realization of CNOT gates between two stabilized cat qubits in modes a1 and a2 depends on the use of the following three components:
[0079] 1) Control qubit Jump operator for Dissipation stabilization is performed using, where a1 is the photon extinction operator of mode a1, and is a complex number defining a cat qubit, or one of the stabilization schemes described above,
[0080] 2) By adding a "feedforward" Hamiltonian, also called the "CNOT" Hamiltonian or "longitudinal" Hamiltonian, to the circuit, Equation has, here is the complex amplitude of the Hamiltonian, and is the photon annihilation operator of mode a1, and is the photon annihilation operator of mode a2, and is a complex number defining a cat qubit,
[0081] 3) Control qubit Target qubit depending on the state of Jump operator for This involves performing dissipation stabilization using, where is the 2-photon extinction rate, and is the photon annihilation operator of mode a1, and is the photon annihilation operator of mode a2, and is a complex number defining the cat qubit, or is one of the dissipation stabilization schemes described above (a), e), f) and g)) adapted to be conditional to the auxiliary qubit state.
[0082] Component 2 can be implemented in various ways depending on the superconducting quantum circuit topology. In a context where the target qubit and the control qubit are nonlinearly coupled, this can be achieved by applying radiation having the control qubit frequency to the target qubit and / or the control qubit. Applying radiation to the target qubit and / or the control qubit means that radiation reaching the nonlinear part of the superconducting quantum circuit coupling the target qubit and the control qubit is applied to the superconducting quantum circuit, thereby inducing a feedforward Hamiltonian.
[0083] The best theoretical implementation uses the three components mentioned above. However, the applicant's experiments have found that the first two components provide a good compromise between ease of implementation and quality of results.
[0084] Component 3 replaces the conventional stabilization performed on the target qubits to stabilize the cat states when applied. Without Component 3, the target qubits do not receive any stabilization of the cat states while the components for performing the gate are applied. The same applies to all embodiments described below: during the gate operation or measurement operation, the steady-state stabilization of the target cat qubits is turned off, and this can be replaced by Component 3 during the gate operation.
[0085] In fact, theoretically, a CNOT gate can be realized with only components 1 and 3 without a feedforward Hamiltonian, but in practice, since the fidelity of the CNOT gate is low without this term, it is important to implement component 2).
[0086] As a result, the realization of the CNOT gate between the control qubit and the target qubit can be viewed as consisting of three main steps:
[0087] S1) A step of applying dissipation stabilization to the target qubit and the control qubit,
[0088] S2) A step of applying radiation having the control qubit resonant frequency, such that the feedforward Hamiltonian generated from the radiation having the control qubit resonant frequency acts substantially simultaneously on the target qubit and the control qubit,
[0089] S3) After a selected gate duration, turn off the radiation having the control qubit resonant frequency, and apply the dissipation stabilization to the target qubit for a selected re-stabilization duration.
[0090] In step S2), applying radiation having the control qubit resonant frequency to achieve component 2 can be performed in various ways depending on the superconducting quantum circuit topology. This can be done by applying radiation to the superconducting quantum circuit in any way such that the radiation reaches a nonlinear part of the superconducting quantum circuit that couples the target qubit and the control qubit, thereby inducing a feedforward Hamiltonian.
[0091] For example, this can be accomplished by directly emitting radiation to a nonlinear element coupling the target qubit and the control qubit. In some embodiments, such as that disclosed in EP23305298.4, this nonlinear element may be part of the target qubit. In other embodiments, the radiation may be introduced in a different way. The most important fact is that the radiation reaches a part of the superconducting quantum circuit that nonlinearly couples the target qubit and the control qubit to achieve the feedforward Hamiltonian of component 2 as described above.
[0092] Steps S1) through S3) include cases where component 3 is included or not included during step S2). When component 3 is used, it replaces target qubit dissipation stabilization during step S2). When component 3 is not used, target qubit dissipation stabilization is still suppressed during step S2), and the selected gate duration must be shorter than the target qubit decoherence time.
[0093] While experimenting on the CNOT quantum gates of EP23305297.6, the applicant was very surprised to discover that the above step sequence has error decorrelation effects similar to those in the theoretical paper by Claes et al., but without the need to introduce random single-qubit gates. As a result, not only is it possible to make CNOT fidelity measurements more precise, but it is also much faster and less prone to errors than the method theorized in the paper by Claes et al.
[0094] F. Modes of Implementation
[0095] More precisely, the applicant has discovered a method shown in Fig. 3 that enables the significant measurement of all three probability values for quantifying CNOT fidelity.
[0096] FIG. 1 shows a computer device as a block diagram of a device (2) (e.g., a network node, a connected device, etc.) according to an embodiment. As shown in FIG. 1, the device may include a processing circuit (PC) (102) that may include one or more processors (P) (104); a network interface (106) that includes a transmitter (Tx) (108) and a receiver (Rx) (110) for enabling the device to transmit data to other computing devices connected to a network (112) (e.g., an Internet Protocol (IP) network) to which the network interface (106) is connected, and to receive data from the other computing devices; and a local storage unit (also known as a "data storage system") (114) that may include one or more non-volatile storage devices and / or one or more volatile storage devices.
[0097] In embodiments where the PC (102) includes a programmable processor, a computer program product (CPP) (116) may be provided. The CPP (116) includes a computer readable medium (CRM) (118) that stores a computer program (CP) (120) that includes computer readable instructions (CRI) (122). The CRM (118) may be a non-transient computer readable medium such as magnetic media (e.g., hard disk), optical media, memory devices (e.g., random access memory, flash memory), etc.
[0098] The processors (104) include any known means for performing automated computation, such as CPUs, GPUs, CPU and / or GPU grids, remote computation grids, specifically configured FPGAs, specifically configured ASICs, specialized chips such as SOCs or NOCs, AI specialized chips, etc.
[0099] In an embodiment, the data storage unit (114) may store CNOT execution parameters (e.g., gate duration, re-stabilization time, noise bias qubit parameters, cat size, etc.), sets of CNOT iterations, upper limits, ready state phase values, and any other data discussed below.
[0100] In the example described herein, the data storage unit (114) may be realized in any suitable manner, namely by a hard disk drive, a solid-state drive, a flash memory, memory embedded in a processor, a remote storage unit accessible from the cloud, etc. The data storage unit (114) may also store any temporary data that may be generated during the execution of the invention, as well as measurements, parameters, or probabilities determined during the execution of the method.
[0101] Hereinafter, the concepts of frequency and angular frequency will be referred to as frequency for the sake of brevity. Those skilled in the art will readily identify which is relevant from the context.
[0102] Figure 2 shows an exemplary schematic diagram of a computer program (120).
[0103] The computer program (CP) (120) includes three main modules that work together:
[0104] - Preparation module (1210),
[0105] - Measurement module (1220), and
[0106] - Fidelity calculation module (1230).
[0107] The preparation module (1210) can be used to determine elements for performing the method, such as an upper limit N of the number of gates for determining the required average values. As shown below, there are various ways to determine N.
[0108] The measurement module (1220) may be used to control the execution of measurements used to determine the CNOT gate fidelity. In some embodiments, determining the upper limit N may involve using the measurement module (1220). Generally speaking, the measurement module (1220) controls the application of component 2 to perform the CNOT gate, as well as the application of radiation to establish and stabilize the qubits. The measurement module (1220) may also be used to control the preparation of logic states for applying the CNOT gate.
[0109] Finally, the fidelity calculation module (1230) can be used to calculate CNOT gate fidelity parameters based on the measurements performed. As shown below, this includes fitting the measurements to exponential curves based on an exponential function of the number of CNOT gate iterations.
[0110] It will be easy to understand that the above module presentation is primarily a functional view of the actions performed by a computer program when executing a method. The modules can be combined, fused, intertwined, or otherwise connected within the computer program.
[0111] FIG. 3 shows a general diagram of an embodiment of the method according to the present invention.
[0112] F1. Method Reset
[0113] In the first operation (300), the function Nmax() is executed to determine the array Rep[] of the gate iterations. This function can be executed, for example, by the preparation module (1210).
[0114] As shown below, the method relies on determining the average values of the Pauli operators of the control qubit after the CNOT gate is executed n consecutive times, where n varies between 0 and an upper limit. This upper limit is the bit flip probability value (or bit flip fidelity parameter) for the target qubit Cases where it is determined, and phase flip probability values (or phase flip fidelity parameters) for the control qubit and for the target qubit It may differ when determining.
[0115] The function Nmax() is the bit flip fidelity parameter Maximum number of iterations of CNOT gates to determine Nbf and / or phase flip fidelity parameters for control qubits and for the target qubit The maximum number of iterations Npf of CNOT gates to determine can be determined.
[0116] The selection by the interval n of the number of repeated CNOT gates between [0;Nbf] to measure bit flip fidelity and between [0;Npf] to measure phase flip fidelity and the sampling function Nmax() is now described. Based on prior knowledge of gate performance, the applicant has identified three ways of determining these factors.
[0117] For the sake of brevity, Nbf and Npf will be referred to as Nmax hereinafter, as they play the same functional role. The purpose of Nmax and sampling is to accurately fit the parameters. (average value of measurements of the target qubit's Pauli operator Z) or It is to decompose the attenuations of (the average value of the measurement obtained by adding complex times the value of the Pauli operator Y to the Pauli operator X of the control qubit or target qubit).
[0118] As mentioned above, since the CNOT gate is bias-preserving, Nmax and sampling, on the one hand, On the other hand, with the measurements of and It differs among the measurements. In particular, and Is It is expected to be several orders of magnitude larger. Therefore, because its attenuation is much slower, the choice of sampling and Nmax is It is much more important for measurement.
[0119] The first possibility is to repeat for Nmax until convergence is reached. Starting with a first Nmax with uniform sampling, perform the measurement sequence of the following operation (320) or operation (330), and then perform the fitting of the following operation (340) or operation (350). Subsequently, the contrast of the measurement after Nmax gates can be analyzed. If the contrast is less than 0.2 times the initial contrast, reduce Nmax. If the contrast is greater than 0.8 times the initial contrast, enlarge Nmax. If the contrast is between these two values, use the fitting result to determine the next Nmax int(4 / (1-2* Set to ))
[0120] For the measurement, Nmax can be initialized to a value of 50 using a scaling factor of 5 and a sampling of Nmax / 10. and For the measurement, Nmax can be initialized to a value of 10 using a scaling factor of 2 and a sampling of 1.
[0121] A second possibility for the measurement is to decompose the exponential decay using sampling to powers of n between 0 and a large value of Nmax. For example, the following sampling for n, i.e., p=[0,1,2,...9] This can be used, which corresponds to Nmax = 19683 gates. Then, the smallest power at which the contrast becomes less than 0.3 times the initial contrast is identified, and this can be used as Nmax in subsequent measurements using smaller sampling.
[0122] Measurements and and A third possibility valid for all measurements is to use prior knowledge of the system. From single CAT measurements of phase flips and bit flips (or other noise-biased qubits used), and knowing the duration of the CNOT gate, , and We can infer an upper bound for . The upper bounds are , , It is indicated by. These upper limits are It can be used to derive Nmax using, where p= or max( , ) is. Sampling is selected so that there are about 10 points within the interval.
[0123] Other methods, such as selecting an arbitrarily high value known to guarantee reliable results, can be used to determine Nmax. As can be easily seen from the above, the method, on the one hand, In measurement and on the other hand and Similar policies are applied to the measurements. As a result, only or and Only can be measured, in which case only Nbf or only Npf needs to be determined. This will also appear in operations (320 to 350).
[0124] Consequently, the result of the operation (300) may be stored in two vectors Repbf[] and Reppf[], or in a single vector Rep[] with an indication of a value Npf expected to be lower than Nbf. As shown below, depending on the order in which the measurements are performed, Rep[] may be implicitly defined by only Nbf and Npf.
[0125] F2. Measurements of average Pauli operators
[0126] After operation (300) is performed, the measurement module (1220) can be used to perform measurements required by the method. In the example shown below, a loop is executed in which the vector Rep[] is popped in operation (310), and then measurement operations (320 and 330) are performed for the corresponding values of n.
[0127] More precisely, in operation (320), the function Meas_Avg_Z(n) is executed to determine the value of the Pauli Z operator after n repetitions of the CNOT gate. More precisely, this is the measurement control qubit logic state and measurement target qubit logic state It involves determining. These logic states will be used to initialize the control qubit and target qubit before applying the CNOT gate n times. After determining these logic states, the control qubit is in the state or It is prepared as, and the target qubit is in state or It is prepared as follows. Then, the CNOT gate is repeated n times, that is, steps S1) through S3) are performed sequentially and this sequence is repeated n times. As described in Section E, the CNOT gate may or may not include component 3. Finally, after the CNOT gate is repeated, the Pauli operator Z of at least the target qubit is measured. In another embodiment, the Pauli operator Z of the control qubit is also measured for the reasons shown below. As is customary for quantum measurements, the average measurement of the target qubit for the number of repetitions n and optionally the average measurement of the control qubit for the number of repetitions n This operation is repeated tens or hundreds of times to obtain the average value(s). It is important that the preparation of the control qubit and the target qubit must be the same for each iteration to determine the average value(s).
[0128] Similarly, in operation (330), the function Meas_Avg_XY(n) is executed to determine the values of the Pauli X and Y operators after n iterations of the CNOT gate. There are some differences between the function Meas_Avg_XY(n) and the function Meas_Avg_Z(n):
[0129] - The function Meas_Avg_XY(n) always measures the Pauli X and Y operators for both the control qubit and the target qubit, and
[0130] - The function Meas_Avg_XY(n) prepares the control qubit and target qubit to states different from the states of the function Meas_Avg_Z(n). Specifically, in the function Meas_Avg_XY(n), the measurement control qubit logic state , phase included in the range [0;2π] , logical state of target qubit for measurement , and the phase included in the set of values {0;π} is determined and fixed first, and then the control qubit is the state It is prepared as, and the target qubit is in state It is prepared as. As in the function Meas_Avg_Z(n), for the target qubit, using the same preparation of the states and for control qubits Measurements are repeated to determine.
[0131] Due to the characteristics of the movements, and Is and It can be determined by averaging the measurements, or the average measurements of the target qubit for the number of iterations n and , and and Calculate first and add and You can obtain.
[0132] obviously, In cases where only is measured (each, and (If only measured), the operation (330) (each, operation (320)) can be bypassed. Similarly, if n > Npf, the operation (330) can be bypassed.
[0133] This embodiment represents one efficient way of popping Rep[] to perform measurements, but there are many other ways that can be considered, provided that all measurements are properly performed to determine average values. This also implies that while the above operations (320 and 330) involve the repetition of measurements to directly determine average values for a given n, these measurements can be performed in a completely different order, provided that sufficient measurements are obtained for each value of n using the same preparation states before the average values are determined. Furthermore, although the above is described as a loop, it can be described as any other type of measurement sequence that enables obtaining average values. Finally, as described above, not all integers need to be tested, and some sampling may be performed.
[0134] F3. Determination of fidelity values
[0135] Finally, once the measurement loop is terminated, the fidelity calculation module (1230) can be used to determine fidelity values.
[0136] As with the above measurements, this is, on the one hand, of the operation (320). Regarding the measurement and, on the other hand, the operation (330). and Measurements are performed through two operations (340 and 350) respectively. Clearly, In cases where only is measured (each, and (If only measured), the operation (350) (each, operation (340)) can be bypassed.
[0137] The operation (340) This is performed by executing the function FitX(Z[]) to determine the curve(s) based on the exponent of n to calculate it. In fact, the applicant Two ways in which it can be calculated were discovered: a simpler and less precise method and a more complex and completely accurate method.
[0138] According to a simpler method, Only needs to be measured. More precisely, the measurements is the bit flip probability value for the target qubit curve to derive Fitted to, and here This is attributed to state preparation and measurement errors regarding the target qubit. This fitting can be performed using any known method for fitting exponential curves, and and It enables everyone to make their own decisions. As a side effect, corresponds to the value of the fitted curve when n is 0.
[0139] According to a more complex method, and All need to be measured. More precisely, these measurements are fitted simultaneously to each of the following two curves:
[0140] , and
[0141]
[0142] Here It is attributed to state preparation and measurement errors regarding the target qubit, and is due to errors occurring in the target qubit during step S2), and is due to errors occurring in the target qubit during step S3), and It is attributed to state preparation and measurement errors for the control qubit, and is due to errors occurring in the control qubit during step S2), and is due to errors occurring in the control qubit during step S3), and This is due to state readiness errors of the control qubit.
[0143] In other words, this fitting can be performed in any conventional manner, and Values that enable calculation and return and It will enable the derivation of
[0144] In an alternative embodiment, each of the two curves can be fitted independently of each other. Since the fitting is one-dimensional and can be performed in parallel, the fitting is slightly faster at the expense of the precision of the results.
[0145] The operation (350) and This is performed by executing the function FitZ(X[];Y[]), which determines curves based on the exponent of n, to calculate it. Here, too, the applicant and Two ways in which it can be calculated were discovered: a simpler and less precise method and a more complex and completely accurate method.
[0146] According to a simpler method, and It is fitted simultaneously to each of the following two curves:
[0147] - , and
[0148] - ,
[0149] Here and This is attributed to state preparation and measurement errors for the target qubit and control qubit, respectively. Here, too, this fitting can be performed in any known manner for fitting exponential curves, and and , and and It allows you to directly decide all of them. Incidentally, and corresponds to the value of the fitted curve when n is 0.
[0150] According to a more complex method, and It is fitted simultaneously to each of the following two curves:
[0151] - , and
[0152] -
[0153] Here It is attributed to state preparation and measurement errors for the control qubit, and is due to errors occurring in the control qubit during step S2), and is caused by errors occurring in the control qubit during step S3), and It is due to state readiness errors of the target qubit, and It is attributed to state preparation and measurement errors regarding the target qubit, and is due to errors occurring in the target qubit during step S2), and This is due to errors occurring in the target qubit during step S3).
[0154] In an alternative embodiment, each of the two curves can be fitted independently of each other. Since the fitting is one-dimensional and can be performed in parallel, the fitting is slightly faster at the expense of the precision of the results.
[0155] Here, too, this fitting can be performed in any known way of fitting polynomial curves, and parameters , , and It allows determining. Afterwards, the fidelity values are and It can be calculated as.
[0156] As shown above, the simpler method or the more complex method , and Any of these can be used for each. Therefore, the functions FitX() and FitZ() can be modified to accommodate any of these combinations.
[0157] After that, the method was terminated and the CNOT gate was characterized.
[0158] Figure 4 uses a simpler method Figure 5 shows an exemplary fitting for obtaining, and uses a more complex method. and This shows an exemplary fitting to obtain .
[0159] These measurements can be used in various ways to optimize the parameters of the CNOT gate. The operating principle is to modify some key parameters of the CNOT gate and identify how the set of errors changes along with them. The optimization routine can be performed as follows:
[0160] 1. class For the parameter k of the CNOT gate between:
[0161] a. Set value k
[0162] b. Calibrate the CNOT gate (if necessary)
[0163] c. Execute measurement sequence
[0164] d. and Execute measurement sequence
[0165] 2. as a function of {pX T ,pZ T ,pZ C Reporting}
[0166] 3. Select optimal operating points defined by iterative code or LDPC code metrics.
[0167] For example, phase flips can be prioritized by optimizing the reduction in gate duration due to their direct proportionality, or bit flip measurements can be prioritized to optimize the re-stabilization duration, which is determined by the shortest time that minimizes errors.
[0168] Parameters can be swept independently or together. The parameters being swept are, for example, the control cat qubit size. , target cat qubit size , CNOT gate duration , CNOT pump amplitude , Target Qubit re-stabilization duration , CNOT pump pulse shape, includes but is not limited to delays between stabilization pulses and CNOT pump pulses.
[0169] Therefore, the above method shows that it combines physical measurements and calculations to measure CNOT gate fidelity values and enable the optimization of gate parameters.
Claims
Claim 1 A method for measuring the probability of bit flips and / or phase flips while performing a CNOT gate between a control qubit having a control qubit resonant frequency and a target qubit having a target qubit resonant frequency, wherein the CNOT gate is performed by a sequence of the following operations: S1) applying dissipative stabilization to the target qubit and the control qubit; S2) applying radiation having the control qubit resonant frequency such that a Hamiltonian arising from the radiation having the control qubit resonant frequency acts substantially simultaneously on the target qubit and the control qubit; and S3) after a selected gate duration, turning off the radiation having the control qubit resonant frequency and applying the dissipative stabilization to the target qubit for a selected re-stabilization duration; and the method comprises: a) providing a superconducting quantum circuit comprising a control qubit and a target qubit that are both noise-biased qubits stabilized in a dissipative manner and are non-linearly coupled to each other; b) including between 0 and a phase flip upper limit. an operation to determine a set of phase flip CNOT iterations comprising multiple distinct integers and / or a set of bit flip CNOT iterations comprising multiple distinct integers included between 0 and a bit flip upper limit; c) an operation to perform the following steps c1) through c5) for each integer npf in the set of phase flip CNOT iterations and / or perform the following steps c6) through c10) for each integer nbf in the set of bit flip CNOT iterations: c1) Measurement control qubit logic state , phase included in the range [0;2π] , logical state of target qubit for measurement , and the phase included in the set of values {0;π} Steps to set up, c2) The state of the above control qubit Prepare as, and the above target qubit state The preparation stage, c3) A step of performing the CNOT gate npf times between the control qubit and the target qubit of operation c2), c4) A step of measuring the Fouly operator X of the target qubit, the Fouly operator Y of the target qubit, the Fouly operator X of the control qubit, and the Fouly operator Y of the control qubit, c5) A step of repeating operations c2) to c4) to obtain an average value for each measurement of operation c4), c6) Measurement control qubit logic state and measurement target qubit logic state Steps to set up, c7) The state of the above control qubit or Prepare as, and the above target qubit state or The preparation stage, c8) A step of performing the CNOT gate nbf times between the control qubit and the target qubit of operation c7), c9) A step of measuring the Pauli operator Z of the target qubit, and c10) a step of repeating operations c7) through c9) to obtain an average value for the measurement of operation c9), and d) if available, the measurements of operation c5) and By fitting the phase flip probability value for the control qubit to each curve based on the exponential function of the number of CNOT iterations and phase flip probability value for the above target qubit Derive and the measurements of operation c10) By fitting it to a curve based on the exponential function of CNOT iterations, the bit flip probability value for the target qubit A method for measuring probability that includes an action for deriving. Claim 2 In claim 1, the operation d) is a phase flip probability value for the target qubit To derive, the measurements curve It includes fitting to, where n is the number of CNOT iterations, and A method for measuring probability attributable to state preparation and measurement errors for the above target qubit. Claim 3 In claim 1 or 2, the operation d) is a phase flip probability value for the control qubit To derive, the measurements curve It includes fitting to, where n is the number of CNOT iterations, and A method for measuring probability attributable to state preparation and measurement errors for the above-mentioned control qubit. Claim 4 In claim 1 or 2, the operation d) is the measurements curve As a fitting to, where n is the number of CNOT iterations, and is due to state preparation and measurement errors for the above control qubit, and is due to errors occurring in the control qubit during step S2), and is due to errors occurring in the control qubit during step S3), and is the fitting, and the phase flip probability value for the control qubit, attributable to state preparation errors of the target qubit. A method of measuring probability that includes calculating. Claim 5 In any one of paragraphs 1, 3 and 4, the operation d) is the measurements curve As a fitting to, where n is the number of CNOT iterations, and is due to state preparation and measurement errors regarding the above target qubit, and is due to errors occurring in the target qubit during step S2), and is the fitting, and the phase flip probability value for the target qubit, attributable to errors occurring in the target qubit during step S3). A method of measuring probability that includes calculating. Claim 6 In claim 1, the above operation d) is the measurements of operation c5) each curve and As fitting simultaneously to, where n is the number of CNOT iterations, and is due to state preparation and measurement errors for the above control qubit, and is due to errors occurring in the control qubit during step S2), and is due to errors occurring in the control qubit during step S3), and is due to state preparation errors of the above-mentioned target qubit, and is due to state preparation and measurement errors regarding the above target qubit, and is due to errors occurring in the target qubit during step S2), and is the simultaneous fitting and phase flip probability value for the target qubit, which is attributed to errors occurring in the target qubit during step S3). and phase flip probability value for the above control qubit A method of measuring probability that includes calculating. Claim 7 In any one of claims 1 to 6, the operation d) is a bit flip probability value for the target qubit To derive the measurements from operation c10) curve It includes fitting to, where n is the number of CNOT iterations, and A method for measuring probability attributable to state preparation and measurement errors for the above target qubit. Claim 8 In any one of claims 1 to 6, the operation c9) further comprises measuring the Pauli operator Z of the control qubit, and the operation d) measures the measurements of operation c10) on each of the respective curves and As fitting simultaneously to, where n is the number of CNOT iterations, and is due to state preparation and measurement errors regarding the above target qubit, and is due to errors occurring in the target qubit during step S2), and is due to errors occurring in the target qubit during step S3), and is due to state preparation and measurement errors for the above control qubit, and is due to errors occurring in the control qubit during step S2), and is due to errors occurring in the control qubit during step S3), and is the simultaneous fitting, which is due to state preparation errors of the control qubit, and the bit flip probability value for the target qubit A method of measuring probability that includes calculating. Claim 9 A method for measuring probability, wherein in any one of claims 1 to 8, step S2) comprises turning off the dissipation stabilization for the target qubit, or applying another stabilization conditional to the control qubit for the target qubit. Claim 10 A computer program (120) comprising instructions (122) that cause the processing circuit to perform the method of any one of claims 1 to 9 when executed by the processing circuit (102). Claim 11 A carrier comprising a computer program (120) according to paragraph 10, wherein the carrier comprises one of an electronic signal, an optical signal, a wireless signal, or a computer-readable storage medium. Claim 12 A computer program product (116) comprising a non-transient computer-readable medium (118) on which a computer program (120) according to paragraph 10 is stored.