JP7124184B2 - Fidelity Estimation for Quantum Computing Systems - Google Patents

Description

This specification relates to quantum computing.

A quantum circuit is a model of quantum computation in which the computation involves a sequence of quantum gates. Quantum circuits are sensitive to errors due to, for example, decoherence and other quantum noise. The effect of errors in quantum circuits may be characterized by the fidelity of the quantum circuit. Fidelity is a quantum circuit metric that indicates the quality and reliability of the quantum circuit.

The present specification relates to estimating quantum hardware fidelity in quantum computing systems. In particular, this document describes techniques for estimating the fidelity of complex non-Clifford quantum circuits with multiple qubits.

In general, one inventive aspect of the subject matter described herein is the action of accessing a set of quantum gates and the action of sampling a subset of quantum gates from the set of quantum gates, wherein the subset of quantum gates is a quantum circuit. which defines the action, the action of applying a quantum circuit to a quantum system and making measurements on the quantum system to determine the output information of the quantum system, and the quantum system based on the application of the quantum circuit to the quantum system. It can be implemented in a method that includes the action of calculating output information and the action of estimating fidelity of a quantum circuit based on the determined and calculated output information of the quantum system.

Other implementations of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the method. A system of one or more computers can be configured to perform a particular operation or action by installing software, firmware, hardware, or a combination thereof on the system that causes the system to perform the action when it operates. can. One or more computer programs, when executed by a data processing apparatus, can be configured to perform particular operations or actions by including instructions that cause the apparatus to perform actions.

These and other implementations can each optionally include one or more of the following features, alone or in combination. In some implementations, estimating the fidelity of the quantum system includes fitting the determined output information of the quantum system to the calculated output information of the quantum system.

In some cases, fitting the determined output information of the quantum system to the computed output information of the quantum system to estimate the fidelity of the quantum circuit is the computed output information of the quantum system and the perfect mixture ( totally mixed), and estimating the fidelity of the quantum circuit by comparing the defined convex combinations with the determined output information of the quantum system.

In some implementations, convex joins are given by:

ここで、αは量子回路の忠実度を表し、|ψ〉は量子システムへの量子回路の適用に基づく量子システムの計算された量子状態を表し、I/Nは完全混合状態を表す。

where α represents the fidelity of the quantum circuit, |ψ〉 represents the calculated quantum state of the quantum system based on the application of the quantum circuit to the quantum system, and I/N represents the perfect mixed state.

Optionally, the method comprises repeatedly sampling a subset of quantum gates from a set of quantum gates until completion of an event, each subset of quantum gates defining a respective quantum circuit; For each sampled subset, applying a respective quantum circuit to the quantum system and performing respective measurements on the quantum system to determine output information of the quantum system; and applying the respective quantum circuit to the quantum system. and estimating the fidelity of each quantum circuit based on the determined output information and the calculated output information of the quantum system.

In some implementations, event completion occurs when the estimated fidelity uncertainty falls below a predetermined threshold.

In some cases, the set of quantum gates includes a universal set of quantum gates.

In some cases, the set of quantum gates includes single-qubit quantum gates and two-qubit quantum gates.

In some implementations, each gate in the set of quantum gates is associated with a respective quantum gate fidelity.

In other implementations, the sampled subset of quantum gates includes the same number of quantum gates of comparable respective quantum gate fidelities.

In some cases, sampling the subset of quantum gates from the set of quantum gates includes randomly sampling the subset of quantum gates from the set of quantum gates.

The subject matter described herein may be implemented in particular ways to achieve one or more of the following advantages.

Quantum hardware, eg systems of quantum gates, are inherently error prone and errors need to be characterized before they can be corrected. Full characterization by processes such as quantum process tomography is impractical, for example, from a computational cost and efficiency point of view. For example, quantum process tomography becomes extremely expensive as the number of qubits in the quantum system increases, as the number of measurements required grows exponentially. In addition, full characterization is often unnecessary, as in practice estimating more general quantities such as average fidelity may be sufficient.

An alternative method for characterizing errors involves using a restricted set of quantum gates in quantum hardware. For example, randomized benchmarking with Clifford gates is a greatly extended method for measuring the fidelity of single-qubit and two-qubit gates. However, such techniques cannot be applied to directly measure the fidelity of quantum circuits employing universal quantum gate sets. Such methods are used because the quantum states produced by these definitive families of circuits can be very different in important aspects from the quantum states produced by circuits employing universal quantum gates. The results obtained may therefore not be immediately of interest or may be considered exemplary and impractical. For example, Clifford circuits are always efficiently simulated using classical computers and may not exhibit a Porter-Thomas distribution.

As the complexity and diversity of quantum hardware increases, it is imperative to measure circuit fidelity for quantum circuits that are not of the type that can be easily and efficiently simulated by classical computers.

A system implementing fidelity estimation for quantum computing systems as described herein can estimate the fidelity of increasingly complex quantum hardware.

Systems implementing fidelity estimation for quantum computing systems as described herein are applicable to both digital and analog models of quantum computing. With a digital model of quantum computation, the system does not require the use of a limited set of quantum gates. For example, a system may utilize complex random quantum circuits composed of gates chosen from a universal set of quantum gates, thus increasing complexity of quantum circuits with increasing numbers of qubits and quantum gates. Direct measurement of quantum circuit fidelity becomes possible. Similarly, for analog models of quantum computing, the system allows directly determining the fidelity of quantum hardware implementing continuous Hamiltonian evolution.

Unlike other systems and methods for estimating the fidelity of quantum circuits, the system implementing fidelity estimation for quantum computing systems as described herein is such that the fidelity of the quantum circuit is It allows the power of the qubit number to be estimated without having to make several measurements of it.

The details of one or more implementations of the subject matter of this specification are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the subject matter will become apparent from the description, drawings, and claims.

FIG. 1 shows an exemplary system for fidelity estimation; FIG. 1 shows an exemplary system for fidelity estimation; FIG. 4 is a flow diagram of an exemplary process for benchmarking fidelity of quantum circuits; FIG. FIG. 4 is a flow diagram of an exemplary process for fitting the determined output information of the quantum system to the calculated output information of the quantum system to estimate the fidelity of the quantum circuit; FIG. 4 is a flow diagram of an exemplary process for benchmarking the fidelity of quantum hardware; FIG. FIG. 4 is a flow diagram of an exemplary process for fitting the determined output information of the quantum system to the calculated output information of the quantum system to estimate the fidelity of the quantum hardware;

Like reference numerals and designations in the various drawings indicate like elements.

This specification describes methods and systems for fidelity benchmarking for quantum hardware, eg, quantum circuits. A random instance of a quantum circuit from a given universal family of available quantum gates is selected, and the statistics of the selected quantum circuit for the selected measurements are numerically calculated using classical simulations. calculated to A sequence of runs of the same quantum circuit is performed and measurements of the quantum hardware are made. The fidelity of a quantum circuit is estimated using numerically obtained prediction statistics and experimentally determined statistics.

Exemplary Operating Environment FIG. 1A shows an exemplary system 100 for fidelity estimation. Exemplary system 100 implements classical or quantum mechanical computing on one or more classical or quantum computing devices at one or more locations where the systems, components, and techniques described below can be implemented. It is an example of a system implemented as a computer program.

The system includes quantum hardware 102 in communication with fidelity estimation system 104 . Quantum hardware 102 includes a quantum system that may include one or more qubits 106 , eg, qubits 108 . One or more qubits may be used to perform algorithmic operations or quantum computations. The particular realization of one or more qubits depends on the type of algorithmic operation or quantum computation that the quantum computing device is performing. For example, qubits may include qubits implemented by atomic, molecular, or solid-state quantum systems. In other examples, the qubits may include, but are not limited to, superconducting qubits or semiconductor qubits. For clarity, four qubits are shown in FIG. 1A, but the system may include a smaller or larger number of qubits.

Each of the one or more qubits 106 may interact with one or more other qubits, eg, through respective controllable couplings. In some examples, one or more qubits 106 may undergo nearest neighbor interactions.

One or more qubits 106 may be arranged in various ways. The particular arrangement of one or more qubits may depend on the algorithmic operation or quantum computation the qubits are being used to perform. In some examples, the qubits may be arranged in a one-dimensional array, such as a chain. In other examples, the qubits may be arranged in a two-dimensional array, such as a grid. For clarity, the four qubits are shown in a one-dimensional array in FIG. 1, but the system may arrange the qubits in other ways.

Quantum hardware 102 includes a set of quantum gates 110 . The set of quantum gates 110 includes single-qubit gates, such as quantum gate 112, and two-qubit gates, such as quantum gate 114. FIG. A single-qubit quantum gate is a quantum gate that operates on a single qubit. Exemplary single-qubit gates include, but are not limited to, Hadamard gates, Pauli X, Y, or Z gates, or phase shift gates. A two-qubit quantum gate is a quantum gate that operates on two qubits. Exemplary two-qubit gates include, but are not limited to, swap gates, control gates, tofoli gates, or Fredkin gates.

The set of quantum gates 110 may include a universal set of quantum gates. A universal set of quantum gates is a set of gates that can reduce any possible computational operation on a quantum computing device. For example, one example of a universal set of single and two-qubit quantum gates includes Hadamard gates, π/8 gates, and controlled-NOT gates.

A set of quantum gates 110 may be sampled to define one or more quantum circuits, such as quantum circuit 116 . For clarity, quantum circuit 116 includes a fixed number of representative quantum gates, e.g., quantum gates 112 and 114, but quantum circuits defined by a sampled set of quantum gates may be larger or Fewer quantum gates may be included.

Sampled quantum circuit 116 receives as input a quantum system, eg, one or more qubits, prepared in an initial state 122, eg, ground state. The quantum circuit operates on the quantum system and outputs the quantum system in final state 120 . Here, the final state is determined by the operations performed on the quantum system by the quantum circuit.

Each quantum gate within the set of quantum gates 110 and each quantum circuit defined in a subset of the set of quantum gates 110 is associated with a respective gate fidelity or quantum circuit fidelity. Quantum gate fidelity and quantum circuit fidelity provide a measure of how reliably a gate or circuit transforms an input into an expected output. For example, a Pauli X quantum gate operates on a single qubit, mapping the 0 state to the 1 state and the 1 state to the 0 state. The fidelity of a Pauli X gate indicates how accurately and reliably the mapping is achieved, e.g., whether the gate reliably maps the 0 state to the 1 state and vice versa It may contain numbers in between.

Quantum hardware 102 includes one or more measurement devices 118 , such as measurement device 124 . Measurement device 118 may operate on the quantum system, eg, measurement device 124 operates on the quantum system in final state 120 to determine properties of the quantum system device.

Fidelity estimation system 104 may include classical or quantum mechanical processing devices and communicates with quantum hardware 102 . The fidelity estimation system 104 may be configured to access the set of quantum gates 110 and sample a subset of quantum gates from the set of quantum gates 110 to define each quantum circuit, eg, quantum circuit 116. good. Fidelity estimation system 104 causes a defined quantum circuit to be repeatedly applied to a quantum system, e.g., one or more qubits 106, and uses one or more measurement devices 118 to obtain the quantum system's output information. A respective measurement may be made on the quantum system, eg, to determine a statistic.

Fidelity estimation system 104 calculates output information, e.g., expected statistics, of the quantum system based on application of the quantum circuit to the quantum system, e.g., after applying a quantum circuit defined on the quantum system; fitting the determined output information of the quantum system to the calculated output information of the quantum system to estimate the fidelity of the quantum circuit. Estimating fidelity of quantum circuits is described in more detail below with respect to FIGS.

FIG. 1B shows an exemplary system 150 for fidelity estimation. Exemplary system 150 is a classical or quantum mechanical computing device on one or more classical or quantum computing devices at one or more locations in which the systems, components, and techniques described below may be implemented. It is an example of a system implemented as a computer program.

The system includes quantum hardware 152 in communication with fidelity estimation system 154 . Quantum hardware 152 includes a quantum system that may include one or more qubits 156 , eg, qubits 158 . As described above with respect to FIG. 1A, one or more qubits may be used to perform algorithmic operations or quantum computations. The particular realization of one or more qubits depends on the type of algorithmic operation or quantum computation that the quantum computing device is performing. For example, qubits may include qubits implemented by atomic, molecular, or solid-state quantum systems. In other examples, the qubits may include, but are not limited to, superconducting qubits or semiconductor qubits. For clarity, four qubits are shown in FIG. 1B, but the system may include a smaller or larger number of qubits.

Each of the one or more qubits 156 may interact with one or more other qubits, eg, through respective controllable couplings. In some examples, one or more qubits 156 may undergo nearest neighbor interactions.

One or more qubits 156 may be arranged in various ways. The particular arrangement of one or more qubits may depend on the algorithmic operation or quantum computation the qubits are being used to perform. In some examples, the qubits may be arranged in a one-dimensional array, such as a chain. In other examples, the qubits may be arranged in a two-dimensional array, such as a grid. For clarity, the four qubits are shown in a one-dimensional array in FIG. 1, but the system may arrange the qubits in other ways.

Quantum hardware 152 includes one or more components 160 for performing continuous Hamiltonian evolution. The one or more components 160 for performing continuous Hamiltonian evolution implement one or more Hamiltonians, which in turn define the evolution of the quantum system to which it is applied, the unitary operator may be determined. For example, component 160 may implement Hamiltonian H, which in turn yields unitary operator 162 . A unitary operator 162 defines the evolution of a quantum system, provided with an initial state 164 and resulting in a final state 166 of the quantum system.

Each successive Hamiltonian evolution of a quantum system is associated with a respective quantum hardware fidelity. Quantum hardware fidelity, as described above with respect to FIG. 1A, is a measure of how reliably the hardware transforms inputs into expected outputs.

Quantum hardware 152 includes one or more measurement devices 168 , such as measurement device 172 . Measurement device 168 may operate on the quantum system to determine properties of the quantum system, eg, measurement device 172 operates on the quantum system in final state 166 .

Fidelity estimation system 154 may include classical or quantum mechanical processing devices and communicates with quantum hardware 152 . Fidelity estimation system 154 may be configured to access quantum hardware 512 and select components 160 for a particular continuous Hamiltonian evolution. The fidelity estimation system 154 is for the quantum hardware to repeatedly perform continuous Hamiltonian evolution corresponding to selected components, e.g., one or more qubits 156, on the quantum system to determine the output information of the quantum system. , the respective measurements may be performed on the quantum system.

The fidelity estimation system 154 calculates the output information of the quantum system based on performing a selected continuous Hamiltonian evolution on the quantum system and determines the quantum system's decision to estimate the fidelity of the quantum hardware. and fitting the calculated output information to the calculated output information of the quantum system. Estimating quantum hardware fidelity is described in more detail below with respect to FIGS.

Programming the Hardware FIG. 2 is a flowchart of an exemplary process 200 for benchmarking the fidelity of quantum circuits. For convenience, process 200 is described as being performed by a system of one or more classical or quantum mechanical computing devices at one or more locations. For example, a quantum computing system, such as quantum computing system 100 of FIG.

The system accesses a set of quantum gates (step 202). A set of quantum gates may include one or more single-qubit gates. Each quantum gate in the set of quantum gates may be associated with a respective quantum gate fidelity. The set of quantum gates may include one or more two-qubit gates. Exemplary single and two-qubit gates are described above with respect to FIG. 1A. In some implementations, the set of quantum gates includes a universal set of quantum gates. A universal set of quantum gates is described above with respect to FIG. 1A.

The system samples a subset of quantum gates from the set of quantum gates (step 204). In some implementations, the system may randomly sample a subset of quantum gates from the set of quantum gates. A subset of sampled quantum gates defines a quantum circuit. For example, by randomly sampling a subset of quantum gates from the available set of quantum gates, the system generates random instances of quantum circuits.

In some implementations, the system may repeatedly sample a set of quantum gates or a subset of quantum gates, each sampled subset defining a respective quantum circuit. The system may sample a subset of quantum gates containing the same number of quantum gates of comparable respective quantum gate fidelities, e.g., instances of quantum circuits defined by the sampled subsets of quantum gates are comparable may include the same number of quantum gates with similar quantum gate fidelity. By sampling a subset of quantum gates containing the same number of quantum gates of comparable respective quantum gate fidelity, the system can improve the consistency of results obtained by process 200 and avoid large systematic errors. .

The system applies the quantum circuit to the quantum system and performs measurements on the quantum system to determine output information, eg, statistics of the quantum system (step 206). For example, the system includes, or possibly accesses, a quantum system, e.g., a quantum system comprising one or more qubits as shown in FIG. The circuit may be applied repeatedly to the initialized state of the quantum system. For each quantum circuit application, the system may perform respective measurements on the quantum system and use the measurement results to determine the output information of the quantum system. As an example, the system samples a subset of the quantum gates that define each quantum circuit, runs m runs of the quantum circuit on the quantum system of interest, and performs a computationally measured sequence of bitstrings {x ₁ ,x ₂ ,…,x _m }.

As explained above, in some implementations, the system may repeatedly sample subsets of quantum gates from a set of quantum gates, each sampled subset defining a respective quantum circuit. In such a case, the system may iteratively apply each sampled quantum circuit to the quantum system and, for each sampled circuit, determine the respective statistics of the quantum system on the quantum system. each measurement.

The system calculates output information of the quantum system, eg expected, eg exact or ideal statistics, based on applying the quantum circuit to the quantum system (step 208). For example, the system may use available computational techniques, eg classical computing techniques, to compute the output information of the quantum system after applying the quantum circuit to the quantum system.

Continuing with the above example, to determine the output information of the quantum system, the system may also compute a set of probabilities {p(y _j )} corresponding to the probability of obtaining each possible bitstring y _j . good. As described above with respect to step 204, in some implementations the system may repeatedly sample a subset of quantum gates from the set of quantum gates, each sampled subset defining a respective quantum circuit. do. In such cases, the system may compute, for each sampled quantum circuit, a set of probabilities corresponding to the probability of obtaining each possible bitstring.

The system estimates the fidelity of the quantum circuit based on the determined and calculated output information of the quantum system (step 210). The system may estimate the fidelity of the quantum circuit by fitting the determined output information of the quantum system to the calculated output information of the quantum system. The system calculates the results of the measurements made in step 206 as (i) the output information of the quantum system based on the application of the quantum circuit to the quantum system as calculated in step 208, and (ii) the statistics of the fully mixed quantum states. may be fitted to the target mixture. Fitting the determined output information of the quantum system to the calculated output information of the quantum system to estimate the fidelity of the quantum circuit is described in more detail below with respect to FIG.

If the system repeatedly samples a subset of quantum gates to define multiple quantum circuits, then the system uses each determined output information for the quantum system to estimate the respective fidelity of each quantum circuit. to each computed output information of the quantum system. The system may repeatedly sample a subset of quantum gates from the set of quantum gates until the completion of the event, eg, when the estimated fidelity uncertainty is below a predetermined threshold. By increasing the number of iterations, the uncertainty of the estimated fidelity may be reduced to a desired threshold of certainty, for example according to the inverse square root of the iteration number.

FIG. 3 illustrates an exemplary process for fitting determined output information, e.g., statistics, of a quantum system to computed output information, e.g., statistics, of a quantum system to estimate fidelity of a quantum circuit. 300 flow chart. For convenience, process 300 is described as being performed by a system of one or more classical or quantum mechanical computing devices at one or more locations. For example, process 300 can be performed by one or more classical processors appropriately programmed according to the specification, such as classical processor 104 of FIG. 1A.

式(1)において、αは量子回路の忠実度を表し、|ψ〉は量子システムへの量子回路の適用に基づく量子システムの計算された量子状態を表し、I/Nは|ψ〉を含むヒルベルト空間の次元Nを有する完全混合状態を表す。 The system defines the computed output information of the quantum system described above with respect to step 208 of FIG. 2, and a convex combination of perfect mixed quantum states (step 302). For example, a convex combination may be given by equation (1) below.

In equation (1), α represents the fidelity of the quantum circuit, |ψ〉 represents the calculated quantum state of the quantum system based on the application of the quantum circuit to the quantum system, and I/N contains |ψ〉 represents a perfect mixed state with dimension N in the Hilbert space.

The system estimates the fidelity of the quantum circuit (step 304 ). For example, the system may estimate the fidelity of the quantum circuit by comparing the defined convex combination to the determined output information of the quantum system and determining the value of the parameter α.

を数値的に計算してもよい。一定の仮定の下で、たとえば量子回路は十分に長い(回路の深さは、log(n)において可能な補正までn^1/Dよりも速く増えることはなく、ここでnはキュービットの数であり、Dはキュービットアレイの寸法であり、たとえば図1Aに示すように、1Dアレイのキュービットの場合、D=1、深さ=nであり、またはキュービットの任意のペア間で2キュービットゲートが実行される仮定の構成に対して一定の深さ、もしくはnの対数の深さでは、Dは無限である場合がある)と仮定すると、パラメータα、たとえば量子回路忠実度は、α=c+ln(N)+γによって推定されてもよく、ここでγはオイラー定数であり、cは上記で定義される。いくつかの実装形態では、αの推定における誤差は、k/m^1/2によって与えられてもよく、ここでk≒1である。これは必要とされる測定の数を表してもよく、キュービットの数とは無関係である。 Continuing with the example given above in FIG. 2, the system computes each sampled subset of quantum gates for the corresponding experimentally obtained sequence of bitstrings {x ₁ , x ₂ , . . . , x _m }. to the amount

can be calculated numerically. Under certain assumptions, e.g. a quantum circuit is long enough (the depth of the circuit does not grow faster than n ^1/D to a possible correction in log(n), where n is the number of qubits , and D is the dimension of the qubit array, for example, for a 1D array of qubits, D=1, depth=n, or 2 between any pair of qubits, as shown in Figure 1A. Assuming that for the hypothetical configuration in which the qubit gate is performed, D may be infinite at a constant depth, or logarithmic depth of n), the parameter α, e.g., the quantum circuit fidelity, is It may be estimated by α=c+ln(N)+γ, where γ is Euler's constant and c is defined above. In some implementations, the error in estimating α may be given by k/m ^1/2 , where k≈1. This may represent the number of measurements required and is independent of the number of qubits.

を使用する代わりに、システムは、量

、たとえば確率の2乗和を使用してもよい。他の量もまた使用されてもよい。本量は量子回路のシミュレーションを使用して計算されてもよい統計集合であることが必須条件であり、しかも本量は量子回路の物理的実装における誤差に等しく反応しなければならない。 In some implementations, the system may estimate the fidelity of a quantum circuit through numerical comparisons with any number of statistical aggregates. For example, the quantity as in the above case

Instead of using

, for example, the sum of squared probabilities may be used. Other amounts may also be used. It is imperative that the quantity be a set of statistics that may be computed using simulations of the quantum circuit, and that the quantity should respond equally to errors in the physical implementation of the quantum circuit.

As explained above, in some implementations, the system may repeatedly sample a subset of quantum gates and iteratively estimate the corresponding fidelity for the quantum circuit defined by the subset of quantum gates. By repeatedly estimating fidelity for quantum circuits, the system can increase the reliability of fidelity estimates and reduce the likelihood that systematic errors or correlations will affect the results obtained. As a simple example, by repeatedly estimating the fidelity, the system can determine that the quantum hardware is working as intended.

FIG. 4 is a flowchart of an exemplary process 400 for benchmarking quantum hardware fidelity. For convenience, process 400 is described as being performed by a system of one or more classical or quantum mechanical computing devices at one or more locations. For example, a quantum computing system, such as quantum computing system 150 of FIG. 1B, appropriately programmed according to the description herein, can perform process 400.

The system accesses quantum hardware (step 402). Quantum hardware may be configured to perform one or more different continuous Hamiltonian evolutions, as described above with respect to FIG. 1B. Each successive Hamiltonian evolution may be associated with a respective quantum hardware fidelity.

The system selects a particular continuous Hamiltonian evolution (step 404). For example, a system may select one or more components configured to implement a particular Hamiltonian that determines the unitary operator that defines the evolution of the quantum system to which it applies. In some cases, the system may randomly select a particular continuous Hamiltonian evolution.

In some implementations, the system may iteratively select a continuous Hamiltonian evolution. For example, in some cases, quantum hardware is configured to perform one or more different continuous Hamiltonian evolutions on one or more interacting qubits, with each qubit interaction having an associated respective fidelity. may be In these cases, the system may iteratively select successive Hamiltonian evolutions containing interactions of comparable fidelity. By choosing a continuous Hamiltonian evolution containing qubit interactions of comparable fidelity, the system can improve the consistency of the results obtained by process 400 and avoid large systematic errors.

The system performs a selected continuous Hamiltonian evolution of the quantum system and makes measurements on the quantum system to determine the output information value of the quantum system (step 406). For example, the system includes or optionally accesses a quantum system, e.g., a quantum system including one or more qubits as shown in FIG. The selected continuous Hamiltonian evolution may be iteratively performed by selecting one or more corresponding components that implement the Hamiltonian yielding unitary operators that define the evolution. For each evolution of the quantum system, the system may make respective measurements on the quantum system and use the measurements to determine the output information of the quantum system.

As explained above, in some implementations, the system may iteratively select a continuous Hamiltonian evolution. In such a case, the system iterates through each selected continuous Hamiltonian evolution of the quantum system and performs each measurement on the quantum system to determine the respective output information of the quantum system for the selected continuous Hamiltonian evolution. may be performed.

The system computes the output information of the quantum system on the quantum system based on performing the selected continuous Hamiltonian evolution (step 408). For example, the system may use available computational techniques, eg, classical computing techniques, to compute the output information of the quantum system after a selected continuous evolution of the quantum system.

The system estimates the fidelity of the quantum hardware based on the determined and calculated output information of the quantum system (step 410). The system may estimate the fidelity of the quantum hardware by fitting the determined output information of the quantum system to the calculated output information of the quantum system. The system combines the results of the measurements made in step 406 with (i) the quantum system's output information based on performing the selected continuous Hamiltonian evolution on the quantum system as computed in step 408, and (ii) the complete It may be fitted to statistical mixtures with mixed quantum states. Fitting the determined output information of the quantum system to the calculated output information of the quantum system to estimate the fidelity of the quantum hardware is described in more detail below with respect to FIG.

If the system iteratively selects a continuous Hamiltonian evolution, the system selects each determined value for the quantum system to estimate the respective fidelity of each quantum hardware corresponding to each selected continuous Hamiltonian evolution. Fit the output information to each calculated output information of the quantum system. The system may iteratively select a continuous Hamiltonian evolution until the completion of the event, eg, when the estimated fidelity uncertainty is below a predetermined threshold. By increasing the number of iterations, the uncertainty of the estimated fidelity may be reduced to a desired threshold of certainty, for example according to the inverse square root of the iteration number.

FIG. 5 is a flowchart of an exemplary process 500 for fitting the determined output information of a quantum system to the calculated output information of a quantum system to estimate fidelity of quantum hardware. For convenience, process 500 is described as being performed by a system of one or more classical or quantum mechanical computing devices at one or more locations. For example, one or more classical processors appropriately programmed according to the specification, such as classical processor 104 of FIG. 1, can perform process 500 .

式(1)において、αは量子回路の忠実度を表し、|ψ〉は量子システム上で連続ハミルトニアン進化を行うことに基づく量子システムの計算された量子状態を表し、I/Nは|ψ〉を含むヒルベルト空間の次元Nを有する完全混合状態を表す。 The system defines the computed output information of the quantum system described above with respect to step 408 of FIG. 4 and a convex combination of perfect mixed quantum states (step 502). For example, a convex combination may be given by equation (1) below.

In equation (1), α represents the fidelity of the quantum circuit, |ψ〉 represents the computed quantum state of the quantum system based on performing continuous Hamiltonian evolution on the quantum system, and I/N is |ψ〉 represents a perfect mixture state with dimension N in the Hilbert space containing .

The system estimates the fidelity of the quantum hardware by comparing the defined convex combination in equation (1) with the determined output information of the quantum hardware described above with respect to step 406 of FIG. 504). For example, the system may estimate the fidelity of the quantum hardware by comparing the defined convex combination to the determined output information of the quantum system and determining the value of the parameter α.

As explained above, in some implementations, the system may iteratively select a continuous Hamiltonian evolution and iteratively estimate the corresponding fidelity for the quantum hardware corresponding to the continuous Hamiltonian evolution. By repeatedly estimating the fidelity for quantum hardware, the system can increase the reliability of the fidelity estimate and reduce the likelihood that systematic errors or correlations will affect the results obtained. As a simple example, by repeatedly estimating the fidelity, the system can determine that the quantum hardware is working as intended.

Implementations of digital and/or quantum objects and digital functional operations and quantum operations described herein can be tangibly embodied in digital electronic circuits, suitable quantum circuits, or more generally in quantum computing systems. in digital and/or quantum computer software or firmware, in digital and/or quantum computer hardware including the structures disclosed herein and their structural equivalents, or in one or more of them May be implemented in combination. The term "quantum computing system" may include, but is not limited to, a quantum computer, a quantum information processing system, a quantum cryptographic system, or a quantum simulator.

Implementations of digital and/or quantum objects described herein may be implemented as one or more digital and/or quantum computer programs, for example to be executed by a data processing apparatus, or It may be implemented as one or more modules of digital and/or quantum computer program instructions encoded on a tangible, non-transitory storage medium for controlling the operation of a data processing apparatus. A 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 qubits, or a combination of one or more thereof. be. Alternatively or additionally, the program instructions are transmitted to suitable receiver apparatus for execution by an artificially generated propagated signal, such as a data processing apparatus, capable of encoding digital and/or quantum information. may be encoded on machine-generated electrical, optical, or electromagnetic signals generated to encode digital and/or quantum information for

The terms quantum information and quantum data refer to information or data carried by, held or stored in a quantum system, where the least nontrivial system is a qubit, e.g., a system that defines units of quantum information. be. The term "qubit" is understood to encompass any quantum system that may be properly approximated as a two-level system in the corresponding context. Such quantum systems may include, for example, multi-level systems with more than two bells. By way of example, such systems may include atomic qubits, electronic qubits, photon qubits, ion qubits, or superconducting qubits. In many implementations, the computational basis state is identified by the ground, first excited state, but other setups are contemplated where the computational state is identified by the higher-level excited state. understood to be The term "data processing apparatus" refers to digital and/or quantum data processing hardware and includes, by way of example, programmable digital processors, programmable quantum processors, digital computers, quantum computers, multiple digital and quantum processors or computers, and their It encompasses all kinds of apparatus, devices and machines for processing digital and/or quantum data, including combinatorial. The device may be a dedicated logic circuit, such as an FPGA (Field Programmable Gate Array), an ASIC (Application Specific Integrated Circuit), or a quantum simulator, such as a quantum data processor designed to simulate or generate information about a particular quantum system. It can also be or further include a device. In particular, quantum simulators are purpose-built quantum computers that are incapable of performing universal quantum computations. A device, possibly in addition to hardware, code that creates an execution environment for digital and/or quantum computer programs, e.g. code that makes up processor firmware, protocol stacks, database management systems, operating systems, or It can include one or more combinations of.

A digital computer program, sometimes called or described as a program, software, software application, module, software module, script, or code, may be any programming language, including compiled or interpreted languages, or declarative or procedural languages. A digital computer program may be written in any form, and may be deployed in any form, including as a stand-alone program or as modules, components, subroutines, or other units suitable for use in a computing environment. can be done. Quantum computer programs, sometimes called or described as programs, software, software applications, modules, software modules, scripts, or code, are written in programming languages, including compiled or interpreted languages, or declarative or procedural languages. It may be written in any form, converted into a suitable quantum programming language, or written in a quantum programming language, such as QCL or Quipper.

Digital and/or quantum computer programs may, but need not, correspond to files in the file system. A program may store other programs or data, e.g., in part of a file containing one or more scripts stored in a markup language document, in a single file dedicated to the program, or in multiple coordinated files. ), eg, in a file that stores one or more modules, subprograms, or portions of code. A digital and/or quantum computer program may be written on one digital or quantum computer or multiple computers located at one site or distributed across multiple sites and interconnected by a digital and/or quantum data communication network. can be deployed to run on any digital and/or quantum computer. A quantum data communication network is understood to be a network that may transmit quantum data using quantum systems, for example qubits. Generally, digital data communication networks cannot transmit quantum data, but quantum data communication networks may transmit both quantum and digital data.

The processes and logic flows described herein can be executed by one or more programmable digital and/or quantum computers, operating accordingly on one or more digital and/or quantum processors, input digital and It runs one or more digital and/or quantum computer programs to perform functions by operating on quantum data and generating output. Processes and logic flows may also be performed by dedicated logic circuits, such as FPGAs or ASICs, or quantum simulators, or by a combination of dedicated logic circuits or quantum simulators and one or more programmed digital and/or quantum computers. It is possible and it is also possible for the device to be implemented as these.

A system of one or more digital and/or quantum computers is "configured to" perform a particular operation or action means software, firmware, hardware, or any other software, firmware, or hardware that, when in operation, causes the system to perform operations or actions. means that the system has installed a combination of One or more digital and/or quantum computers are configured to perform a particular operation or action when one or more programs are executed by a digital and/or quantum data processing device. contains instructions that cause an action or action to be taken. A quantum computer may also receive instructions from a digital computer that, when executed by a quantum computing device, cause the device to perform operations or actions.

Digital and/or quantum computers suitable for executing digital and/or quantum computer programs are based on general purpose or dedicated digital and/or quantum processors, or both, or any other kind of central digital and/or quantum processing unit be able to. Generally, a central digital and/or quantum processing unit transfers instructions and digital and/or quantum data from read-only memory, random-access memory, or quantum data, such as quantum systems suitable for transmission of photons, or combinations thereof. will receive.

The essential elements of a digital and/or quantum computer are a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and digital and/or quantum data. The central processing unit and memory may be supplemented by dedicated logic circuits or quantum simulators or may be incorporated into dedicated logic circuits or quantum simulators. Generally, a digital and/or quantum computer also includes one or more mass storage devices for storing digital and/or quantum data, such as magnetic, magneto-optical disks, optical disks, or for storing quantum information. or operable to receive digital and/or quantum data from or transfer digital and/or quantum data to these mass storage devices, or both will be connected to However, digital and/or quantum computers need not have such devices.

Digital and/or computer readable media suitable for storing digital and/or quantum computer program instructions and digital and/or quantum data include, by way of example, semiconductor memory devices such as EPROM, EEPROM, and flash memory devices, magnetic disks , for example internal or removable disks, magneto-optical disks, CD-ROM and DVD-ROM disks, and quantum systems, for example trapped atoms or electrons, in any form of non-volatile digital and/or quantum memory, media, memory Including devices. Quantum memories are devices that can store quantum data with high fidelity and efficiency for long periods of time, such as light-matter interfaces where light is used for transmission, and quantum features of quantum data such as superposition or quantum coherence. , is understood to be a substance for preservation.

The various systems described herein, or control of portions thereof, are stored on one or more non-transitory machine-readable storage media and run on one or more digital and/or quantum processing devices It can be implemented in a digital and/or quantum computer program product containing instructions. The systems described herein, or portions thereof, can each be implemented as an apparatus, method, or system, wherein the system includes one or more digital and/or quantum processing devices and and a memory for storing executable instructions to perform the described operations.

Although this specification contains many specific implementation details, these should not be construed as limitations on the scope of what may be claimed, but rather are specific to the specific implementation. It should be construed as a description of the features that may exist. Certain features that are described in this specification in the context of separate implementations can also be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable subcombination. Further, while features are described above as functioning in certain combinations, and may originally be claimed as such, one or more features from the claimed combination may in some cases be It may be deleted from that combination, and a claimed combination may cover a subcombination, or a variation of a subcombination.

Similarly, although acts may be shown in the figures in a particular order, this does not mean that such acts may be performed in the specific order shown, or in any sequence, or all illustrated to achieve a desired result. should not be understood to require that the actions of Multitasking and parallel processing may be advantageous in some environments. Furthermore, the separation of various system modules and components in the implementations described above should not be understood to require such separation in all implementations, and the program components and systems described generally It should be understood that they may be integrated together in a single software product or packaged in multiple software products.

A particular implementation of the subject matter has been described. Other implementations are within the scope of the claims. For example, the actions recited in the claims may be performed in a different order and still achieve desirable results. As an example, the processes illustrated in the accompanying figures do not necessarily require the particular order or sequence shown to achieve desirable results. In some cases, multitasking and parallel processing can be advantageous.

100 systems
102 Quantum Hardware
104 Fidelity Estimation System
106 qubits
108 qubits
110 quantum gate
112 Quantum Gate
114 Quantum Gate
116 Quantum Circuit
118 Measuring Device
120 final state
124 measuring devices
150 systems
152 Quantum Hardware
154 Fidelity Estimation System
156 qubits
158 qubits
160 components
162 unitary operators
164 initial state
166 final state
168 Measuring Device
172 Measuring Devices

Claims (11)

A method for fidelity benchmarking to quantum hardware, comprising:
Iteratively: (i) applying, via the quantum hardware, a random quantum circuit composed of gates from a universal set of quantum gates to a quantum system; and (ii) applying, via the quantum hardware, output information of the quantum system. measuring the quantum system to determine
using a classical computer to simulate the application of the random quantum circuit to the quantum system to determine expected statistics of the quantum system;
using the classical computer to estimate the fidelity of the random quantum circuit based on the determined output information and the expected statistics of the quantum system;
A method, including estimating the fidelity of the random quantum circuit based on the determined output information and the expected statistics of the quantum system using the classical computer; 2. The method of claim 1, comprising comparing statistics and convex combinations of perfect mixed quantum states with the determined output information of the quantum system. The step of comparing the determined prediction statistics of the quantum system and a convex combination of perfect mixed quantum states with the determined output information of the quantum system comprises comparing the determined output information of the quantum system with the quantum system. 3. The method of claim 2, comprising fitting the determined prediction statistic of and the convex combination of perfect mixed quantum states. The convex combination is

where α represents the fidelity of a quantum circuit, |ψ〉 represents the simulated quantum state of the quantum system based on the application of the quantum circuit to the quantum system, and I/N represents the perfection 3. The method of claim 2, representing mixed quantum states. 5. The step of claim 4, wherein fitting the determined output information of the quantum system to the convex combination of the determined prediction statistics of the quantum system and a perfect mixed quantum state comprises solving for α. Method. 2. The method of claim 1, wherein the set of quantum gates includes single-qubit quantum gates and two-qubit quantum gates. a device,
one or more qubits and
a universal set of one or more quantum gates;
with one or more measuring devices
quantum hardware including
one or more classical processors in data communication with said quantum hardware;
with
An apparatus, wherein the quantum hardware and one or more classical processors are configured to implement the method of any one of claims 1-6. 8. The device of claim 7, wherein the one or more qubits are superconducting qubits. 8. The device of Claim 7, wherein the one or more qubits form a one-dimensional array. 8. The device of Claim 7, wherein the one or more qubits form a two-dimensional array. 8. The apparatus of claim 7, wherein each of said one or more qubits undergoes nearest neighbor interaction.

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