CN117521831B - Quantum error automatic calibration method based on graphic processor and related equipment - Google Patents
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Abstract
The present disclosure relates to a quantum error automated calibration method and related equipment based on a graphics processor, the method comprising: after a target quantum processor runs a target quantum circuit, automatically acquiring a quantum measurement result of a quantum bit in the target quantum processor, and sending the quantum measurement result to a graphics processor; calculating an expected value of the target observability after measurement error calibration on the graph processor based on the quantum measurement result; and carrying out quantum logic gate error calibration on the expected value of the target observability quantity on the graph processor to obtain the expected value after the gate error calibration. The efficiency of quantum error calibration is improved by implementing automated calibration of quantum errors by means of a graphics processor.
Description
Technical Field
The disclosure relates to the technical field of quantum error calibration, in particular to a quantum error automatic calibration method based on a graphics processor and related equipment.
Background
In the computer field, the occurrence of errors is a very common phenomenon. In quantum computing, the evolution of the quantum states should follow the quantum wire rules performed. However, due to various unavoidable disturbances of the external environment or the hardware itself, etc., the actual quantum states and qubits may evolve differently from expected, resulting in errors in computation. We call these disturbances noise. Unlike classical bit errors, qubit errors are more complex. Not only the 0 or 1 value of the qubit may change, but the qubit may also have a phase, similar to the direction in which they are pointing, as well as change.
These noises can have an impact on the accuracy of the final quantum computation result, and thus calibration errors are important in quantum computation. Quantum error calibration is a key step in quantum computing, aimed at correcting and reducing the effect of noise on the computation results by taking specific technical means.
In the related art, the quantum error calibration needs to manually acquire related data to perform calibration calculation, so that the calculation efficiency is low, and based on the method, the automatic quantum error calibration method and related equipment based on the graphics processor are provided.
Disclosure of Invention
The disclosure aims to provide a quantum error automatic calibration method and related equipment based on a graphics processor, so as to improve the efficiency of quantum error calibration.
To achieve the above object, a first aspect of embodiments of the present disclosure provides a quantum error automation calibration method based on a graphics processor, the method including:
after a target quantum processor runs a target quantum circuit, automatically acquiring a quantum measurement result of a quantum bit in the target quantum processor, and sending the quantum measurement result to a graphics processor;
calculating an expected value of the target observability after measurement error calibration on the graph processor based on the quantum measurement result;
And carrying out quantum logic gate error calibration on the expected value of the target observability quantity on the graph processor to obtain the expected value after the gate error calibration.
Optionally, before the automatically acquiring the quantum measurement result of the qubit in the target quantum processor, the method further includes:
acquiring a calibration matrix representing a measurement error between an ideal measurement result and a noisy measurement result of the quantum processor, and transmitting the calibration matrix to a graphic processor;
the calculating, on the graphics processor, the expected value of the target observability after the measurement error calibration based on the quantum measurement result, including:
and calculating an expected value of the target observability quantity after measurement error calibration on the graph processor based on the quantum measurement result and the calibration matrix.
Optionally, the calculating, on the graphics processor, the expected value of the target observability amount after the measurement error calibration based on the quantum measurement result and the calibration matrix includes:
calculating, on the graphics processor, a target observability amount of the expected value after the measurement error calibration based on the following formula:
；
；
wherein,as a result of the desired value(s),lfor sequence number, M is the corresponding expected value component in the target observability quantity- >Is (are) observable components ofThe number of measurements allocated, N being the number of qubits involved in the operation of the target quantum circuit,/-)>，Is->Is applied to the observable component of the kth qubit, and>is the inverse of the calibration matrix of the kth qubit, < >>The quantum measurement result of the mth measurement of the kth quantum bit.
Optionally, the quantum logic gate error calibration is an error calibration based on a kriford data regression, and before the automatically obtaining the quantum measurement result of the quantum bit in the target quantum processor, the method further includes:
calculating, on a graphics processor, parameter values for parameters of a regression function for performing a cliford data regression based on machine learning, the independent and dependent variables of the regression function being observable noisy and ideal expectations, respectively;
performing quantum logic gate error calibration on the expected value of the target observability on the graphics processor to obtain the expected value after gate error calibration, wherein the quantum logic gate error calibration comprises the following steps:
and constructing a regression function on the graph processor based on the parameter values of the parameters of the regression function, and inputting the expected value of the target observability into the regression function to execute error calibration based on the Clerodard data regression so as to obtain the expected value after door error calibration.
Optionally, the calculating, on the graphics processor, parameter values of parameters of a regression function for performing cliford data regression based on machine learning includes:
selecting a regression function for performing a regression of the cliford data;
initializing parameter values of parameters of the regression function;
constructing a test quantum circuit on a target quantum processor, running the test quantum circuit, measuring to obtain a noise-containing operation result, obtaining a noise-containing expected value based on the noise-containing operation result, and transmitting the noise-containing expected value to a graphic processor;
constructing a virtual test quantum circuit on a graphic processor, and operating the virtual test quantum circuit to obtain an ideal operation result, and obtaining an ideal expected value based on the ideal operation result;
calculating, on a graphics processor, a loss function value for a preset machine learning loss function based on the noisy expected value and the ideal expected value;
and optimizing the parameter value of the regression function based on the loss function value on the graph processor, and obtaining the optimized parameter value when a preset optimization condition is met, wherein the optimized parameter value is used as the parameter value of the parameter of the regression function for carrying out the Keliford data regression.
Optionally, the performing quantum logic gate error calibration on the expected value of the target observability on the graphics processor to obtain the expected value after gate error calibration includes:
and performing quantum logic gate error calibration based on symmetry inspection on the expected value of the target observability quantity on the graph processor to obtain the expected value after gate error calibration.
Optionally, the target observables are hamiltonian amounts of target quantum circuits, and the performing, on the graphics processor, quantum logic gate error calibration based on symmetry inspection on expected values of the target observables, to obtain the expected values after gate error calibration includes:
acquiring a first expected value of a symmetry check operator, acquiring a second expected value of the Hamiltonian quantity of the target quantum circuit and the operator product of the symmetry check operator, and sending the second expected value to the graphic processor;
and carrying out quantum logic gate error calibration based on symmetry test on the expected value of the Hamiltonian amount of the target quantum circuit on the basis of the first expected value and the second expected value on a graph processor to obtain an expected value after gate error calibration.
A second aspect of the disclosed embodiments provides a quantum error automation calibration device based on a graphics processor, the device comprising:
The measuring result acquisition module is used for automatically acquiring a quantum measuring result of a quantum bit in the target quantum processor after the target quantum processor runs the target quantum circuit, and sending the quantum measuring result to the graphic processor;
the measurement error calibration module is used for calculating an expected value of the target observability after measurement error calibration on the graph processor based on the quantum measurement result;
and the gate error calibration module is used for executing quantum logic gate error calibration on the expected value of the target observability on the graphic processor to obtain the expected value after the gate error calibration.
A third aspect of the disclosed embodiments provides a computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps of the method of any of the first aspects above.
A fourth aspect of an embodiment of the present disclosure provides an electronic device, including:
a memory having a computer program stored thereon;
a processor for executing the computer program in the memory to implement the steps of the method of any of the above first aspects.
Based on the technical scheme, the expected value is obtained by calculation according to the measurement result of the quantum bit in the obtained target quantum circuit, the process combines with measurement error calibration to reduce the influence of errors introduced by quantum measurement noise on the calculated expected value, then quantum logic gate error calibration is executed, the error influence introduced by the noise of the quantum logic gate is further reduced, classical calculation of the calibration process is executed through a graphic processor, the error calibration efficiency is improved by means of strong calculation force, the process is automatically operated without excessive manual intervention, and the improvement of the error calibration efficiency is promoted.
Additional features and advantages of the present disclosure will be set forth in the detailed description which follows.
Drawings
The accompanying drawings are included to provide a further understanding of the disclosure, and are incorporated in and constitute a part of this specification, illustrate the disclosure and together with the description serve to explain, but do not limit the disclosure. In the drawings:
FIG. 1 is a block diagram illustrating a quantum error automation calibration system based on a graphics processor, according to an exemplary embodiment.
FIG. 2 is a flow chart illustrating a method of automated calibration of quantum errors based on a graphics processor, according to an exemplary embodiment.
FIG. 3 is a block diagram illustrating a quantum error automation calibration device based on a graphics processor, according to an example embodiment.
Fig. 4 is a block diagram of an electronic device 700, according to an example embodiment.
Detailed Description
Specific embodiments of the present disclosure are described in detail below with reference to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating and illustrating the disclosure, are not intended to limit the disclosure.
Fig. 1 is a block diagram illustrating a graphics processor-based quantum error automation calibration system including a graphics processor (GPU, graphics processing unit) and a quantum controller, wherein the graphics processor is connected to the quantum controller, the quantum controller is configured to connect to an external quantum processor (QPU, quantum Processing Unit), control the quantum processor to perform quantum calculations, obtain quantum operation results of the quantum processor, and the like, according to an exemplary embodiment.
The quantum controller can be constructed by adopting the existing central processing unit to realize the functions of operation control and the like, and coordinate, transit and control the interaction of the GPU and the QPU in the quantum error correction process. For example, a central processing unit and a graphics processor can be connected through a high-bandwidth communication channel to construct a quantum controller and provide various expansion interfaces for the outside.
FIG. 2 is a flow chart illustrating a method of quantum error automation calibration based on a graphics processor, which may be implemented using the quantum error automation calibration system based on a graphics processor described above, according to an exemplary embodiment, the method comprising:
s201, after a target quantum processor runs a target quantum circuit, automatically acquiring a quantum measurement result of a quantum bit in the target quantum processor, and sending the quantum measurement result to a graphics processor.
S202, calculating an expected value of the target observability quantity after measurement error calibration on the graph processor based on the quantum measurement result.
S203, quantum logic gate error calibration is carried out on the expected value of the target observability quantity on the graph processor, and the expected value after gate error calibration is obtained.
In step S201, the target quantum processor may be a quantum processor connected to a quantum controller for executing a target quantum circuit to be operated, the target quantum circuit being used for implementing quantum computation to be operated, and in a specific embodiment, the target quantum circuit may be a quantum circuit of a variable component sub-algorithm (Variational Quantum Algorithm, VQA).
Quantum circuits, which are one embodiment of quantum programs and weigh sub-logic circuits as well, are the most commonly used general quantum computing models, representing circuits that operate on qubits under an abstract concept, and their composition includes qubits, circuits (timelines), and various quantum logic gates, and finally the result often needs to be read out through quantum measurement operations.
Unlike conventional circuits, which are connected by metal lines to carry voltage or current signals, in a quantum circuit, the circuit can be seen as being connected by time, i.e., the state of the qubit naturally evolves over time, as indicated by the hamiltonian operator, during which it is operated until a logic gate is encountered.
One quantum program is corresponding to one total quantum circuit, and the quantum program refers to the total quantum circuit, wherein the total number of quantum bits in the total quantum circuit is the same as the total number of quantum bits of the quantum program. It can be understood that: one quantum program may consist of a quantum circuit, a measurement operation for the quantum bits in the quantum circuit, a register to hold the measurement results, and a control flow node (jump instruction), and one quantum circuit may contain several tens of hundreds or even thousands of quantum logic gate operations. The execution process of the quantum program is a process of executing all quantum logic gates according to a certain time sequence. Note that the timing is the time sequence in which a single quantum logic gate is executed.
The quantum controller can control the target quantum processor to operate the target quantum circuit, and after the target quantum circuit finishes the preset quantum calculation, the quantum measuring equipment can be controlled to measure the quantum bit in the target quantum processor to obtain a quantum measuring result, and the measuring result is automatically obtained and sent to the graphic processor. The process can be automatically operated based on a preset program without excessive manual operation.
In step S202, the target observability amount may be a preselected observability amount, for example, hamiltonian amount, and after the quantum measurement result is obtained, the quantum measurement error is calibrated by using the powerful computing capability of the graphics processor, so as to obtain an expected value corresponding to the target observability amount after the measurement error is calibrated. Quantum measurement errors are introduced by the quantum measurement itself.
Specifically, a calibration program of the quantum measurement error can be stored in the graphics processor itself or an external storage medium in advance, after the graphics processor acquires the quantum measurement result, the calibration program is operated, and operation is performed based on a preset calibration operation flow and the quantum measurement result, so as to obtain an expected value after the measurement error calibration, and reduce the influence of errors caused by noise in the measurement process. For example, for Hamiltonian H, the desired value can be calculated first after the quantum measurement s is obtained The desired value can also be +.>And then carrying out measurement error calibration on the expected value to obtain a calibrated expected value. Of course, the error calibration parameter can also be directly introduced into the calculation process of the expected value to directly calculate the period after error calibrationThe present invention is not particularly limited to the expected value.
In step S203, the graphics processor may perform further quantum logic gate error calibration calculations on the expected values calculated in step S202 to reduce the effects of quantum logic gate errors.
In particular, in classical computing, the most basic unit is a bit, and the most basic control mode is a logic gate, and the purpose of the control circuit can be achieved by a combination of logic gates. Similarly, the way in which the qubits are handled is a quantum logic gate. Quantum logic gates are used, which are the basis for forming quantum lines, and include single-bit quantum logic gates, such as Hadamard gates (H gates, ada Ma Men), brix gates (X gates, brix gates), brix-Y gates (Y gates, briy gates), brix-Z gates (Z gates, brix Z gates), RX gates (RX gates), RY gates (RY gates), RZ gates (RZ gates), and the like; multi-bit quantum logic gates such as CNOT gates, CR gates, iSWAP gates, toffoli gates, and the like. Quantum logic gates are typically represented using unitary matrices, which are not only in matrix form, but also an operation and transformation. The general function of a quantum logic gate on a quantum state is to calculate by multiplying the unitary matrix by a vector corresponding to the right vector of the quantum state. For example, the quantum state right vector |0 >The corresponding vector may beQuantum state right vector |1>The corresponding vector may be +.>。
Different from quantum measurement errors, quantum logic gate errors are introduced by defects of a quantum logic gate, in order to reduce the errors, a calibration program of the quantum measurement errors can be stored in a storage medium externally connected with a graphics processor, after an expected value is obtained, the calibration program can be automatically operated, and quantum logic gate errors are calibrated on the obtained expected value to obtain an expected value after gate error calibration. Quantum logic gate error calibration can be achieved using methods such as Clifford (Clifford) based data regression, symmetry-based inspection, and connection moment expansion.
For the VQA line, the expected value is obtained through measurement and error calibration after each quantum line is operated, the expected value can be used for further iteratively updating the parameters of the VQA line, and the parameter iterative updating based on the expected value can be more rapid and efficient through error calibration, so that noise introduced by subsequent calculation is less.
Based on the technical scheme, the expected value is obtained by calculation according to the measurement result of the quantum bit in the obtained target quantum circuit, the process combines with measurement error calibration to reduce the influence of errors introduced by quantum measurement noise on the calculated expected value, then quantum logic gate error calibration is executed, the error influence introduced by the noise of the quantum logic gate is further reduced, classical calculation of the calibration process is executed through a graphic processor, the error calibration efficiency is improved by means of strong calculation force, the process is automatically operated without excessive manual intervention, and the improvement of the error calibration efficiency is promoted.
Optionally, in step S201, before automatically acquiring the quantum measurement result of the quantum bit in the target quantum processor, the method further includes:
step S20a, a calibration matrix representing the measurement error between the ideal measurement result and the noisy measurement result of the quantum processor is obtained and sent to a graphic processor;
for step S202, calculating, on the graphics processor, a target observably measured expected value after measurement error calibration based on the quantum measurement result, including:
s2021, calculating an expected value of the target observability quantity after measurement error calibration on the graph processor based on the quantum measurement result and the calibration matrix.
In experiments, projection measurements may be performed on a computational basis and the measurement results analyzed to extract quantum state information. However, due to readout noise, the probability distribution deviates from the ideal distribution, which leads to errors in the estimation. For measurement error calibration, before step S201 is performed, S20a may be performed, and preparation for measurement error calibration calculation may be performed by, for example, a quantum controller.
In particular, the measurement error can be described as a classical random process, i.e. any given ideal measurement is converted into a noisy measurement, the measurement error can be described by a calibration matrix, e.g. using And->Representing the noisy measurement result and the ideal measurement result, respectively, the relation between the two can be based on a calibration matrix +.>Description of:
further subsequent measurement error calibration may be implemented based on this principle. In order to facilitate the subsequent execution of the measurement error calibration, in step S20a, the calibration matrix is acquired first and sent to the graphics processor.
After the calibration matrix is acquired, in step S2021, the expected value may be calculated by using the error information reflected by the calibration matrix and combining with the quantum measurement result, and the influence of the measurement error may be reduced during calculation. Optionally, in step S2021, calculating, on the graphics processor, a measured error calibrated expected value of the target observability based on the quantum measurement result and the calibration matrix, including:
calculating, on the graphics processor, a target observability amount of the expected value after the measurement error calibration based on the following formula:
；
；
wherein,as a result of the desired value(s),lfor sequence number, M is the corresponding expected value component in the target observability quantity->Is (are) observable components ofThe number of measurements allocated, N being the number of qubits involved in the operation of the target quantum circuit,/-)>，Is->Is applied to the observable component of the kth qubit, and >Is the inverse of the calibration matrix of the kth qubit, < >>The quantum measurement result of the mth measurement of the kth quantum bit.
The formula will actually beThe inverse is applied to the noisy measurements to estimate the expected value of the observables. Wherein the target observables O can be decomposed into brix as follows:
wherein,is the tensor product of a single-bit bubble operator. Each->Can be expressed in tensor product form:
calibration matrixMay also be expressed in tensor product form:
wherein,p (x|y) represents the value of +.>Under the condition of->In the case of (2), the measurement result is +.>And may further obtain a calibration matrix based thereon.
Optionally, the quantum logic gate error calibration is an error calibration based on the kriford data regression, and before automatically obtaining the quantum measurement result of the quantum bit in the target quantum processor in step S201, the method further includes:
s20b, calculating parameter values of parameters of a regression function for performing the Keliford data regression on a graph processor based on machine learning, wherein independent variables and dependent variables of the regression function are observably noise-containing expected values and ideal expected values respectively;
in step S203, quantum logic gate error calibration is performed on the expected value of the target observability on the graphics processor, to obtain the expected value after gate error calibration, which may include:
S2031, constructing a regression function on the graph processor based on the parameter values of the parameters of the regression function, and inputting the expected value of the target observability into the regression function to execute error calibration based on the Keliford data regression to obtain the expected value after door error calibration.
Specifically, the CZ gate error can be suppressed by using the Keliford data regression, which is critical in that a regression function is fittedTo add a noise-containing desired value +.>Mapping to an ideal expected value corrected for error +.>The formula is as follows:
in one embodiment, the regression functionCan be a linear function such as +.>The α and β are fitting coefficients, however, in other embodiments, other models may be used for the regression function, and the present invention is not limited thereto.
In order to perform the preparation for performing the criford data regression, step S20b may be performed before step S201 is performed, and the regression function may be trained by means of a training process of machine learning to obtain parameter values of the parameters of the regression function.
Optionally, in S20b, calculating, on the graphics processor, parameter values of parameters of a regression function for performing cliford data regression based on machine learning, includes:
S20b1, selecting a regression function for carrying out the Keliford data regression;
s20b2, initializing parameter values of parameters of the regression function;
s20b3, constructing a test quantum circuit on the target quantum processor, running the test quantum circuit and measuring to obtain a noise-containing operation result, obtaining a noise-containing expected value based on the noise-containing operation result, and sending the noise-containing expected value to the graphic processor;
s20b4, constructing a virtual test quantum circuit on the graphic processor, running the virtual test quantum circuit to obtain an ideal operation result, and obtaining an ideal expected value based on the ideal operation result;
s20b5, calculating a loss function value of a preset machine learning loss function on the graph processor based on the noise-containing expected value and the ideal expected value;
and S20b6, optimizing the parameter value of the regression function based on the loss function value on the graph processor, and obtaining the optimized parameter value as the parameter value of the parameter of the regression function for carrying out the Keliford data regression when the preset optimization condition is met.
In step S20b1, a specific function model may be selected among the regression functions set in advance, for example, a linear function is selected. Then in step S20b2, the selected regression function is initialized, i.e. its parameters are given initial values, e.g. parameters may be randomly assigned within a certain range.
In step S20b3, a test quantum circuit is set up on the target quantum processor, where the test quantum circuit may be different from the target quantum circuit, for example, may be a relatively simple quantum circuit that is convenient to operate, and the test quantum circuit is operated to obtain a noise-containing operation result, and then a noise-containing expected value is calculated according to the noise-containing operation result. And sending the noise expected value obtained by operation to a graphics processor.
In step S20b4, a virtual test quantum wire is constructed on the graphics processor, which is identical to the model of the test quantum wire on the target quantum processor. And operating the virtual test quantum circuit to obtain an ideal operation result, and calculating an ideal expected value according to the ideal operation result, wherein the ideal expected value is the same as the observable corresponding to the noise-containing expected value, for example, the ideal expected value and the observable can both correspond to the target observable.
In step S20b5, the ideal expected value may be used as a label, the noise-containing expected value may be used as a sample calculation result, and the two may be brought into a preset machine learning loss function, and the loss function value may be calculated. The preset machine learning loss function may employ, for example, a mean square error loss function.
In step S20b6, on the graphics processor, the bias derivative of the loss function value with respect to the parameter may be calculated, and the parameter may be optimized by using a gradient descent algorithm, and when a preset optimization condition is satisfied, for example, the iteration reaches a certain number of times or the loss function value is smaller than a threshold value, the finally calculated parameter value is used as the optimized parameter value to construct the regression function. If the preset optimization condition is not satisfied, the step S20b3 may be executed in a return manner, and the iterative calculation may be performed until the preset optimization condition is satisfied.
By automatically calculating the parameter values of the regression function by means of the machine learning method using artificial intelligence, the calculation efficiency can be improved and an accurate regression function can be provided. It should be noted that, the step S20b and the step S20a may be performed simultaneously without any restriction on the order of execution.
In step S2031, the graphics processor constructs a regression function using the obtained parameter values, and may input the expected value calculated in step S202 as an argument to the regression function, and use the function value of the calculated regression function as an expected value after gate error calibration, so as to reduce the influence of the quantum logic gate error.
Optionally, in step S203, quantum logic gate error calibration is performed on the expected value of the target observability on the graphics processor, to obtain a gate error calibrated expected value, including:
s203a, quantum logic gate error calibration based on symmetry test is performed on the expected value of the target observability on the graph processor, and the expected value after gate error calibration is obtained.
In S203a, quantum logic gate error calibration based on symmetry inspectionThe symmetry of the quantum system is exploited. Hamiltonian amount operator for systemTo describe, symmetry of the system is expressed in terms of unitary operator +. >To describe (i.e.)>And->Satisfy the relationship of the ease of useHamiltonian operator->Can be->Block diagonalization is performed in the eigenspace of (a). If one wants to calculate +.>The eigenstates of (2) may be +.>Is studied within a single eigenspace S. In practice, noise may deviate the state of a quantum computer or quantum processor from the eigenspace S. Therefore, by discarding the unconditional results while the inspection system is still in S during or after the computation is completed, the effect of noise on quantum computation can be reduced.
If the object is a closed-shell molecule, the heuristic wave function is located in the even-space of total particle number and spin, so the eigenvalue of the symmetry check operator of correct symmetry is always 1. By projecting the system hamiltonian into the even-space, we get:
wherein,is a density matrix of the quantum system, < >>Is->Density matrix projected to even-space subspace, +.>The operator is checked for the ith symmetry. In the formula, tr represents the trace of the matrix, and the result is the expected value of the corresponding operator, so that the symmetry inspection principle can be used for calibrating the quantum logic gate error.
Optionally, in step S203a, quantum logic gate error calibration based on symmetry test is performed on the expected value of the target observability, to obtain the expected value after gate error calibration, where the target observability is hamiltonian of the target quantum circuit, and the method includes:
S203a1, obtaining a first expected value of the symmetry check operator, obtaining a second expected value of the Hamiltonian quantity of the target quantum circuit and the operator product of the symmetry check operator, and sending the second expected value to the graphics processor.
S203a2, performing quantum logic gate error calibration based on symmetry test on the expected value of Hamiltonian quantity of the target quantum circuit on the basis of the first expected value and the second expected value on a graph processor to obtain an expected value after gate error calibration.
In step S203a1, a quantum wire may be subjected to correlation measurement with a quantum controller to obtain a symmetry check operatorIs +.>And->And->Second expected value of the operator product of +.>And sent to the graphics processor.
In step S203a2, the first expected value may be setAnd a second desired value->Substitution formula:
further calculating the expected value of Hamiltonian after the error calibration of the quantum logic gate based on symmetry test. Wherein, since the target observability amount is the hamiltonian amount of the target quantum wire, in step S202, the desired value +.>Can directly add->Substituting a formula, wherein the formula is obtained based on the formula of the Hamiltonian projection of the system to an even-space subspace. Wherein (1) >，/>And +.>The expected value after the measurement error calibration in step S202 and the error calibration based on the criford data regression in step S2031 may also be obtained at the same time.
Optionally, the target observables are hamiltonian amounts of the target quantum circuits, the expected values are ground state energies, in step S203, quantum logic gate error calibration is performed on the expected values of the target observables on the graphics processor, to obtain expected values after gate error calibration, including:
S203A, quantum logic gate error calibration based on connection moment expansion is performed on the ground state energy on the graph processor, and the ground state energy after gate error calibration is obtained.
The connection moment expansion method is derived from the Horn-Weinstein (HW) theory, and based on this method, the energy can be expressed as follows:
wherein,for evolution time +.>As a wave function of the quantum state, I is the junction moment. The formula uses taylor expansion to expand energy into an expansion that connects moments I. By projecting a quantum state onto the ground state of H, which is non-orthogonal to the ground state and +.>Toward infinity, the formula gives the exact ground state energy. The connection moment is defined based on the following formula:
in practice, the evolution time is a finite value, in order to facilitate calculation, the desired value corresponding to the hamiltonian and the higher order number of hamiltonian may be used to represent the connection moment, and the formula is truncated to a specific higher order number of hamiltonian, for example, to the 3 rd power of hamiltonian, so as to obtain the formula:
Wherein,equal to the desired value of Hamiltonian>，/>，。
In step S203A, the ground state energy may be further calculated as an expected value after error calibration based on the above principle.
Optionally, in step S203A, quantum logic gate error calibration based on the connection moment expansion is performed on the graphics processor to obtain gate error calibrated ground state energy, including:
S203A1, determining the highest power number a of Hamiltonian in a preset ground state energy calculation formula which is unfolded by using a connecting moment;
S203A2, obtaining expected values of all b powers of Hamiltonian quantity, and sending the expected values to a graphic processor, wherein b is more than or equal to 2, and b is less than or equal to a;
S203A3, performing quantum logic gate error calibration based on the connection moment expansion on the ground state energy based on expected values of all b powers of the Hamiltonian and the preset ground state energy calculation formula expanded by the connection moment on the graph processor, and obtaining the ground state energy after gate error calibration.
In step S203A1, it may be determined that the above-described ground state energy calculation formula expanded with the connection moment needs to be truncated to a multi-order and low-order hamiltonian amount desired value, for example, it is determined that the highest power number a of the hamiltonian amount to be truncated is 3. at a=3, most of the ground state energy can be reproduced already.
In step S203A2, all the desired values of the higher-order Ha Midu amounts less than or equal to a, for example, a=3, may be obtained by using the quantum controllerAnd->. Since the target observability amount is hamiltonian, the +.>. These expected values are all sent to the graphics processor. Of course, acquired->、/>And->The desired values may be first subjected to the measurement error calibration of the previous steps and the quantum logic gate error calibration.
In step S203A3, the obtained expected value may be substituted into the above formula on the graphics processor to calculate the ground state energy, and implement the calibration of the gate error.
FIG. 3 is a diagram illustrating a quantum error automation calibration device based on a graphics processor, see FIG. 3, according to an exemplary embodiment, the device comprising:
the measurement result obtaining module 310 is configured to automatically obtain a quantum measurement result of a qubit in the target quantum processor after the target quantum processor runs the target quantum circuit, and send the quantum measurement result to the graphics processor;
a measurement error calibration module 320, configured to calculate, on a graphics processor, an expected value of the target observability amount after measurement error calibration based on the quantum measurement result;
The gate error calibration module 330 is configured to perform quantum logic gate error calibration on the expected value of the target observability on the graphics processor, so as to obtain the expected value after the gate error calibration.
Optionally, the apparatus further comprises:
the calibration matrix acquisition module is used for acquiring a calibration matrix representing a measurement error between an ideal measurement result and a noisy measurement result of the quantum processor before the measurement result acquisition module automatically acquires the quantum measurement result of the quantum bit in the target quantum processor, and transmitting the calibration matrix to the graphic processor;
the measurement error calibration module is further configured to:
and calculating an expected value of the target observability quantity after measurement error calibration on the graph processor based on the quantum measurement result and the calibration matrix.
Optionally, the measurement error calibration module is further configured to:
calculating, on the graphics processor, a target observability amount of the expected value after the measurement error calibration based on the following formula:
；
；
wherein,as a result of the desired value(s),lfor sequence number, M is the corresponding expected value component in the target observability quantity->Is (are) observable components ofThe number of measurements allocated, N being the number of qubits involved in the operation of the target quantum circuit,/-) >，Is->Is applied to the observable component of the kth qubit, and>is the inverse of the calibration matrix of the kth qubit, < >>The quantum measurement result of the mth measurement of the kth quantum bit.
Optionally, the quantum logic gate error calibration is an error calibration based on a kriford data regression, the apparatus further comprising:
the parameter value acquisition module is used for calculating parameter values of parameters of a regression function for carrying out the Kelly ford data regression on the graph processor based on machine learning before the measurement result acquisition module automatically acquires the quantum measurement result of the quantum bit in the target quantum processor, wherein independent variables and dependent variables of the regression function are respectively an observable noise-containing expected value and an ideal expected value;
the door error calibration module is further configured to:
and constructing a regression function on the graph processor based on the parameter values of the parameters of the regression function, and inputting the expected value of the target observability into the regression function to execute error calibration based on the Clerodard data regression so as to obtain the expected value after door error calibration.
Optionally, the parameter value obtaining module is further configured to:
selecting a regression function for performing a regression of the cliford data;
Initializing parameter values of parameters of the regression function;
constructing a test quantum circuit on a target quantum processor, running the test quantum circuit, measuring to obtain a noise-containing operation result, obtaining a noise-containing expected value based on the noise-containing operation result, and transmitting the noise-containing expected value to a graphic processor;
constructing a virtual test quantum circuit on a graphic processor, and operating the virtual test quantum circuit to obtain an ideal operation result, and obtaining an ideal expected value based on the ideal operation result;
calculating, on a graphics processor, a loss function value for a preset machine learning loss function based on the noisy expected value and the ideal expected value;
and optimizing the parameter value of the regression function based on the loss function value on the graph processor, and obtaining the optimized parameter value when a preset optimization condition is met, wherein the optimized parameter value is used as the parameter value of the parameter of the regression function for carrying out the Keliford data regression.
Optionally, the door error calibration module is further configured to:
and performing quantum logic gate error calibration based on symmetry inspection on the expected value of the target observability quantity on the graph processor to obtain the expected value after gate error calibration.
Optionally, the target observability amount is a hamiltonian amount of a target quantum wire, and the gate error calibration module is further configured to:
acquiring a first expected value of a symmetry check operator, acquiring a second expected value of the Hamiltonian quantity of the target quantum circuit and the operator product of the symmetry check operator, and sending the second expected value to the graphic processor;
and carrying out quantum logic gate error calibration based on symmetry test on the expected value of the Hamiltonian amount of the target quantum circuit on the basis of the first expected value and the second expected value on a graph processor to obtain an expected value after gate error calibration.
Optionally, the target observability amount is hamiltonian amount of a target quantum wire, the expected value is ground state energy, and the gate error calibration module is further configured to:
and performing quantum logic gate error calibration based on connection moment expansion on the ground state energy on the graph processor to obtain the ground state energy after gate error calibration.
Optionally, the door error calibration module is further configured to:
determining the highest power number a of Hamiltonian in a preset ground state energy calculation formula expanded by using a connecting moment;
acquiring expected values of all b powers of the Hamiltonian amount, and sending the expected values to a graphic processor, wherein b is more than or equal to 2, and b is less than or equal to a;
And performing quantum logic gate error calibration based on the connection moment expansion on the ground state energy based on expected values of all b powers of the Hamiltonian quantity and the preset ground state energy calculation formula expanded by the connection moment on the graph processor to obtain the ground state energy after gate error calibration.
The specific manner in which the various modules perform the operations in the apparatus of the above embodiments have been described in detail in connection with the embodiments of the method, and will not be described in detail herein.
Fig. 4 is a block diagram of an electronic device 700, according to an example embodiment. As shown in fig. 4, the electronic device 700 may include: a processor 701, a memory 702. The electronic device 700 may also include one or more of a multimedia component 703, an input/output (I/O) interface 704, and a communication component 705.
The processor 701 is configured to control the overall operation of the electronic device 700 to perform all or part of the steps of the above-described quantum error automatic calibration method based on a graphics processor. The memory 702 is used to store various types of data to support operation on the electronic device 700, which may include, for example, instructions for any application or method operating on the electronic device 700, as well as application-related data, such as contact data, messages sent and received, pictures, audio, video, and so forth. The Memory 702 may be implemented by any type or combination of volatile or non-volatile Memory devices, such as static random access Memory (Static Random Access Memory, SRAM for short), electrically erasable programmable Read-Only Memory (Electrically Erasable Programmable Read-Only Memory, EEPROM for short), erasable programmable Read-Only Memory (Erasable Programmable Read-Only Memory, EPROM for short), programmable Read-Only Memory (Programmable Read-Only Memory, PROM for short), read-Only Memory (ROM for short), magnetic Memory, flash Memory, magnetic disk, or optical disk. The multimedia component 703 can include a screen and an audio component. Wherein the screen may be, for example, a touch screen, the audio component being for outputting and/or inputting audio signals. For example, the audio component may include a microphone for receiving external audio signals. The received audio signals may be further stored in the memory 702 or transmitted through the communication component 705. The audio assembly further comprises at least one speaker for outputting audio signals. The I/O interface 704 provides an interface between the processor 701 and other interface modules, which may be a keyboard, mouse, buttons, etc. These buttons may be virtual buttons or physical buttons. The communication component 705 is for wired or wireless communication between the electronic device 700 and other devices. Wireless communication, such as Wi-Fi, bluetooth, near field communication (Near Field Communication, NFC for short), 2G, 3G, 4G, NB-IOT, eMTC, or other 5G, etc., or one or a combination of more of them, is not limited herein. The corresponding communication component 705 may thus comprise: wi-Fi module, bluetooth module, NFC module, etc.
In an exemplary embodiment, the electronic device 700 may be implemented by one or more application specific integrated circuits (Application Specific Integrated Circuit, abbreviated ASIC), digital signal processor (Digital Signal Processor, abbreviated DSP), digital signal processing device (Digital Signal Processing Device, abbreviated DSPD), programmable logic device (Programmable Logic Device, abbreviated PLD), field programmable gate array (Field Programmable Gate Array, abbreviated FPGA), controller, microcontroller, microprocessor, or other electronic components for performing the graphics processor-based quantum error automation calibration method described above.
In an exemplary embodiment, the electronic device 700 may further include a graphics processor for performing steps in a graphics processor-based quantum error automation calibration method that may be performed on the graphics processor.
In another exemplary embodiment, a computer readable storage medium is also provided that includes program instructions that, when executed by a processor, implement the steps of the above-described graphics processor-based quantum error automation calibration method. For example, the computer readable storage medium may be the memory 702 including program instructions described above that are executable by the processor 701 of the electronic device 700 to perform the graphics processor-based quantum error automation calibration method described above.
The preferred embodiments of the present disclosure have been described in detail above with reference to the accompanying drawings, but the present disclosure is not limited to the specific details of the above embodiments, and various simple modifications may be made to the technical solutions of the present disclosure within the scope of the technical concept of the present disclosure, and all the simple modifications belong to the protection scope of the present disclosure.
In addition, the specific features described in the foregoing embodiments may be combined in any suitable manner, and in order to avoid unnecessary repetition, the present disclosure does not further describe various possible combinations.
Moreover, any combination between the various embodiments of the present disclosure is possible as long as it does not depart from the spirit of the present disclosure, which should also be construed as the disclosure of the present disclosure.
Claims (8)
1. A method for automated calibration of quantum errors based on a graphics processor, the method comprising:
acquiring a calibration matrix representing a measurement error between an ideal measurement result and a noisy measurement result of a target quantum processor, and transmitting the calibration matrix to a graphic processor;
after a target quantum processor runs a target quantum circuit, automatically acquiring a quantum measurement result of a quantum bit in the target quantum processor, and sending the quantum measurement result to a graphics processor;
Calculating, on the graphics processor, a target observability amount of the expected value after the measurement error calibration based on the following formula:
；
；
wherein,as a result of the desired value(s),lfor sequence number, M is the corresponding expected value component in the target observability quantity->Is>The number of measurements allocated, N being the number of qubits involved in the operation of the target quantum circuit,/-)>，/>Is->Is applied to the observable component of the kth qubit, and>is the inverse of the calibration matrix of the kth qubit, < >>Quantum measurements for an mth measurement of a kth quantum bit;
and carrying out quantum logic gate error calibration on the expected value of the target observability quantity on the graph processor to obtain the expected value after the gate error calibration.
2. The method of claim 1, wherein the quantum logic gate error calibration is an error calibration based on kriford data regression, the method further comprising, prior to the automatically obtaining quantum measurements of qubits in the target quantum processor:
calculating, on a graphics processor, parameter values for parameters of a regression function for performing a cliford data regression based on machine learning, the independent and dependent variables of the regression function being observable noisy and ideal expectations, respectively;
Performing quantum logic gate error calibration on the expected value of the target observability on the graphics processor to obtain the expected value after gate error calibration, wherein the quantum logic gate error calibration comprises the following steps:
and constructing a regression function on the graph processor based on the parameter values of the parameters of the regression function, and inputting the expected value of the target observability into the regression function to execute error calibration based on the Clerodard data regression so as to obtain the expected value after door error calibration.
3. The method of claim 2, wherein calculating, on the graphics processor, parameter values for parameters of a regression function for performing cliford data regression based on machine learning, comprises:
selecting a regression function for performing a regression of the cliford data;
initializing parameter values of parameters of the regression function;
constructing a test quantum circuit on a target quantum processor, running the test quantum circuit, measuring to obtain a noise-containing operation result, obtaining a noise-containing expected value based on the noise-containing operation result, and transmitting the noise-containing expected value to a graphic processor;
constructing a virtual test quantum circuit on a graphic processor, and operating the virtual test quantum circuit to obtain an ideal operation result, and obtaining an ideal expected value based on the ideal operation result;
Calculating, on a graphics processor, a loss function value for a preset machine learning loss function based on the noisy expected value and the ideal expected value;
and optimizing the parameter value of the regression function based on the loss function value on the graph processor, and obtaining the optimized parameter value when a preset optimization condition is met, wherein the optimized parameter value is used as the parameter value of the parameter of the regression function for carrying out the Keliford data regression.
4. The method of claim 1, wherein performing quantum logic gate error calibration on the desired value of the target observability on the graphics processor to obtain the gate error calibrated desired value comprises:
and performing quantum logic gate error calibration based on symmetry inspection on the expected value of the target observability quantity on the graph processor to obtain the expected value after gate error calibration.
5. The method of claim 4, wherein the target observables are hamiltonian amounts of target quantum circuits, and wherein performing, on the graphics processor, a symmetry-check-based quantum logic gate error calibration on the target observables' expected values, resulting in gate error calibrated expected values, comprises:
acquiring a first expected value of a symmetry check operator, acquiring a second expected value of the Hamiltonian quantity of the target quantum circuit and the operator product of the symmetry check operator, and sending the second expected value to the graphic processor;
And carrying out quantum logic gate error calibration based on symmetry test on the expected value of the Hamiltonian amount of the target quantum circuit on the basis of the first expected value and the second expected value on a graph processor to obtain an expected value after gate error calibration.
6. A quantum error automation calibration device based on a graphics processor, the device comprising:
the calibration matrix acquisition module is used for acquiring a calibration matrix representing a measurement error between an ideal measurement result and a noisy measurement result of the quantum processor before the measurement result acquisition module automatically acquires the quantum measurement result of the quantum bit in the target quantum processor, and transmitting the calibration matrix to the graphic processor;
the measuring result acquisition module is used for automatically acquiring a quantum measuring result of a quantum bit in the target quantum processor after the target quantum processor runs the target quantum circuit, and sending the quantum measuring result to the graphic processor;
the measurement error calibration module is used for calculating an expected value of the target observability after the measurement error calibration based on the following formula on the graph processor:
；
；
wherein,as a result of the desired value(s),lfor sequence number, M is the corresponding expected value component in the target observability quantity- >Is>The number of measurements allocated, N being the number of qubits involved in the operation of the target quantum circuit,/-)>，/>Is->Is applied to the observable component of the kth qubit, and>is the firstAn inverse of said calibration matrix of k qubits,/i>Quantum measurements for an mth measurement of a kth quantum bit;
and the gate error calibration module is used for executing quantum logic gate error calibration on the expected value of the target observability on the graphic processor to obtain the expected value after the gate error calibration.
7. A computer readable storage medium, on which a computer program is stored, characterized in that the program, when being executed by a processor, implements the steps of the method according to any one of claims 1-5.
8. An electronic device, comprising:
a memory having a computer program stored thereon;
a processor for executing the computer program in the memory to implement the steps of the method of any one of claims 1-5.
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