Quantum calculation method and device for sparse coding

Abstract

The invention relates to a method and apparatus for performing quantum computing. The method comprises sparse coding, a set B of M single particle functions fj is defined for the number N of particles and the size of the basis set in the physical system, where each function fj is a function from the single particle space, and two monotonically increasing mappings k and r are defined, which assign a positive real number to each single particle function fj, and for the parameters, a set B of M single particle functions fj is defined. A reduced tensor product basis of the single particle function fj is selected, where T belongs to R (where T < 1) defines a reduction in the number of basis functions, pq and pr are parameters of the selected pq-norm and pr-norm, and K and R are selected based on error characteristics of the reduced tensor product basis.

Description

Technical Field

[0001] This invention belongs to the field of quantum computing. Background Technology

[0002] The potential advantages of quantum algorithms over those on classical computers are substantially limited by the number and quality of available qubits. The object of this invention is to provide a compact and efficient representation of the state function of a many-body Hamiltonian operator, which reduces the number of qubits required for meaningful simulation of such an operator on a quantum computer.

[0003] Current quantum computing hardware devices provide between 100 and 1000 physical qubits (which obey a fairly large error). The first quantum computing hardware device has been introduced, requiring 4 logical qubits (or at least qubits obeying a sufficiently small error). It is anticipated that approximately 100 logical qubits will be needed to realize the advantage of quantum computing hardware over classical computing hardware.

[0004] The state function of a many-body Hamiltonian operator is a function of a Hilbert space with specific symmetries. In the case of bosons (e.g., photons), the state function is symmetric, the particles are interchanged, and bosons have integer spin. In the case of fermions (e.g., electrons), the state function is antisymmetric, the two particles are interchanged, and fermions have spin ½ or spin -½. To perform quantum computation, the many-body state is approximated in a finite-dimensional Hilbert space and encoded using a finite number of qubits. This applies to algorithms for quantum hardware in the current era of Noisy Intermediate Scale Qubits (NISQ) (e.g., the Variational Quantum Eigensolver, VQE) and algorithms for future Fault-Tolerant Qubit (FTQ) quantum hardware (such as Quantum Phase Estimation (QPE) methods and Hamiltonian simulation methods).

[0005] The computational resources required to compute a multi-particle system are typically measured in terms of the number of particles N in the system and the size of the basis set M (i.e., the number of spin orbitals to be considered). In the case of fermions and formulas using second quantization, the Jordan-Wigner (JW) and Bravyi-Kitaev (BK) mapping schemes are used, where the number of qubits is linearly related to the number of single-particle basis (or orbitals) considered in the method. Here, the required number of qubits is M because fermionic Fock states are directly mapped to an M-qubit quantum register. This means that, where M single-particle spin orbitals approximate the wavefunction of N electrons, these states can be mapped to n = O(M) qubits. Furthermore, there are techniques that utilize any known symmetry of the system to reduce the number of qubits used. Typically, the number of qubits is reduced by one for each symmetry. These representations also include many-body states that do not represent N particles. If only multi-particle states corresponding to exactly N particles are represented, so-called efficient or compact encoding (or mapping) can also be used with the aid of binary encoding. For a fixed number of upward-spinning electrons N… u and the down-spin electron N d (where N=N) u +N d ), can map the state to M qubits (see Chamaki, D., Metcalf, M., & de Jong, WA (2022)). Compact molecular simulations were performed on a quantum computer via combinatorial mapping and variational state preparation (arXiv preprint: 2205.11742). Also in the first quantization, the Slater determinant involved in the M single-particle spin orbitals can be represented by... Optimal encoding of qubits (see Babbush, R., Berry, DW, Sanders, YR, Kivlichan, ID, Scherer, A., Wei, AY,... & Aspuru-Guzik, A. (2017)). Exponentially more precise quantum simulation of fermions in the configuration interaction representation. (Quantum Science & Technology, 3(1), 015006). Binary encoding using qubits has also been used in cases with special subsets of the Slater determinant, where the eigenvalues ​​and functions of the Hamiltonian have already been solved using classical algorithms on classical hardware to determine these subsets (Yoffe, D., Natan, A., and Makmal, A. (2023)). A qubit-efficient variational selected configuration-interaction method (arXiv preprint: 2302.06691).

[0006] Reference documents EP4290421A1, US 2024 / 0071576 A1, US2023206100A1, US2023016119A1, WO2021203202A1, US2023385681A1 and US11735291B2 illustrate methods for quantum computing. Summary of the Invention

[0007] As mentioned at the beginning, the object of the present invention is to provide a compact and efficient representation of the state function of a multibody Hamiltonian operator, which reduces the number of qubits required to meaningfully simulate such a Hamiltonian operator on a quantum computer.

[0008] This is achieved by a method or apparatus for performing quantum computing according to the independent claim. Advantageous embodiments can be found in the dependent claims and the following description.

[0009] Therefore, a method for performing quantum computing is proposed. This method includes sparse coding, where, for the number of particles N and the basis set in the physical system... The size (which can be seen as corresponding to the number of orbitals to be considered), M single-particle functions f jThe set B (where each function f) j From single-particle space to The function is defined as Furthermore, a monotonically increasing mapping k is defined that assigns positive real numbers to each single-particle function f. j For parameters Single-particle function f j The reduced tensor product basis set Selected as

[0010] ,

[0011] in, (in, Define the reduction in the number of basis functions. K is the parameter of the selected p-norm, and K is based on the reduced tensor product basis set. The error characteristics are used to select the product. Here, ⊗ represents products such as tensor product, antisymmetric product, wedge product, etc.

[0012] A device for performing quantum computing is also proposed. This device includes an encoder for sparse coding, configured to produce a reduced tensor product basis set for the physical system. Among them, for the number of particles N and the basis set in the physical system... The size (which can be seen as corresponding to the number of orbitals to be considered), M single-particle functions f j The set is defined as Furthermore, a monotonically increasing mapping k is defined that assigns positive real numbers to each single-particle function f. j The device is configured to transmit single-particle function f j Reduced tensor product basis set Select as

[0013] ,

[0014] in, (in Define the reduction in the number of basis functions, and This is the parameter of the selected p-norm. The device is configured to be based on the reduced tensor product basis set. The error characteristic is chosen by selecting K. For example, for fermions, this could include a partially antisymmetric tensor product, and for bosons, it could include a partially symmetric tensor product.

[0015] In a device or method, for example, p may be chosen to represent the 1-norm. For example, it can also be chosen as the Euclidean norm. Or, for the maximum norm, choose it as .

[0016] In addition to the aforementioned devices and methods, this application also relates to another device and method for performing quantum computing, which is based on two discretization parameters K and R, rather than just one discretization parameter K as shown above. Specifically, a method for performing quantum computing includes sparse coding, wherein, for the number of particles N in the physical system and the size of the basis set M (which can be considered to correspond to the number of orbits under consideration), M single-particle functions f j The set B is defined as Furthermore, two monotonically increasing mappings k and r are defined, which assign positive real numbers to each single-particle function f. j ,

[0017] Among them, for parameters and parameters Single-particle function f j Reduced tensor product basis set Selected as

[0018] ,

[0019] in, (Where T < 1) defines the reduction in the number of basis functions. and It is the selected p q -norm and p r - The parameters of the norm, and K and R are based on the reduced tensor product basis set. The error characteristics are used to select it.

[0020] Furthermore, the device used to perform quantum computing includes an encoder for sparse coding, which is configured to produce a reduced tensor product basis set for the physical system. Among them, for the number of particles N and the basis set in the physical system The size (which can be considered to correspond to the number of orbitals under consideration), M single-particle functions f j The set B is defined as Furthermore, two monotonically increasing mappings k and r are defined, which assign positive real numbers to each single-particle function f. j ,

[0021] The device is configured to transmit single-particle function f j Reduced tensor product basis set Select as

[0022] ,

[0023] Where T (where T < 1) defines the reduction in the number of basis functions, p q and p r It is the selected p q -norm and p r - The parameter of the norm,

[0024] The device is configured to be based on the reduced tensor product basis set. The error characteristics are used to select K and R.

[0025] Here, the first term with mapping k is similar to the one described above. The terms in this can be viewed as similar to Fourier bases, where, additionally, a second term is considered. In the example, in the case of two maps k and r, the idea of ​​constructing the underlying basis set is similar to constructing a smooth partition of the Fourier space used in the Fourier space within a suitably compact support product domain. Then, a discrete Fourier basis set is defined on each subdomain. Then, on each band-limited function in the Fourier space, the inverse Fourier transform is applied to define the relevant basis functions in the real space, where the map k is associated with the corresponding subdomain in the Fourier space, and the map... It is associated with the corresponding wave vector of the discrete Fourier basis, and then the wave vector is similar to an index associated with localization in real space.

[0026] It should be understood that aspects of the invention explained in conjunction with one of these methods can also be claimed for use in the corresponding device, and vice versa.

[0027] In a device or method, the reduced representation of a multi-particle wavefunction is achieved by limiting the number of multi-particle tensor product basis functions considered. This is achieved by terminating through a threshold. and threshold Consider implementing a single-particle function, if applicable. The mapping k is monotonically increasing, and the lowest and first values ​​assigned by k are greater than or equal to 1: Note that mapping k can be defined as acting on function f, or directly on index j. i This also applies to the mapping r. Thus, the product terms exhibit a controlled property that ensures subsequent terms make a small contribution to the wavefunction with approximate continuity. Therefore, truncation according to a defined threshold does not lead to unexpected properties. Terminating single-particle functions in this way means ignoring high eigenvalues, as the high correlation between single-particle functions becomes less important. Due to the smoothness of the solution, higher-order tensors (e.g., high-degree polynomials) become increasingly less important, thus the tensor product (e.g., polynomial) basis across the space is truncated.

[0028] In a device or method, K can be based on a reduced tensor product basis set that depends on K. or It is selected based on the convergence characteristics. For example, the initial value of K = K1 can be used for the first calculation. The initial value of K1 can be selected and input by the user, for example. In the device or method, an initial calculation is performed for K = K1. The value of K continuously increases, such as K = K2, K = K3,... where K1 < K2 < K3 <..., and the results of various calculations are compared with each other. If the change in the calculation result depending on K exhibits convergence characteristics as K increases, it can be determined that the method is converging and delivering reliable results. Therefore, K is finally selected such that there are convergence characteristics for the selected K, as determined by the above convergence study. The initial selection can be a low value of K, and then K can be continuously increased, such as increasing in steps of 1. Alternatively, K can be increased by multiplying K by a factor (such as multiplying by 2). Additionally or alternatively, if an error formula is available and the asymptotic error characteristics are known, a set of several values of K (such as 3 values of K) may be sufficient to extrapolate the characteristics.

[0029] For , when there is an additional parameter R, R and K can be selected as . In another example, R and K can be selected as . In the example, R can be selected as or , where a is a factor that can be selected to be close to 1. Moreover, the remaining factors can be selected, for example, as b = 1, c = 1, and d = 2, or as different numbers, especially integers. Note that this depends on the properties of the state function. For example, in the case of the eigenvalues of a discrete spectrum, it is well known that the corresponding eigenfunctions decay exponentially in space and are therefore called bound states. In addition, these eigenfunctions are in a special Sobolev space of dominating mixed smoothness. Here, will be selected because the error decay characteristics of a specific error estimation term are algebraic with respect to K and exponential with respect to R.

[0030] In the device or method, M can be . That is, the set of single-particle functions can be infinite. As an approximation, M can be finite or truncated. In the case of finite M, the reduced tensor product basis set or no longer increases from a certain K (and R). In the example, M can remain infinite, and the truncation is achieved by truncating K (and R).

[0031] Additional parameter (where T < 1) defines a reduction in the number of basis functions, which can also be referred to as "sparsification". This sparsification can vary within the method or device of the present invention. For example, T can be chosen as T = 0. T can be chosen such that 0 < T < 1. T can be chosen as . Thus, in the present device or method, T is chosen to be greater than -∞, i.e., -∞ < T < 1. The limit T → -∞ is excluded according to the proposed device or method.

[0032] Specifically, for as defined above, for T = 0, a special case is achieved, where takes the following form:

[0033] ,

[0034] For example, if the single-particle functions f j form a Fourier basis, this is the hyperbolic case or hyperbolic intersection. For 0 < T < 1, a more reduced (more sparse) basis set than is achieved, where the special case T → 1 represents the smallest possible set, which can be interpreted as considering only the single-particle axes, i.e., . According to the proposed device or method, the special case T → 1 can be included. For -∞ < T < 0, a set larger than is obtained. The limit T → -∞ corresponds to the case without sparsification, which can be represented as

[0035] ,

[0036] where p > 0 defines the norm. Here, again, p is typically chosen to represent the 1-norm. For example, it can also be chosen as for the Euclidean norm, or as for the max-norm. represents the full tensor product space with respect to M single-particle functions, which can be regarded as including all Slater determinants of the FCI method (in contrast, according to the chosen sparsification, the present device or method only employs a selection of Slater determinants). Therefore, this limit is not generally envisaged within the current method, as it does not reduce the basis set envisaged according to the present invention. The full tensor product space can be used as a reference for the device of the present method. When approximating the full tensor product space by truncating K, the basis set increases sharply with the increase of K. The effect of the currently proposed device and method is that the growth rate of the required number of qubits is greatly reduced, which is a function of the number of spin orbitals (or spatial orbitals) involved. That is, for the present invention, the reduced tensor product basis set contains elements, which can be represented using only Encoding (here, 1 qubit) express Conversely, for the full tensor product space, the set includes... This results in a progressively larger number of elements.

[0037] For reduced tensor product basis sets The number of orbitals is expressed as follows (assuming M is infinite):

[0038] ,

[0039] In other words, as K increases, the cost increases linearly except for the logarithmic term. In contrast, for the full tensor product space, this set includes... The number of elements leads to an asymptotically substantial increase in the number of elements. The orbital number is expressed as...

[0040] .

[0041] That is, for the entire set, the cost increases exponentially with K.

[0042] It should be noted that in typical applications, N is much smaller than M.

[0043] Furthermore, compared to methods using unreduced tensor product spaces, this device and method can also reduce the number of qubits required for a given error tolerance.

[0044] Specifically, the inventors have recognized that the findings of Yserentant, H. in Springer 2010, “Regularity and approximability of electronic wavefunctions,” and the research of Griebel, M. and Hamaekers, J. in Zeitschrift für Physikalische Chemie, 2010, 224(3-4), 527-543, “Tensor product multiscale many-particle spaces with finite-order weights for the electronic Schrödinger equation,” show that, in the special case of T=0, K-dependent The error characteristics may be similar to those of the fully unreduced tensor product basis set. That is, for those specific cases, the reduced tensor product basis set... The asymptotic error characteristic corresponds to The asymptotic error characteristics, in addition to the logarithmic term. In the context of this invention, besides the reduced number of qubits as described above, another advantage may be that, based on findings for specific cases, this error characteristic can be advantageous, as well as for the general case presented herein.

[0045] Therefore, the error of this device or method is comparable to the error that would occur if the full tensor product space were used and truncated via K.

[0046] For as defined above In the special case of T=0, the following form applies:

[0047]

[0048] The full tensor space in the limit T→-∞, which is typically excluded from sparsification by the method proposed in this paper, can be represented as:

[0049]

[0050] and Compared to the example, using This allows for more complex discretizations that can be considered in terms of spatial discretization. Nevertheless, the aforementioned advantages regarding the reduced growth rate apply here in the same way.

[0051] Choosing R=K as a special case results in having virtually only a single discretization parameter. Using R=K and choosing T=0, we can again expect the asymptotic error property of the sparse set to be equal to the property of the full tensor product basis / unreduced tensor product basis, up to the logarithmic term.

[0052] In the example, set B can be chosen as a subset of the eigenfunctions of the single-particle Hamiltonian operator, and mapping k can be chosen to assign associated eigenvalues ​​to each single-particle function f in the set. j Functions. For example, the Hamiltonian operator can be the Schrödinger operator.

[0053] Mapping k can be viewed as sorting the basis according to its oscillation level or smoothness level s (wavenumber in the case of Fourier basis). Mapping r can be viewed as sorting the basis at a given smoothness s according to its distance from the origin, where the distance to neighboring basis decreases as the level increases from s to s+1. This is analogous to wavelets with level / scale index and spatial index.

[0054] In the example, in this device or method, the reduced tensor product basis set is... or It can be provided to the hardware system in the form of a quantum hardware system or a hybrid quantum hardware system, reducing the tensor product basis set. or Specifically, it is represented by qubits contained in the hardware system.

[0055] For example, physical systems can be based on reduced tensor product basis sets. or Simulation on hardware systems, especially for calculating the ground state of physical systems to determine energy levels or for further analysis.

[0056] The device may include a hardware system in the form of a quantum hardware system or a hybrid quantum hardware system, wherein the device may be configured to provide a reduced tensor product basis set to the hardware system. or . Attached Figure Description

[0057] The invention will now be described in an exemplary and non-limiting manner with reference to the accompanying drawings.

[0058] in, Figure 1a A quantum computing method based on reduced compact coding with parameters k, K, T, and p is shown, which employs quantum hardware.

[0059] Figure 1b A quantum computing method based on reduced compact coding with parameters k, K, T, and p is shown, which employs hybrid quantum hardware;

[0060] Figure 2a The diagram shows the parameters k, r, K, R, T, p. q p r A quantum computing method based on reduced compact coding, employing quantum hardware; and

[0061] Figure 2b The diagram shows the parameters k, r, K, R, T, p. q p r A quantum computing method based on reduced compact coding, which employs hybrid quantum hardware. Detailed Implementation

[0062] Refer to all Figures 1a to 2b This illustrates a quantum computing method employing a quantum computing device. In each case, the method includes sparse coding as described below. In the example, the ground state of a physical system containing N particles is to be approximated. For example, this could be the ground state of a molecule whose Hamiltonian operator has fermionic eigenfunctions. However, the method is not limited to such Hamiltonian operators or eigenfunctions, and it can also be specifically applied to boson systems.

[0063] For example, a set of Hamiltonian operators and single-particle functions is provided as input to this method. Specifically, the Hamiltonian operator is chosen as the single-particle Schrödinger operator, and the single-particle function is chosen as the eigenfunction f of the single-particle Schrödinger operator. j A subset B is defined as This specifically forms an L2-orthogonal basis for the corresponding single-particle Hilbert space, and can assign an order to this subset. Here, M can be kept infinite, M=∞.

[0064] Turn Figure 1a and Figure 1b In this method, the single-particle function f j Reduced tensor product basis set Selected as

[0065]

[0066] Therefore, a monotonically increasing mapping k is defined, which assigns positive numbers to each single-particle function f. l In this example, k is a mapping that assigns the associated eigenvalues ​​to each single-particle basis function. Furthermore, based on the reduced tensor product basis set... The error characteristics are used to select the parameter K, and the parameter T is chosen to have -∞ < T < 1. T defines the reduction or sparsification of the number of basis functions. In this example, T is chosen to be T = 0, which corresponds to the hyperbola set. However, 0 < T < 1 or -∞ < T < 0 are also possible options. For example, in this method, a convergence study is performed to verify that for T = 0, As K increases, convergence is observed. Subsequently, a choice is made at... The value of K within the convergence range.

[0067] The reduced tensor product basis set includes the defined mapping K and the determined values ​​of T and K. Provided to the hardware system. (Reference) Figure 1a This could be fault-tolerant qubit (FTQ) quantum hardware, such as quantum phase estimation (QPE), or a device employing Hamiltonian simulation methods. See also Figure 1b This could also be hybrid quantum hardware, such as Noisy Intermediate Scale Qubit (NISQ) devices, for example, that incorporate a hybrid variational quantum eigensolver (VQE), which may include classical hardware components.

[0068] Then, reduce the tensor product basis set. It is represented by qubits contained in the corresponding hardware system. These considerations related to the hardware system, with necessary modifications, also apply to... Figure 2a and Figure 2b The situation.

[0069] For example, in the case of an electronic system with N particles, including N u Upward spin electrons and N d Down-spin electrons, where N=N u +N d For T=0, the reduced set can be written as

[0070] ,

[0071] Where ∧ is the antisymmetric tensor product (the definition of other sets can be similarly modified, such as sets dependent on T or the entire set), and the up-spin single-particle basis functions and down-spin single-particle functions are given by the following sets:

[0072] and

[0073] .

[0074] Compared to the full representation corresponding to →-∞ without sparsification, the number of qubits occupied by this representation is significantly reduced, and it can be expressed as:

[0075]

[0076] Alternatively, in the case of fermions, it can be represented as:

[0077] ,

[0078] At the same level of precision, the rate of decrease in the number of required qubits as a function of the number of spin orbitals (or spatial orbitals) involved. That is, the reduced tensor product basis set with sparsity. Manifestation

[0079]

[0080] Compared to the complete series, it is characterized by

[0081]

[0082] In the case of multi-electron states with up-spin and down-spin electrons as described above, similarly, for the reduced tensor product basis set, we obtain:

[0083]

[0084] In comparison:

[0085] For a complete base set

[0086] Specifically, consider the calculation of the FeMoco cofactor in nitrogenase, which involves N=54 electrons, as an example. For the case where the up-spin electrons and down-spin electrons are equal, i.e., N... u =N d =27, so the K=M=108 Gaussian spin orbital can be considered a single-particle function. This leads to the use of conventional coding... 157 qubits are used for the sparse coding described herein, which relies on a reduced tensor product basis set. Furthermore, in the case of using a planar wave-like basis set, it can be assumed that... Each spin orbital, which will lead to qubits, and with the introduction of sparse coding, Compared to individual qubits.

[0087] Therefore, the problem can be encoded onto an appropriate number of qubits in the hardware system, thus enabling the solution based on the reduced tensor product basis set. Simulate the underlying physical system on the hardware system. For example... Figure 1a and Figure 1b As shown, the hardware can provide an approximation of the ground state of a physical system as output. Therefore, this invention can be used to reduce the number of qubits required to represent the multiparticle wavefunction of a Hamiltonian relative to a molecule. In particular, many new problems in chemistry and physics can be simulated on a quantum computer due to our encoding, resulting in a significantly reduced number of qubits. This potentially accelerates the development of energy materials, particularly active pharmaceutical ingredients.

[0088] Turn Figure 2a and Figure 2b In another example, the Hamiltonian operator and a set of single-particle functions are provided as input to the method. Specifically, the single-particle function is chosen as f. j A subset B is defined as This specifically forms an L2-orthogonal basis for the corresponding single-particle Hilbert space, and an order can be assigned to this subset. In this example, the reduced tensor product basis set of the single-particle function... Selected as

[0089]

[0090] Furthermore, monotonically increasing mappings k and r are defined, where each mapping k and r represents a single-particle function f. jAllocate positive numbers. In addition, the parameters K and R are selected according to the error characteristics of the reduced tensor product basis set , and the parameter (where -∞ < T < 1) is selected.

[0091] The reduced tensor product basis set including the defined mappings k and r and the determined values of T, K, and R is provided to a hardware system, such as Figure 2a or Figure 2b as shown, and then the corresponding calculations are performed using the hardware system.

[0092] For example, if the described system is a fermionic system including a total of N particles (such as electrons), where N = N u + N d , then it can be written as follows:

[0093] ,

[0094] [[ID=2-eight]]where the single-particle basis functions for up spin and down spin are given by the following sets respectively:

[0095] And,

[0096] .

[0097] For the special case of T = 0, it has the following form:

[0098] .

Claims

1. A method for performing quantum computing, The method includes sparse coding, wherein, For the number of particles N and the basis set in a physical system The size of M single-particle functions f j The set B is defined as , where each function f j From single-particle space to The function f is defined, and a monotonically increasing mapping k is defined, which assigns positive real numbers to each single-particle function f. j , where, for parameters The single-particle function f j Reduced tensor product basis set Selected as ， in, Define a reduction in the number of basis functions, where T < 1, p is the parameter of the chosen p-norm, and K is based on the reduced tensor product basis set. The error characteristics are used to select it.

2. A method for performing quantum computing, The method includes sparse coding, wherein, For the number of particles N and the basis set in a physical system The size of M single-particle functions f j The set B is defined as , where each function f j From single-particle space to The function f is defined, and two monotonically increasing mappings k and r are defined, which assign positive real numbers to each single-particle function f. j , Among them, for parameters and parameters The single-particle function f j Reduced tensor product basis set Selected as in, Define a reduction in the number of basis functions, where T < 1, p q and p r It is the selected p q -norm and p r - The parameters of the norm, and K and R are based on the reduced tensor product basis. The error characteristics are used to select it.

3. The method according to claim 2, wherein, R and K were chosen as .

4. The method according to claim 2, wherein, R and K were chosen as .

5. The method according to any one of the preceding claims, wherein, K is selected based on the convergence properties of the reduced tensor product basis set, which depend on K.

6. The method according to any one of claims 1-5, wherein T is selected as T=0.

7. The method according to any one of claims 1-5, wherein T is selected as 0. <T<1。 8. The method according to any one of claims 1-5, wherein T is selected as .

9. The method according to any one of the preceding claims, wherein, The set B is selected as a subset of the eigenfunctions of the single-particle Hamiltonian operator, and the mapping k assigns the associated eigenvalues ​​to each single-particle function in the set.

10. The method according to any one of the preceding claims, wherein, The reduced tensor product basis set Provided to the hardware system in the form of a quantum hardware system or a hybrid quantum hardware system, wherein the reduced tensor product basis set is specifically represented by qubits contained in the hardware system.

11. The method according to claim 10, wherein, Based on the reduced tensor product basis set The physical system is simulated on the hardware system, particularly for calculating the ground state of the physical system.

12. The method according to any one of the preceding claims, wherein, 。 13. A device for performing quantum computing, the device comprising an encoder for sparse coding, the encoder being configured to produce a reduced tensor product basis set for a physical system. ,in, For the number of particles N and the basis set in the physical system The size of M single-particle functions f j The set B is defined as , where each function f j From single-particle space to The function f is defined, and a monotonically increasing mapping k is defined, which assigns positive real numbers to each single-particle function f. j , The device is configured to transmit the single-particle function f j Reduced tensor product basis set Select as ， Where T∈R defines the reduction in the number of basis functions, where T<1, p is a parameter of the selected p-norm, and where the device is configured based on the reduced tensor product basis set. K is selected based on its error characteristics.

14. A device for performing quantum computing, the device comprising an encoder for sparse coding, the encoder being configured to produce a reduced tensor product basis set for a physical system. , in, For the number of particles N and the basis set in a physical system The size of M single-particle functions f j The set B is defined as , where each function f j From single-particle space to The function f is defined, and two monotonically increasing mappings k and r are defined, which assign positive real numbers to each single-particle function f. j The device is configured to transfer the single-particle function f j Reduced tensor product basis set Select as ， where T e R defines a reduction in the number of basis functions, where T < 1, p q and p r are parameters of the selected p q -norm and p r -norm, respectively. The device is configured to be based on the reduced tensor product basis set. The error characteristics are used to select K and R.

15. The device of claim 13 or 14, further comprising a hardware system in the form of a quantum hardware system or a hybrid quantum hardware system, the device being configured to provide the reduced tensor product basis set to the hardware system.

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