CN115204404B - Method and device for inhibiting errors in fermi subsystem measurement - Google Patents
Method and device for inhibiting errors in fermi subsystem measurement Download PDFInfo
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Abstract
The embodiment of the invention provides a method and a device for inhibiting errors in fermi subsystem measurement, wherein the method comprises the following steps: determining a first reduced density matrix carrying noise based on the measurement made by the first fermi subsystem; inputting the first reduced density matrix into a pre-trained error suppression model, and obtaining a second reduced density matrix after noise reduction; the energy of the first fermi subsystem is determined based on the second reduced density matrix.
Description
Technical Field
The invention relates to the field of quantum computing, in particular to a method and a device for inhibiting errors in fermi subsystem measurement.
Background
Quantum computing and quantum simulation have recently received a great deal of attention from many technological personnel and companies as an efficient way to solve the problems of the simulated quantum system. Quantum computing has the advantage of lower computational time complexity for certain problems over classical computers on the one hand, and quantum computers have been used to solve some of the specific problems as quantum regulatory technologies mature gradually on the other hand. In recent years, a large number of quantum device-oriented computing technologies have been developed and used for practical use. These quantum computing techniques are generally targeted methods constructed with respect to the characteristics of limited number of qubits and noise that can be handled by recent quantum devices, and with the goal of achieving computation with practical significance in smaller scale systems. For example, quantum computing and auxiliary techniques for solving the problem of quantum chemical electronic structures are now a technical hotspot.
But recently the effect of quantum computing techniques has generally relied on quantum error mitigation techniques that reduce observed noise by classical post-processing of measurement results after the completion of the computational implementation. However, the existing quantum error suppression method only faces the calculation process that the number of controllable quantum bits is limited and the number of circuit layers is shallow. For deeper quantum circuits, the gradual accumulation of noise in the calculation process can lead to the failure of an error suppression algorithm, and the existing quantum error suppression algorithm often brings additional calculation cost, so that the defect that the system cannot be scaled to a larger system exists.
Therefore, a new solution to suppress errors in quantum measurements is needed.
Disclosure of Invention
The embodiment of the invention provides a method and a device for inhibiting errors in fermi subsystem measurement. By utilizing the method, measurement errors in the measurement of the fermi subsystem can be suppressed, and the accuracy of the measurement result is effectively improved; and can determine the system energy on the premise of consuming less measurement resources, thereby being applicable to the measurement of the large-scale fermi subsystem.
The technical scheme adopted by the invention for solving the technical problems is that one aspect provides a method for inhibiting errors in measurement of a fermi subsystem, which comprises the following steps:
determining a first reduced density matrix carrying noise based on the measurement made by the first fermi subsystem;
inputting the first reduced density matrix into a pre-trained error suppression model to obtain a second reduced density matrix after noise reduction;
an energy of the first fermi subsystem is determined based on the second reduced density matrix.
Preferably, the fermi subsystem is an electronic system, the first reduced density matrix is a two-electron reduced density matrix carrying noise, and the second reduced density matrix is a two-electron reduced density matrix after noise reduction.
Preferably, the error suppression model is trained by:
acquiring a noisy third reduced density matrix and an ideal fourth reduced density matrix of the second fermi subsystem, wherein the third reduced density matrix and the fourth reduced density matrix are two-electron reduced density matrices;
inputting the third reduced density matrix into an error suppression model to obtain a fifth reduced density matrix;
determining a first loss based on a first difference between the fifth reduced density matrix and the fourth reduced density matrix, and updating parameters of the error suppression model at least with the aim that the first loss tends to be smaller.
Preferably, the method further comprises:
according to the fourth reduced density matrix, determining a first two-hole reduced density matrix and a first electron-hole reduced density matrix based on the Wick theorem;
determining a second two-hole reduced density matrix and a second electron-hole reduced density matrix based on the Wick theorem according to the fifth reduced density matrix;
determining a second loss based on a second difference of the fifth reduced density matrix and the fourth reduced density matrix, based on a second difference of the first two-hole reduced density matrix and the second two-hole reduced density matrix, and based on a second difference of the first electron-hole reduced density matrix and the first electron-hole reduced density matrix;
said updating parameters of said error mitigation model, at least with the aim of a reduced tendency of the first loss, comprises:
the parameters of the error suppression model are updated with the aim that the first loss and the second loss tend to become smaller.
Preferably, the difference between the fifth reduced density matrix and the fourth reduced density matrix comprises:
the difference between the Frobenius norms of the fifth reduced density matrix and the fourth reduced density matrix.
Preferably, the second difference of the fifth reduced density matrix and the fourth reduced density matrix comprises a difference of ranks of the fifth reduced density matrix and the fourth reduced density matrix;
a second difference between the first two-hole reduced density matrix and the second two-hole reduced density matrix, comprising a difference in rank of the first two-hole reduced density matrix and the second two-hole reduced density matrix;
the second difference between the first electron-hole reduced density matrix and the first electron-hole reduced density matrix comprises a difference in rank between the first electron-hole reduced density matrix and the first electron-hole reduced density matrix.
Preferably, determining the energy of the first fermi subsystem based on the second reduced density matrix comprises:
according to the two-electron reduced density matrix after noise reduction, determining a single-electron reduced density matrix after noise reduction;
and determining the energy of the first Fermi subsystem according to the two-electron reduced density matrix after noise reduction and the single-electron reduced density matrix after noise reduction.
In a second aspect, an apparatus is provided for suppressing errors in fermi subsystem measurements, the apparatus comprising:
a noise matrix acquisition unit configured to determine a first reduced density matrix carrying noise based on a measurement result performed on the first fermi subsystem;
the noise matrix determining unit is configured to input the first reduced density matrix into a pre-trained error suppression model to obtain a second reduced density matrix after noise reduction;
and a system amount determining unit configured to determine an energy of the first fermi subsystem based on the second reduced density matrix.
In a third aspect, there is provided a computer readable storage medium having stored thereon a computer program which, when executed in a computer, causes the computer to perform the method of any one of the first and second aspects.
In a fourth aspect, a computing device is provided, including a memory and a processor, wherein the memory has executable code stored therein, and wherein the processor, when executing the executable code, implements the method of any one of the first and second aspects.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for suppressing errors in Fermi subsystem measurements according to an embodiment of the present invention;
FIG. 2 is a flowchart of a training method of an error suppression model according to another embodiment of the present invention;
FIG. 3 is a flowchart of a training method of an error suppression model according to another embodiment of the present invention;
fig. 4 is a block diagram of an apparatus for suppressing errors in fermi subsystem measurement according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As described above, the existing quantum error suppression method only faces the calculation process that the number of controllable quantum bits is limited recently and the number of circuit layers is shallower, and for deeper quantum circuits, the gradual accumulation of noise in the calculation process can cause the failure of the error suppression algorithm, and the existing quantum error suppression algorithm often brings additional calculation overhead, so that the existing quantum error suppression method has the defect that the system cannot be scaled to a larger system. To more clearly illustrate the advantages of the error mitigation schemes for quantum measurements provided by the embodiments of the present description. The conventional quantum error suppression technique and its drawbacks are described in further detail below.
Quantum error suppression techniques mainly include three categories: noise models are independent, specific to the noise model and error suppression algorithms based on machine learning. Noise model-independent error suppression methods include, for example, extrapolation, symmetry verification, and the like. The main process of extrapolation is that firstly, the noise level in the implementation process of quantum circuit is gradually increased and the expected value of the observed quantity of the corresponding quantum is obtained, then, according to a plurality of expected values, under the condition of low noise level, the ideal mapping function of the observed quantity can be obtained by Taylor expansion. And if the symmetry check is successful, screening the measurement result or projecting the measurement result into a subspace meeting the symmetry by utilizing the symmetry of the specific solving problem so as to remove the part of the measurement result which does not meet the limiting condition. However, these have the following problems: since the wrong model is unknown, the variance of the observed quantity is greatly increased, making it difficult to extend these methods into larger scale systems.
The known quantum error suppression algorithm of the noise model generally assumes a noise model of a specific form, such as depolarization noise, and since the noise model generally acts on the quantum system in a linear manner, the most direct error suppression method is to implement the inverse of error generation. For example, a quantum error suppression algorithm-quasi-probability method with known noise models, in consideration of phenomena that the inverse process often accompanies the occurrence of non-physical properties, acts on the quantum circuit with specific probability in the implementation process of the quantum circuit equivalently in quasi-probability form, and restores the inverse operation to obtain an observed expected value after error mitigation in the form of an observed expected value. However, this method also has the following problems: the proposed algorithm for a particular noise model generally relies on the assumption that the noise model can describe the noise form of a real quantum device well enough, and generally is very costly both in terms of noise form and in terms of reasonable noise model itself, the former generally relying on additional state tomography (state tomography) methods, while for the latter, it is difficult for the noise model to describe the error form universally due to the multiple origins of the errors.
For error suppression methods based on machine learning, two forms are generally included, one is to correct for the expected value of the observed quantity, and the other is to implement error suppression for the probability distribution obtained by measurement. The former achieves error suppression by fitting a mapping of noisy observables expectations to ideal expectations, which requires that the ideal expectations in the training set data can be efficiently modeled, such as using a C/fford line to generate data, which can be applied to more general quantum lines once training is completed. The latter is typically based on neural network algorithms, by which error mitigation is achieved by fitting a mapping from noisy probability distributions to ideal probability distributions. However, this method also has the following problems: for some specific problems, the limitation of the error suppression algorithm based on machine learning is large, and when the depth of the quantum circuit in the practical application process is different from that of the training set, deviation of the error suppression result is caused. Furthermore, the method of measuring distribution mapping by fitting is also difficult to apply to large systems on a large scale.
In order to solve the above technical problems, and in particular to suppress measurement errors in measurement of a fermi subsystem, an embodiment of the present invention provides a method for suppressing errors in measurement of a fermi subsystem. Fermi is a generic term for a class of particles, in a group of systems consisting of isotactic particles, if only one particle is allowed to be accommodated in one quantum state of the system, such particles are referred to as fermi, or particles with a spin that is half-odd (e.g., 1/2,3/2 …) are collectively referred to as fermi. The core idea of the scheme for suppressing measurement errors in fermi subsystem measurement provided by the embodiment of the invention is that, first, a neural network model of the reduced density matrix is trained according to the input actual measured reduced density matrix and based on the ideal reduced density matrix of the fermi subsystem and the actual measured reduced density matrix carrying noise. And then, using the neural network model, obtaining a reduced density matrix after noise reduction according to the reduced density matrix carrying noise of the tested fermi subsystem, and further determining the energy of the tested fermi subsystem according to the reduced density matrix after noise reduction.
The method has the following advantages: in the first aspect, compared with an error suppression method unknown to an error model, the method does not need to increase the number of times of quantum state measurement, that is, the cost of a quantum state measurement stage is not increased, and the high efficiency of a quantum computing process can be ensured. In the second aspect, the neural network model can effectively perform targeted error suppression aiming at the situation that specific quantum equipment is used in different quantum computing processes, so that the limitation of the assumed error model form is avoided, and the computing cost caused by methods such as implementation of state chromatography is avoided. In a third aspect, the method enables more efficient training and use of error mitigation models for reduced density matrix mapping of fermi subsystem fits from input to output than general machine learning based methods to fit probability distribution maps from input to output. In addition, the method can also utilize the N-order representational condition as a constraint condition of training (set a training loss function) when training the model, so that the output reduced density matrix is more in line with the physical characteristics of the Fermi subsystem, and can ensure that the processed quantum circuits in different forms can have relatively stable noise reduction effects.
Fig. 1 is a flowchart of a method for suppressing errors in fermi subsystem measurement according to an embodiment of the present invention. As shown in fig. 1, the method at least comprises the following steps:
step 11, determining a first reduced density matrix carrying noise based on the measurement result of the first fermi subsystem;
First, at step 11, a first reduced density matrix carrying noise is determined based on measurements made on the first fermi subsystem.
In this step, a reduced density matrix (e.g., a first reduced density matrix) carrying noise is determined based on a measurement result obtained after measurement for the fermi subsystem to be measured (e.g., a first fermi subsystem). Since the reduced density matrix is obtained from the actual measurement results, the reduced density matrix is a reduced density matrix carrying quantum noise information.
The fermi subsystem is a quantum system composed of fermi subunits. In different embodiments, measurements may be performed on different fermi subsystems to be measured, and the corresponding specific reduced density matrix may be determined according to the measurement results, which is not limited in this specification. In different embodiments, the measurement is performed on the fermi subsystem to be measured, and the specific measurement mode can be different, which is not limited in this specification. In one embodiment, the fermi subsystem may be an electronic system and the first reduced density matrix may be a two-electron reduced density matrix that carries noise.
The fermi subsystem may generally be represented by its corresponding hamiltonian amount. However, the complete hamiltonian of a fermi subsystem is usually determined from the measurement results of a large number of quantum measurements. In contrast, determining the reduced density matrix of the fermi subsystem may be determined by a smaller number of measurements.
Then, in step 12, the first reduced density matrix is input into a pre-trained error suppression model, and a second reduced density matrix after noise reduction is obtained.
In the step, the first reduced density matrix obtained in the step 11 is input into a trained error suppression model, and a second reduced density matrix after noise reduction is obtained. And the obtained second reduced density matrix after noise reduction can be used for determining the energy of the fermi subsystem in the subsequent step.
In the embodiment where the first reduced density matrix is a two-electron reduced density matrix carrying noise, the second reduced density matrix is a two-electron reduced density matrix after noise reduction.
The pre-training method of the error suppression model may be different in different embodiments, and this specification is not limited in this regard. A detailed description of some embodiments employing different specific training patterns is given below.
After the second reduced density matrix is obtained, the energy of the first fermi subsystem is determined based on the second reduced density matrix in step 13.
In this step, the energy of the first fermi subsystem may be determined based on the second reduced density matrix obtained in step 12.
In one embodiment, for an electronic system to be tested composed of N electrons, the hamiltonian H thereof can be expressed as:
wherein, the liquid crystal display device comprises a liquid crystal display device,
and a are fermi generation and annihilation operators, respectively, i, j, k, j is electron ordinal, h ij And V ijkl The single electron and the two electron interaction coefficients, respectively. Quantum state |psi for system under test>The system energy can be expressed as:
E＝<ψ|H|ψ>＝h ij D 1 +V ijkl D 2
wherein D is 1 And D 2 The single-electron and two-electron reduced density matrices (reduced density matrix, RDM) of the system, respectively, may be referred to as 1-RDM and 2-RDM, respectively. In one example, the 2-RDM of the system may be measured efficiently and reduced to 1-RDM.
That is, the 2-RDM of the system under test may be determined by fewer quantum measurements (relative to that required to obtain the full Hamiltonian), the 1-RDM may be obtained from the 2-RDM, and then the energy of the system under test may be determined from the 1-RDM and the 2-RDM.
In the above description of step 12, the error suppression model for outputting the noise reduction reduced density matrix of the fermi subsystem under test may be pre-trained. The specific manner in which the error mitigation model is pre-trained may vary in different embodiments. FIG. 2 is a flowchart of a training method of an error suppression model according to another embodiment of the present invention. In the embodiment shown in fig. 2, the training process of the error suppression model may specifically include the following steps 21-23:
step 22, inputting the third reduced density matrix into an error suppression model to obtain a fifth reduced density matrix;
In step 21, the second fermi subsystem is a specific fermi subsystem corresponding to the training samples (e.g., including the third reduced density matrix and the fourth reduced density matrix) used in the training process, which is not limited to being identical to the first fermi subsystem described in step 11.
In various embodiments, the noisy third reduced density matrix and the ideal fourth reduced density matrix may be obtained by actual or simulated acquisition of the fermi subsystem, as this description is not limited in this regard. In one embodiment, the ideal fourth reduced density matrix may be obtained by quantum simulation by a classical computer. In one embodiment, the noisy reduced density matrix may be determined by a hypothetical noise model or by taking noisy measurements from a quantum device. Furthermore, since the free fermi subsystem can be efficiently modeled by classical computers, and its transformed hamiltonian form can facilitate the generation of sufficiently rich quantum states for training. Thus, in one embodiment, a free fermi subsystem may be employed as the second fermi subsystem.
In addition, a model-updated loss function can be set according to the N representational conditions in model training to obtain a more accurate reduced density matrix conforming to the physical characteristics of the Fermi subsystem through the model. Specifically, for a general local hamiltonian, no complete information of the hamiltonian is needed in principle to estimate the expected value of the hamiltonian, for example, for a 2-local hamiltonian, only the two-electron reduced density matrix needs to be known to estimate the expected value (i.e., the system energy of the quantum system corresponding to the hamiltonian). As previously described, the reduced density matrix measured from the quantum device changes due to the presence of noise, thereby causing an energy estimation error. The N representational conditions are constraints that the reduced density matrix of the fermi subsystem needs to satisfy, and a given reduced density matrix corresponds to an N-body meter subsystem only when these conditions are satisfied; conversely, when a violation occurs, it is stated that a given reduced density matrix does not correspond to any physical system, so we can reduce the effect of noise by projecting the reduced density matrix affected by noise into a physical subspace, i.e., a space that satisfies the N-representability constraint. In one embodiment, since the complete satisfaction of the N representability condition is difficult, the condition may be replaced with a second order approximation of the condition. The second order approximation of this condition, which may be referred to as the 2-positive condition (2-positive), is expressed as follows:
the above formula indicates that two electrons, two holes, one electron and one hole RDM are all semi-positive, and the corresponding physical meaning is that the probability of finding two electrons, two holes, one electron and one hole in any two electron orbitals is equal to zero. As described above, N representability dictates what properties the measured 2-RDM possesses to be physically or chemically possible, but experimentally measured 2-RDM often does not meet these conditions due to the presence of noise. While the neural network is used to fit the output 2-RDM to the ideal 2-RDM, the output 2-RDM is in the N-order representational space so as to further alleviate the negative effects of quantum noise.
FIG. 3 is a flowchart of a training method of an error suppression model according to another embodiment of the present invention. In the embodiment shown in fig. 3, the training process of the error suppression model may specifically include the following steps 31-35:
in step 31, obtaining a noisy third reduced density matrix and an ideal fourth reduced density matrix of the second fermi subsystem, wherein the third reduced density matrix and the fourth reduced density matrix are two-electron reduced density matrices;
in step 32, inputting the third reduced density matrix into an error suppression model to obtain a fifth reduced density matrix;
in step 33, determining a first two-hole reduced density matrix and a first electron-hole reduced density matrix based on the Wick theorem according to the fourth reduced density matrix; determining a second two-hole reduced density matrix and a second electron-hole reduced density matrix based on the Wick theorem according to the fifth reduced density matrix;
in step 34, a second loss is determined based on the second difference of the fifth reduced density matrix and the fourth reduced density matrix, based on the second difference of the first two-hole reduced density matrix and the second two-hole reduced density matrix, and based on the second difference of the first electron-hole reduced density matrix and the first electron-hole reduced density matrix.
In different embodiments, the second difference may also have a different specific determination. In one embodiment, the second difference may be a difference in rank between different matrices. Thus, in this embodiment, the second difference of the fifth reduced density matrix and the fourth reduced density matrix may be a difference of ranks of the fifth reduced density matrix and the fourth reduced density matrix; the second difference between the first two-hole reduced density matrix and the second two-hole reduced density matrix may be a difference in rank between the first two-hole reduced density matrix and the second two-hole reduced density matrix; the second difference between the first electron-hole reduced density matrix and the first electron-hole reduced density matrix may be a difference in rank between the first electron-hole reduced density matrix and the first electron-hole reduced density matrix.
Determining a first loss based on a first difference between the fifth reduced density matrix and the fourth reduced density matrix, step 35; the parameters of the error suppression model are updated with the aim that the first loss and the second loss tend to become smaller.
According to an embodiment of yet another aspect, an apparatus is provided for suppressing errors in fermi subsystem measurements. Fig. 4 is a block diagram of an apparatus for suppressing errors in fermi subsystem measurement according to an embodiment of the present invention, and as shown in fig. 4, the apparatus 400 includes:
a noise matrix acquisition unit configured to determine 41 a first reduced density matrix carrying noise based on a measurement result of the first fermi subsystem;
a noise matrix determining unit configured to 42, input the first reduced density matrix into a pre-trained error suppression model, and obtain a second reduced density matrix after noise reduction;
a system quantity determination unit configured to determine 43 an energy of the first fermi subsystem based on the second reduced density matrix.
According to an embodiment of a further aspect, there is also provided a computer readable medium comprising a computer program stored thereon, which computer, when run, performs the method described above.
According to an embodiment of yet another aspect, there is also provided a computing device including a memory having executable code stored therein and a processor that, when executing the executable code, implements the method described above.
The foregoing describes specific embodiments of the present disclosure. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims can be performed in a different order than in the embodiments and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.
Those of skill would further appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative elements and steps are described above generally in terms of function in order to clearly illustrate the interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied in hardware, in a software module executed by a processor, or in a combination of the two. The software modules may be disposed in Random Access Memory (RAM), memory, read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the invention, and is not meant to limit the scope of the invention, but to limit the invention to the particular embodiments, and any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (7)
1. A method of suppressing errors in a measurement of a fermi subsystem, the fermi subsystem being an electronic system, the method comprising:
determining a first reduced density matrix carrying noise based on a measurement result of the first fermi subsystem, wherein the first reduced density matrix is a two-electron reduced density matrix carrying noise;
inputting the first reduced density matrix into a pre-trained error suppression model, and obtaining a second reduced density matrix after noise reduction, wherein the second reduced density matrix is a two-electron reduced density matrix after noise reduction; the error suppression model is trained by the following process: acquiring a noisy third reduced density matrix and an ideal fourth reduced density matrix of the second fermi subsystem, wherein the third reduced density matrix and the fourth reduced density matrix are two-electron reduced density matrices; inputting the third reduced density matrix into an error suppression model to obtain a fifth reduced density matrix; determining a first loss based on a first difference between the fifth reduced density matrix and the fourth reduced density matrix; according to the fourth reduced density matrix, determining a first two-hole reduced density matrix and a first electron-hole reduced density matrix based on the Wick theorem; determining a second two-hole reduced density matrix and a second electron-hole reduced density matrix based on the Wick theorem according to the fifth reduced density matrix; determining a second loss based on a second difference of the fifth reduced density matrix and the fourth reduced density matrix, based on a second difference of the first two-hole reduced density matrix and the second two-hole reduced density matrix, and based on a second difference of the first electron-hole reduced density matrix and the first electron-hole reduced density matrix; updating parameters of the error suppression model with the aim that the first loss and the second loss tend to be smaller;
an energy of the first fermi subsystem is determined based on the second reduced density matrix.
2. The method of claim 1, wherein the difference between the fifth reduced density matrix and the fourth reduced density matrix comprises:
the difference between the Frobenius norms of the fifth reduced density matrix and the fourth reduced density matrix.
3. The method of claim 2, wherein the second difference of the fifth reduced density matrix and the fourth reduced density matrix comprises a difference in rank of the fifth reduced density matrix and the fourth reduced density matrix;
a second difference between the first two-hole reduced density matrix and the second two-hole reduced density matrix, comprising a difference in rank of the first two-hole reduced density matrix and the second two-hole reduced density matrix;
the second difference between the first electron-hole reduced density matrix and the first electron-hole reduced density matrix comprises a difference in rank between the first electron-hole reduced density matrix and the first electron-hole reduced density matrix.
4. The method of claim 1, wherein determining the energy of the first fermi subsystem based on the second reduced density matrix comprises:
according to the two-electron reduced density matrix after noise reduction, determining a single-electron reduced density matrix after noise reduction;
and determining the energy of the first Fermi subsystem according to the two-electron reduced density matrix after noise reduction and the single-electron reduced density matrix after noise reduction.
5. An apparatus that suppresses errors in fermi subsystem measurements, comprising:
a noise matrix acquisition unit configured to determine a first reduced density matrix carrying noise based on a measurement result of the first fermi subsystem, the first reduced density matrix being a two-electron reduced density matrix carrying noise;
the noise matrix determining unit is configured to input the first reduced density matrix into a pre-trained error suppression model to obtain a second reduced density matrix after noise reduction, wherein the second reduced density matrix is a two-electron reduced density matrix after noise reduction; the error suppression model is trained by the following process: acquiring a noisy third reduced density matrix and an ideal fourth reduced density matrix of the second fermi subsystem, wherein the third reduced density matrix and the fourth reduced density matrix are two-electron reduced density matrices; inputting the third reduced density matrix into an error suppression model to obtain a fifth reduced density matrix; determining a first loss based on a first difference between the fifth reduced density matrix and the fourth reduced density matrix; according to the fourth reduced density matrix, determining a first two-hole reduced density matrix and a first electron-hole reduced density matrix based on the Wick theorem; determining a second two-hole reduced density matrix and a second electron-hole reduced density matrix based on the Wick theorem according to the fifth reduced density matrix; determining a second loss based on a second difference of the fifth reduced density matrix and the fourth reduced density matrix, based on a second difference of the first two-hole reduced density matrix and the second two-hole reduced density matrix, and based on a second difference of the first electron-hole reduced density matrix and the first electron-hole reduced density matrix; updating parameters of the error suppression model with the aim that the first loss and the second loss tend to be smaller;
and a system amount determining unit configured to determine an energy of the first fermi subsystem based on the second reduced density matrix.
6. A computer readable storage medium having stored thereon a computer program which, when executed in a computer, causes the computer to perform the method of any of claims 1-4.
7. A computing device comprising a memory having executable code stored therein and a processor, which when executing the executable code, implements the method of any of claims 1-4.
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