Quantum computing method and system for molecular excited states in the presence of Hamiltonian symmetry

Abstract

Techniques for quantum computing of molecular excited states are provided. For example, a system may include a memory that may store computer executable components. The system may also include a processor that is operably coupled to the memory and may execute the computer executable components stored in the memory. The computer executable components may include an initialization component that may classify multiple excitation operators from a mapped qubit Hamiltonian into sectors based on the commutation characteristics of multiple excitation operators with symmetry in the mapped qubit Hamiltonian. The computer executable components may also include a matrix component that may generate a matrix equation of motion from one of the multiple excitation operators based on the sectors classified by the initialization component.

Description

Technical Field

[0001] The present disclosure relates to quantum computing of molecular excited states, and more particularly, to autonomous quantum computing of molecular excited states in the presence of Hamiltonian symmetry. Background Art

[0002] The calculation of excited state energies of molecules can be an important problem in electronic structure. The equation of motion ("EoM") method is one of the main methods for calculating excited states of molecules on classical computers. To calculate the excited state energies of a molecule, the EoM method builds up multiple matrices whose size increases quadratically in the number of excited states to be considered. The EoM method can be efficiently mapped onto a quantum computer, using the latter to calculate the average of the matrix elements used to calculate the excited state energies.

[0003] However, despite the fact that quantum computing can provide faster computational processing, conventional techniques using EoM methods still scale the matrix quadratically in the number of excited states considered. Quadratic scaling may result in high requirements for quantum computing resources and / or the use of a large number of qubits. For example, conventional EoM methods applied to quantum computing devices may require a large number of qubits to execute. Thus, making the operation of quantum circuits with a large number of gates more difficult.

[0004] Therefore, there is a need in the art to address the aforementioned problems. Summary of the invention

[0005] From a first aspect, the present invention provides a system for performing quantum computing on molecular excited states in the presence of Hamiltonian symmetry, the system comprising: a memory storing computer executable components; a processor operably coupled to the memory and executing the computer executable components stored in the memory, wherein the computer executable components include: an initialization component classifying multiple excitation operators from a mapped quantum bit Hamiltonian into sectors based on commutation characteristics of multiple excitation operators with symmetry in the mapped quantum bit Hamiltonian; and a matrix component generating a motion matrix equation from one of the multiple excitation operators based on the sector classified by the initialization component.

[0006] From another aspect, the present invention provides a system comprising: a memory storing computer executable components; a processor operably coupled to the memory and executing the computer executable components stored in the memory, wherein the computer executable components include: a control component generating a matrix equation of motion from a pair of excitation operators in the mapped qubit Hamiltonian based on the inherent symmetry of the mapped qubit Hamiltonian.

[0007] Viewed from another aspect, the present invention provides a computer-implemented method for performing quantum computation on molecular excited states in the presence of Hamiltonian symmetry, the method comprising:

[0008] By a system operably coupled to the processor, a plurality of excitation operators are classified from a mapped qubit Hamiltonian into sectors based on commutation properties of the plurality of excitation operators having symmetries in the mapped qubit Hamiltonian; and a matrix equation of motion is generated by the system from an excitation operator of the plurality of excitation operators based on the classification.

[0009] Viewed from another aspect, the present invention provides a computer-implemented method for quantum computing molecular excited states in the presence of Hamiltonian symmetry, comprising: generating a matrix equation of motion from a pair of excitation operators in a mapped qubit Hamiltonian based on the symmetry inherent in the mapped qubit Hamiltonian.

[0010] Viewed from another aspect, the present invention provides a computer program product for quantum computing molecular excited states in the presence of Hamiltonian symmetry, the computer program product comprising a computer-readable storage medium having program instructions embodied thereon, the program instructions executable by a processor to cause the processor to: classify, by a system operably coupled to the processor, a plurality of excitation operators from a mapped qubit Hamiltonian into sectors based on commutation characteristics of a plurality of excitation operators having symmetry in the mapped qubit Hamiltonian; and generate, by the system, a matrix equation of motion from one of the plurality of excitation operators based on the classification of the plurality of excitation operators into sectors.

[0011] A computer program product for performing quantum computation on molecular excited states in the presence of Hamiltonian symmetry, the computer program product comprising a computer-readable storage medium having program instructions embodied thereon, the program instructions executable by a processor to cause the processor to: generate, by a system operably coupled to the processor, a matrix equation of motion from a pair of excitation operators in a mapped qubit Hamiltonian based on a symmetry inherent in the mapped qubit Hamiltonian.

[0012] Viewed from another aspect, the present invention provides a computer program product for performing quantum computations on molecular excited states in the presence of Hamiltonian symmetry, the computer program product comprising a computer-readable storage medium readable by a processing circuit and storing instructions for executing by the processing circuit to perform a method for performing the steps of the present invention.

[0013] Viewed from another aspect, the invention provides a computer program stored on a computer readable medium and loadable into the internal memory of a digital computer, the computer program comprising software code portions for performing the steps of the invention when the program is run on a computer.

[0014] The following is an overview to provide a basic understanding of one or more embodiments of the invention. This overview is not intended to identify key or important elements, nor is it intended to delineate any scope of the particular embodiments or any scope of the claims. Its sole purpose is to present concepts in a simplified form as a prelude to the more detailed description that is presented later. In one or more embodiments described herein, systems, computer-implemented methods, apparatus, and / or computer program products are described that can facilitate quantum computing of molecular excited states.

[0015] According to one embodiment, a system is provided. The system may include a memory that may store computer executable components. The system may also include a processor that is operably coupled to the memory and can execute the computer executable components stored in the memory. The computer executable components may include an initialization component that may classify multiple excitation operators from a mapped qubit Hamiltonian into sectors based on the commutation characteristics of multiple excitation operators with symmetry in the mapped qubit Hamiltonian. The computer executable components may also include a matrix component that may generate a motion matrix equation from one of the multiple excitation operators based on the sectors classified by the initialization component. An advantage of such a system is that the Hamiltonian symmetry may be used to reduce the computational requirements of the motion determination method equations.

[0016] In some examples, a first sector in the sectors may include a first pair of excitation operators in the plurality of excitation operators. The first pair of excitation operators may be symmetric, and a second sector in the sectors may include a second pair of excitation operators in the plurality of excitation operators. Similarly, the second pair of excitation operators may be symmetric. An advantage of such a system is that computational redundancy may be reduced when calculating molecular excited states.

[0017] According to one embodiment, a computer-implemented method is provided. The computer-implemented method may include, by a system operably coupled to a processor, classifying a plurality of excitation operators from a mapped qubit Hamiltonian into sectors based on commutation characteristics of a plurality of excitation operators having symmetries in the mapped qubit Hamiltonian. The computer-implemented method may also include, by the system, generating a matrix equation of motion from one of the plurality of excitation operators based on the classification. An advantage of this computer-implemented method is that the number of qubits for running the equation of motion method on a quantum computer may be reduced.

[0018] In some examples, a first sector in the sectors may include a first pair of excitation operators in a plurality of excitation operators. The first pair of excitation operators may be commutated with symmetry, and a second sector in the sectors may include a second pair of excitation operators in a plurality of excitation operators. Similarly, the second pair of excitation operators may be anti-commutated with symmetry. In addition, the computer-implemented method may include: generating, by the system, a second equation of a motion matrix in a second sector based on a second pair of excitation operators. Moreover, the motion matrix equation may be generated based on the first pair of excitation operators. An advantage of this computer-implemented method is that it may be easier to run quantum circuits using a large number of gates than conventional methods; thereby, complex wave functions may be explored using variational quantum eigensolver methods.

[0019] According to one embodiment, a computer program product is provided for performing quantum computations on molecular excited states in the presence of Hamiltonian symmetry. The computer program product may include a computer-readable storage medium having program instructions embodied thereon. The program instructions may be executed by a processor to cause the processor to: classify multiple excitation operators from a mapped qubit Hamiltonian into sectors based on the commutation characteristics of multiple excitation operators having symmetry in the mapped qubit Hamiltonian through a system operably coupled to the processor. The program instructions may also cause the processor to: generate a motion matrix equation from one of the multiple excitation operators based on the classification of the multiple excitation operators into sectors through the system. An advantage of this computer program product is that the number of evaluations of matrix elements used to construct a matrix in the context of the method of equations of motion may be reduced.

[0020] In some examples, the program instructions may further cause the processor to: generate a commutator based on the matrix equation of motion by the system. Moreover, the program instructions may cause the processor to: decrement, by the system, a plurality of qubits that may perform the commutator based on a decrementing value of a position of a reference state of a qubit Hamiltonian that may be considered relative to a symmetry mapping. An advantage of such a computer program product is that quantum computing resources for performing the equation of motion method may be reduced.

[0021] According to one embodiment, a system is provided. The system may include a memory that may store computer executable components. The system may also include a processor that is operably coupled to the memory and may execute the computer executable components stored in the memory. The computer executable components may include a control component that may generate a matrix equation of motion from a pair of excitation operators in the mapped qubit Hamiltonian based on the symmetry inherent in the mapped qubit Hamiltonian. An advantage of such a system may be to prepare one or more matrices for the calculation of the equation of motion while minimizing the use of computing resources.

[0022] In some examples, the system may further include an initialization component that may classify a pair of excitation operators into sectors based on the commutation characteristics of the pair of excitation operators having symmetry. An advantage of such a system is that the system may avoid calculating matrix elements that will present a known result (e.g., zero).

[0023] According to one embodiment, a computer program product is provided for performing quantum computation on molecular excited states in the presence of Hamiltonian symmetry. The computer program product may include a computer-readable storage medium having program instructions embodied thereon. The program instructions may be executed by a processor to cause the processor to: generate a matrix equation of motion from a pair of excitation operators in a mapped qubit Hamiltonian based on a symmetry inherent in the mapped qubit Hamiltonian through a system operably coupled to the processor. An advantage of such a computer program product may be the use of reduced computer resources to perform autonomous quantum computation on one or more matrix equations of motion compared to the prior art.

[0024] In some examples, the program instructions may further cause the processor to: by the system, classify the pair of excitation operators into a plurality of sectors based on the commutation characteristics of the pair of excitation operators having symmetry. Furthermore, by the system, a first excitation operator of the pair of excitation operators and a second excitation operator of the pair of excitation operators may be classified into a first sector in the sectors. An advantage of such a computer program product may be to increase computational efficiency of the equation of motion by utilizing inherent symmetry. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The present invention will now be described by way of example only with reference to a preferred embodiment, as shown in the following figures:

[0026] Figure 1 A block diagram is shown of an exemplary non-limiting system that can facilitate quantum computation of molecular excited states in the presence of Hamiltonian symmetry in accordance with one or more embodiments described herein.

[0027] Figure 2 A block diagram of an exemplary non-limiting system that can facilitate quantum computation of molecular excited states while reducing the number of evaluations of matrix elements required to construct an EoM matrix compared to conventional techniques is shown in accordance with one or more embodiments described herein.

[0028] Figure 3 A block diagram is shown of an exemplary non-limiting system that can facilitate computation of molecular excited states while reducing the number of qubits on a quantum computer running an EoM method compared to conventional techniques in accordance with one or more embodiments described herein.

[0029] Figure 4A block diagram is shown of an exemplary non-limiting system that can facilitate quantum computation of molecular excited states in the presence of Hamiltonian symmetry in accordance with one or more embodiments described herein.

[0030] Figure 5 An illustration of an exemplary non-limiting diagram that may describe the efficacy of one or more systems that may facilitate quantum computation of molecular excited states in the presence of Hamiltonian symmetry according to one or more embodiments described herein.

[0031] Figure 6 Schematic diagram showing an exemplary non-limiting diagram that may depict the efficacy of one or more systems that may facilitate quantum computation of molecular excited states in the presence of Hamiltonian symmetry, according to one or more embodiments described herein.

[0032] Figure 7 A flow chart is shown of an exemplary non-limiting method that can facilitate quantum computation of molecular excited states in the presence of Hamiltonian symmetry according to one or more embodiments described herein.

[0033] Figure 8 A flow chart is shown of an exemplary non-limiting method that can facilitate quantum computation of molecular excited states in the presence of Hamiltonian symmetry according to one or more embodiments described herein.

[0034] Fig. 9 A cloud computing environment is depicted according to one or more embodiments described herein.

[0035] Fig.10 Abstract model layers are depicted in accordance with one or more embodiments described herein.

[0036] Fig.11 A block diagram is shown of an example non-limiting operating environment that can facilitate one or more embodiments described herein. DETAILED DESCRIPTION

[0037] The following detailed description is illustrative only and is not intended to limit the application or use of the embodiments and / or embodiments. In addition, it is not intended to be bound by any explicit or implicit information presented in the previous "background technology" or "abstract" section or "detailed description" section.

[0038] One or more embodiments are now described with reference to the accompanying drawings, wherein like reference numerals are used to refer to like elements throughout the text. In the following description, for the purpose of explanation, many specific details are set forth in order to provide a more thorough understanding of one or more embodiments. However, it is apparent that in various circumstances, one or more embodiments may be practiced without these specific details.

[0039] Given that conventional implementations of the EoM method have problems when computing molecular excited states; the present disclosure may be implemented in the form of a process that reduces the number of matrix entries computed during an implementation of the EoM method to produce a solution that addresses one or more of these problems, wherein the molecular Hamiltonian is mapped to a set of qubits having some Pauli symmetry. Various embodiments described herein may predict which entries of the EoM matrix will be zero, thereby saving a number of average experiments proportional to the number of excitation operators considered. Another advantage of one or more embodiments described herein may include enabling the elimination of one or more qubits in the mapped Hamiltonian.

[0040] Various embodiments of the present invention may provide efficient, effective and autonomous computer processing systems, computer-implemented methods, apparatus and / or computer program products that facilitate quantum computation of molecular excited states in the presence of one or more Hamiltonian symmetries. One or more embodiments may reduce the number of elements to be computed in an EoM method, and / or thereby reduce the number of qubits required to implement the EoM method. For example, various embodiments described herein may classify the excitation operators of a mapped qubit Hamiltonian based on the commutation characteristics of one or more Hamiltonian symmetries (e.g., Pauli symmetry). Each group of excitation operators that may be commutated with one or more symmetries may be grouped into one sector, and each group of excitation operators that may be reversed with one or more symmetries may be grouped into another sector. In addition, matrix elements across sectors may be zero. In addition, for each pair of excitation operators in a corresponding sector, a commutator may be generated based on one or more EoM matrix definitions, and / or then decremented with decrementing values.

[0041] Computer processing systems, computer implemented methods, apparatus and / or computer program products employ hardware and / or software to solve problems that are highly technical in nature (e.g., quantum computation of excited states of molecules in the presence of one or more Hamiltonian symmetries), that are not abstract and cannot be performed as a series of intellectual activities of a human being. For example, various features of the embodiments described herein may be directed to quantum computations that cannot be easily and / or efficiently performed by the intellectual activities of an individual.

[0042] Figure 1A block diagram of an exemplary non-limiting system 100 is shown, which can facilitate the implementation of one or more EoM methods on one or more quantum computing devices. For the sake of brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted. Aspects of the systems (e.g., system 100, etc.), apparatuses, or processes in various embodiments of the present invention may constitute one or more machine-executable components embodied in one or more machines, for example, embodied in one or more computer-readable media (or media) associated with one or more computers. When executed by one or more machines, such as computers, computing devices, virtual machines, etc., such components may cause the machines to perform the described operations.

[0043] like Figure 1 As shown, system 100 may include one or more servers 102, one or more networks 104, and / or one or more input devices 106. Server 102 may include control component 108. Control component 108 may further include receiving component 110, initialization component 112, and / or matrix component 114. Moreover, server 102 may include or otherwise be associated with at least one memory 116. Server 102 may further include system bus 118, which may be coupled to various components, such as, but not limited to, control component 108 and related components, memory 116, and / or processor 120. Although in Figure 1 Server 102 is shown in FIG. 1 , but in other embodiments, multiple devices of various types may be associated with Figure 1 The features shown in Figure 1 In addition, server 102 can communicate with the depicted cloud computing environment via one or more networks 104.

[0044] The one or more networks 104 may include wired and wireless networks, including but not limited to cellular networks, wide area networks (WANs) (e.g., the Internet), or local area networks (LANs). For example, the server 102 may communicate with the one or more input devices 106 (or vice versa) using virtually any desired wired or wireless technology, including but not limited to: cellular, WAN, wireless fidelity (Wi-Fi), Wi-Max, WLAN, Bluetooth technology, combinations thereof, and the like. Furthermore, although in the illustrated embodiment, the control component 108 may be disposed on one or more servers 102, it should be understood that the architecture of the system 100 is not limited thereto. For example, the control component 108 or one or more components of the control component 108 may be located at another computer device, such as another server device, a client device, and the like.

[0045] The one or more input devices 106 may include one or more computerized devices, which may include, but are not limited to, a personal computer, a desktop computer, a laptop computer, a cellular phone (e.g., a smart phone), a computerized tablet (e.g., including a processor), a smart watch, a keyboard, a touch screen, a mouse, combinations thereof, and the like. A user of the system 100 may utilize the one or more input devices 106 to input data into the system 100, thereby sharing the data with the server 102 (e.g., via a direct connection and / or via one or more networks 104). For example, the one or more input devices 106 may send data to the receiving component 110 (e.g., via a direct connection and / or via one or more networks 104). In addition, the one or more input devices 106 may include one or more displays, which may present one or more outputs generated by the system 100 to the user. For example, the one or more displays may include, but are not limited to, a cathode tube display (“CRT”), a light emitting diode display (“LED”), an electroluminescent display (“ELD”), a plasma display panel (“PDP”), a liquid crystal display (“LCD”), an organic light emitting diode display (“OLED”), combinations thereof, and the like.

[0046] A user of the system 100 may input one or more settings and / or commands into the system 100 using one or more input devices 106 and / or one or more networks 104. For example, in various embodiments described herein, a user of the system 100 may operate and / or manipulate the server 102 and / or related components via one or more input devices 106. Additionally, a user of the system 100 may display one or more outputs (e.g., displays, data, visualizations, etc.) generated by the server 102 and / or related components using one or more input devices 106. In various embodiments, a user of the system 100 may provide EoM data (e.g., which may be used to initiate one or more EoM methods) to the server 102 (e.g., the control component 108) using one or more input devices 106 and / or one or more networks 104. Exemplary EoM data may include, but is not limited to: one or more mapped qubit Hamiltonians, one or more excitation operators, one or more reference states, one or more symmetries found from one or more mapped quantum Hamiltonians, one or more decrement values ​​for sectors having one or more reference states, combinations thereof, and the like.

[0047] The receiving component 110 can be operably coupled to one or more input devices 106 (e.g., via a direct electrical connection and / or via one or more networks 104) and / or can receive EoM data input into the system 100. In addition, the receiving component 110 can share the EoM data with one or more components of the server 102 (such as various components of the control component 108).

[0048] For example, receiving component 110 can be operably coupled to one or more related components of control component 108 (eg, via a direct electrical connection and / or via one or more networks 104 ).

[0049] The initialization component 112 can classify one or more excitation operators based on one or more commutation characteristics of the excitation operators having one or more Hamiltonian symmetries (e.g., particle symmetry and / or spatial symmetry). The one or more excitation operators and / or symmetries analyzed by the initialization component 112 can be included in the EoM data received by the receiving component 110. In various embodiments, for each corresponding symmetry, the initialization component 112 can classify the excitation operators into a first sector or a second sector. The first sector can include one or more excitation operators that can be commutated with the target symmetry. In contrast, the second sector can include one or more excitation operators that can be reversed with the target symmetry. In addition, one or more symmetries can be used to associate one or more decrement values, which can be used by the control component 108 to gradually decrement the qubit Hamiltonian, as described later herein. In various embodiments, one or more symmetries can be inherent to the target molecule and / or can be derived from the target qubit Hamiltonian.

[0050] For example, the initialization component 112 can classify one or more excitation operators into two sectors according to the following equation.

[0051]

[0052]

[0053] where "E" can be a set of μ ” and / or “E v "The excitation operator, "S" can represent the target symmetry, "AW C " can represent a set of excitation operators that commutate with the symmetry and / or "W A" can represent a set of excitation operators that are inversely commutated with the symmetry. Therefore, the excitation operators of the mapped qubit Hamiltonian can be classified into a first sector ("C") that can be commutated with the symmetry or a second sector ("A") that can be inversely commutated with the symmetry. The above equation illustrates the classification of the initialization component 112 with respect to one symmetry. However, the architecture of the initialization component 112 is not limited thereto. In the case where multiple symmetries are analyzed, the initialization component 112 can classify other sectors. For example, the number of sectors classified by the initialization component 112 can be =2N, where "N" can represent the number of symmetries. For example, in the case where the initialization component 112 analyzes two symmetries, the excitation operators can be classified into four sectors (e.g., {(commutation, commutation), (commutation, anti-commutation), (anti-commutation, commutation), (anti-commutation, anti-commutation)}). Therefore, the initialization component 112 can perform one or more classifications for multiple symmetries. For example, the number of symmetries can be in the range from 0 to X-1, where "X" can represent the number of subject qubits.

[0054] The matrix component 114 can generate one or more EoM matrices based on the classified excitation operators. For example, the matrix component 114 can generate one or more EoM matrices that include matrix elements from an excitation operator (e.g., “E”), an index of the excitation operator (e.g., “E μ ”, “E v ”) are located in the same sector classified by the initialization component 112. For example, the matrix component 114 can generate one or more EoM matrices for the excitation operator, whose two indices are reversed with the target symmetry (e.g., both indices are contained in the first sector “C” classified by the initialization component 112). In another example, the matrix component 114 can generate one or more EoM matrices for the excitation operator, whose two indices are reversed with the target symmetry (e.g., both indices are contained in the second sector “A” classified by the initialization component 112).

[0055] In one or more embodiments, the matrix component 114 can avoid generating an EoM matrix having excitation operators that intersect multiple sectors classified by the initialization component 112. For example, the matrix component 114 can avoid generating an EoM matrix based on a matrix having a first index (e.g., “EoM”) that is classified within a sector (e.g., the first sector “C”). μ ”) and a second index (e.g., “E”) classified within another sector (e.g., a second sector “A”) v”) to generate one or more EoM matrices. EoM matrix elements based on the excitation operators across multiple sectors classified by the initialization component 112 will be equal to zero; therefore, calculation of such EoM matrix elements is unnecessary because their results are known. Therefore, by only selecting the excitation operator from its index (e.g., “E μ ”, “E v ”) in the same sector classified by the initialization component 112 (e.g., by avoiding generating the EoM matrix for excitation operators across multiple classification sectors), the matrix component 114 can reduce the number of elements to be calculated in the EoM matrix compared to traditional implementations of the EoM method.

[0056] Figure 2 A diagram of an exemplary non-limiting system 100 according to one or more embodiments described herein is shown, the exemplary non-limiting system 100 also including a commutator assembly 202. For the sake of brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted. The commutator assembly 202 can generate one or more commutators based on one or more EoM matrices generated by the matrix assembly 114.

[0057] For example, the commutator assembly 202 may generate one or more commutators according to the following definitions.

[0058]

[0059]

[0060]

[0061]

[0062] where “H” can be the Hamiltonian for mapping qubits and “E” can be a set of qubits with indices “E μ ” and / or “E v " can represent the reference state of the mapped qubit Hamiltonian. For example, the reference state can be the base energy state of the target molecule, where the energy difference between the target state and the reference state can be the excited state of the molecule. For the classification sector (e.g., set to "W C ” or “W A ”) in each pair of excitation operators (e.g., “E μ ” and “E v ”), the commutator assembly 202 can generate one or more commutators (e.g., M μv ,Q μv ,V μv , and / or Wμv ). Thus, as described above with respect to the matrix component 114, the commutator component 202 can generate one or more commutators based on the excitation operators having two indices in the same category.

[0063] Figure 3 A diagram of an exemplary non-limiting system 100 according to one or more embodiments described herein is shown, the exemplary non-limiting system also including a decrement component 302. For the sake of brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted. The decrement component 302 can decrement the number of qubits used to operate the commutator generated by the commutator component 202 based on the decrement value.

[0064] The decrement value may depict a symmetry sector in which a reference state of the mapped qubit Hamiltonian is located. For example, each energy state of the mapped qubit Hamiltonian may be located in a respective sector of a target symmetry, wherein the decrement value may represent the sector of the target symmetry to which the reference state (e.g., "|0>") belongs. The decrement value may, for example, be included in the EoM data input into the system 100. The decrement component 302 may decrement one or more commutators generated by the commutator component 202 using the decrement value to eliminate one or more qubit allocations. For example, the decrement component 302 may decrement the qubit Hamiltonian after generating one or more commutators by multiplying the decrement value with a coefficient in the target qubit Hamiltonian to ensure that the decremented Hamiltonian has the correct sign to the reference state. Thus, the decrement component 302 may reduce the number of qubits required to operate one or more commutators (e.g., generated by the commutator component 202) and / or the EoM matrix (e.g., generated by the matrix component 114) on one or more quantum computing devices.

[0065] Figure 4 A diagram of an exemplary non-limiting system 100 according to one or more embodiments described herein is shown, the exemplary non-limiting system 100 also including a computing component 402. For the sake of brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted. The computing component 402 can solve the long-term equations of the EoM method based on one or more commutators (e.g., decremented by the decrement component 302) and / or the EoM matrix generated by various components of the control component 108 (e.g., the initialization component 112, the matrix component 114, and / or the commutator component 202).

[0066] For example, the computation component 402 can solve the following eigenvalue equation (eg, "Equation 1") using a generated commutator (eg, decreasing commutator) and / or EoM matrix based on the EoM matrix definition described herein.

[0067]

[0068] Where "*" can represent complex conjugation, and / or "E 0n " can be the energy gap between the "nth" excited state and the reference state.

[0069] Advantageously, various embodiments of the system 100 described herein can reduce the number of qubits required to run an EoM method on a quantum computer and / or the number of evaluations of matrix elements required to construct a matrix for the EoM method, as compared to conventional techniques. For example, for a hydrogen molecule ("H2"), the system 100 can enable the EoM method to be performed using 1 qubit, rather than the 4 qubits required by conventional techniques. By utilizing fewer qubits, the system 100 can facilitate the operation of the EoM method on quantum circuits having a greater number of gates than would otherwise be available in conventional techniques, thereby providing the possibility of exploring more complex wave function analysis using variational quantum eigensolver methods. In another example, for a lithium hydride ("LiH") molecule, the system 100 can reduce the number of entry evaluations by a factor of three compared to conventional techniques. For a general molecule, the number of entry evaluations saved by the system 100 can scale in proportion to the number of excited states considered, as compared to conventional techniques.

[0070] Figure 5 500 that can describe the effectiveness of the system 100 with respect to the dissociation curve of H2. For the sake of brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted. Figure 5 As shown, the solid lines can represent the molecular energy states derived using conventional techniques and 2 qubits. For example, the first line 502 can represent the 0th excited state, the second line 504 can represent the first excited state, the third line 506 can represent the second excited state, and the fourth line can represent the third excited state. In addition, the solid circle (e.g., its position is further depicted with an "x") can represent the excited state determined by the system 100 using 1 qubit. As illustrated by the graph 500, the system 100 described herein can achieve the same results as conventional techniques while using fewer qubits to perform quantum computing.

[0071] Figure 6 A diagram showing an exemplary non-limiting graph 600 that can describe the efficacy of the system 100 with respect to the dissociation curve of LiH is shown. For the sake of brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted. Figure 6As shown in the graph 600, the solid lines may represent 24 corresponding excited states of a molecule derived using conventional techniques and 8 qubits, where 300 elements are included in the EoM matrix. Additionally, the solid circles (e.g., whose positions are further depicted with "x") may represent individual excited states determined by the system 100 using 6 qubits, where 100 elements are included in the EoM matrix. As illustrated by the graph 600, the system 100 described herein may obtain the same results as conventional techniques while using fewer qubits and fewer computations (e.g., evaluation of a fewer number of matrix elements), thereby increasing the speed and efficiency of quantum computations used to determine excited states of a molecule.

[0072] Figure 7 A flow chart of an exemplary non-limiting method 700 is shown that can facilitate quantum computation of molecular excited states in the presence of Hamiltonian symmetry in accordance with one or more embodiments described herein. For the sake of brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted.

[0073] At 702, method 700 may include, by system 100 operatively coupled to processor 120 (e.g., via initialization component 112), classifying a plurality of excitation operators from a mapped qubit Hamiltonian into sectors based on commutation characteristics of the plurality of excitation operators having symmetries in the mapped qubit Hamiltonian. For example, the excitation operators may each include two indices, which may be classified by system 100 as a first sector or a second sector. The excitation operator indices that may commutate with the target symmetry may be classified as the first sector, while the excitation operator indices that may be anti-commutated with the target symmetry may be classified as the second sector. For example, the classification at 702 may include forming a first set of excitation operators described herein (“W C ”) and / or a second set of excitation operators (“W A ”).

[0074] At 704, method 700 may include generating, by system 100 (e.g., via matrix component 114 and / or commutator component 202), one or more EoM matrices from one or more excitation operators of the plurality of excitation operators based on the classification at 702. For example, the one or more EoM matrices may be generated from the excitation operators having two indices (e.g., “EoM”) in the same sector classified at 702. μ ” and / or “E v”). Matrix elements derived from excitation operators having respective indices from different sectors may be equal to zero, and thus the generation at 704 may avoid analyzing such excitation operators for EoM matrix formation. Thus, the classification at 702 may guide the EoM matrix formation at 704 to efficiently select excitation operators that may derive an EoM matrix that is equal to an integer other than zero. Thus, the method 700 may advantageously reduce the number of evaluations of matrix elements required to construct one or more EoM matrices, as compared to conventional techniques.

[0075] Figure 8 A flow chart of an exemplary non-limiting method 800 is shown that can facilitate quantum computation of molecular excited states in the presence of Hamiltonian symmetry in accordance with one or more embodiments described herein. For the sake of brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted.

[0076] At 802, method 800 may include, by system 100 operatively coupled to processor 120 (e.g., via initialization component 112), classifying a plurality of excitation operators from a mapped qubit Hamiltonian into sectors based on commutation characteristics of the plurality of excitation operators having symmetries in the mapped qubit Hamiltonian. For example, the excitation operators may each include two indices, which may be classified by system 100 as a first sector or a second sector. The excitation operator indices that may commutate with the target symmetry may be classified as the first sector, while the excitation operator indices that may decommutate with the target symmetry may be classified as the second sector. For example, the classification at 702 may include forming a first set of excitation operators (“W ”) described herein. C ”) and / or a second set of excitation operators (“W A ”).

[0077] At 804, method 800 may include generating, by system 100 (e.g., via matrix component 114 and / or commutator component 202), one or more EoM matrices from one or more excitation operators of the plurality of excitation operators based on the classification at 802. For example, the one or more EoM matrices may be generated from the excitation operators having two indices (e.g., “EoM”) that are classified in the same sector at 802. μ ” and / or “E v ”). Matrix elements derived from excitation operators with respective indices of different sectors may be equal to zero, and thus, the generation at 804 may avoid analyzing such excitation operators for EoM matrix formation. Thus, the classification at 802 may guide the EoM matrix formation at 804 to efficiently select excitation operators that may derive an EoM matrix that is equal to an integer other than zero, while avoiding analyzing excitation operators that may result in an EoM matrix that is equivalent to a known result (e.g., zero).

[0078] At 806, method 800 can include generating, by system 100 (eg, via commutator assembly 202), one or more commutators based on the one or more EoM matrices. For example, one or more commutators can be generated according to various commutator definitions described herein.

[0079] At 808, method 800 may include decrementing, by system 100 (e.g., via decrement component 302), a plurality of qubits of one or more commutators relative to a target symmetry based on a decrementing value of a reference position of a mapped qubit Hamiltonian. For example, the decrementing value may describe a symmetric sector of the mapped qubit Hamiltonian belonging to a reference state. Advantageously, method 800 may reduce the number of qubits required to implement a quantum EoM matrix and / or commutator on a quantum computing device.

[0080] At 810, method 800 may include solving, by system 100 (e.g., via computation component 402), one or more eigenvalue equations based on one or more commutators. For example, the solving at 810 may be performed with respect to Equation 1 described herein. In various embodiments, as a result of the decrement at 808, the one or more eigenvalue equations may be solved at 810 using a decrementing number of qubits.

[0081] First, it should be understood that although the present disclosure includes a detailed description about cloud computing, the implementation of the technical solutions recorded therein is not limited to a cloud computing environment, but can be implemented in combination with any other type of computing environment now known or later developed.

[0082] Cloud computing is a service delivery model for convenient, on-demand network access to a shared pool of configurable computing resources. Configurable computing resources are resources that can be quickly deployed and released with minimal management cost or interaction with the service provider, such as networks, network bandwidth, servers, processing, memory, storage, applications, virtual machines, and services. This cloud model can include at least five characteristics, at least three service models, and at least four deployment models.

[0083] Features include :

[0084] On-demand self-service: Cloud consumers can unilaterally and automatically deploy computing capabilities such as server time and network storage on demand without human interaction with the service provider.

[0085] Broad network access: Computing power can be accessed over the network through standard mechanisms that facilitate the use of the cloud through different types of thin-client or thick-client platforms (e.g., mobile phones, laptops, personal digital assistants (PDAs)).

[0086] Resource pool: The computing resources of the provider are grouped into resource pools and serve multiple consumers through a multi-tenant model, where different physical and virtual resources are dynamically allocated and reallocated on demand. Generally, consumers cannot control or even know the exact location of the provided resources, but can specify the location (such as country, state or data center) at a higher level of abstraction, so it is location-independent.

[0087] Rapid elasticity: The ability to quickly and elastically (sometimes automatically) deploy computing power to scale up quickly, and quickly release it to scale down quickly. To consumers, the computing power available for deployment often appears to be unlimited, and any amount of computing power can be accessed at any time.

[0088] Measurable services: Cloud systems automatically control and optimize resource usage by leveraging metering capabilities at a level of abstraction appropriate to the type of service (e.g., storage, processing, bandwidth, and active user accounts). Resource usage can be monitored, controlled, and reported, providing transparency to both service providers and consumers.

[0089] The service model is as follows :

[0090] Software as a Service (SaaS): The capability provided to consumers is to use the provider's applications running on a cloud infrastructure. Applications can be accessed from a variety of client devices through a thin client interface such as a web browser (e.g., web-based email). Aside from limited user-specific application configuration settings, consumers neither manage nor control the underlying cloud infrastructure including networks, servers, operating systems, storage, or even individual application capabilities.

[0091] Platform as a Service (PaaS): The capability provided to consumers is to deploy applications created or acquired by consumers on the cloud infrastructure, which are created using programming languages ​​and tools supported by the provider. Consumers neither manage nor control the underlying cloud infrastructure including networks, servers, operating systems or storage, but have control over the applications they deploy and may also have control over the configuration of the application hosting environment.

[0092] Infrastructure as a Service (IaaS): The capabilities provided to consumers are processing, storage, network, and other basic computing resources on which consumers can deploy and run arbitrary software including operating systems and applications. Consumers neither manage nor control the underlying cloud infrastructure, but have control over the operating system, storage, and applications they deploy, and may have limited control over selected network components (such as host firewalls).

[0093] The deployment model is as follows :

[0094] Private Cloud: Cloud infrastructure is run solely for an organization. The cloud infrastructure can be managed by the organization or a third party and can exist inside or outside the organization.

[0095] Community Cloud: A cloud infrastructure is shared by several organizations and supports a specific community with common interests (e.g., mission, security requirements, policies, and compliance considerations). A community cloud can be managed by multiple organizations within the community or by a third party and can exist inside or outside the community.

[0096] Public cloud: Cloud infrastructure is provided to the public or to large industry groups and is owned by an organization that sells cloud services.

[0097] Hybrid cloud: A cloud infrastructure consisting of two or more clouds (private, community or public) in a deployment model that remain distinct entities but are bound together by standardized or proprietary technologies (such as cloud burst sharing for load balancing between clouds) that enable data and application portability.

[0098] The cloud computing environment is service-oriented, with characteristics centered on statelessness, low coupling, modularity, and semantic interoperability. The core of cloud computing is the infrastructure that includes a network of interconnected nodes.

[0099] Reference now Fig.10 , which shows an exemplary cloud computing environment 1000 according to an embodiment of the present invention. As shown in the figure, the cloud computing environment 1000 includes one or more cloud computing nodes 1002 with which a local computing device used by a cloud computing consumer can communicate. The local computing device can be, for example, a personal digital assistant (PDA) or a mobile phone 1004, a desktop computer 1006, a laptop computer 1008 and / or an automobile computer system 1010. The cloud computing nodes 1002 can communicate with each other. The cloud computing nodes 10 can be physically or virtually grouped in one or more networks including but not limited to the private cloud, community cloud, public cloud or hybrid cloud or a combination thereof as described above (not shown in the figure). In this way, cloud consumers can request infrastructure as a service (IaaS), platform as a service (PaaS) and / or software as a service (SaaS) provided by the cloud computing environment 1000 without maintaining resources on local computing devices. It should be understood that Fig.10 The various types of computing devices 1004 - 1010 shown are merely illustrative, and the cloud computing node 1002 and the cloud computing environment 1000 may communicate with any type of computing device on any type of network and / or with a network addressable connection (eg, using a web browser).

[0100] Reference now Fig.10 , which shows a cloud computing environment 1000 ( Fig.10 ) provides a set of functional abstraction layers. First of all, it should be understood that Figure 3 The components, layers, and functions shown are only exemplary and the embodiments of the present invention are not limited thereto. Fig.10 As shown, the following layers and corresponding functions are provided:

[0101] The hardware and software layer 1002 includes hardware and software components. Examples of hardware components include: host 1004; server 1006 based on RISC (Reduced Instruction Set Computer) architecture; server 1008; blade server 1010; storage device 1012; network and network components 1014. Examples of software components include: network application server software 1016 and database software 1018.

[0102] Virtualization layer 1020 provides an abstraction layer that can provide examples of the following virtual entities: virtual servers 1022 , virtual storage 1024 , virtual networks 1026 (including virtual private networks), virtual applications and operating systems 1028 , and virtual clients 1030 .

[0103] In one example, the management layer 1032 may provide the following functions: Resource provisioning function 1034: Provide dynamic acquisition of computing resources and other resources for performing tasks in a cloud computing environment; Metering and pricing function 1036: Track the cost of resource usage within the cloud computing environment and provide bills and invoices for this purpose. In one example, the resource may include an application software license. Security function: Provide identity authentication for cloud consumers and tasks, and provide protection for data and other resources. User portal function 1038: Provide access to the cloud computing environment for consumers and system administrators. Service level management function 1040: Provide allocation and management of cloud computing resources to meet the required service levels. Service level agreement (SLA) planning and fulfillment function 1042: Provide pre-arrangement and provision for future demand for cloud computing resources predicted according to the SLA.

[0104] The workload layer 1044 provides examples of functions that may be implemented in a cloud computing environment. In this layer, examples of workloads or functions that may be provided include: mapping and navigation 1046; software development and lifecycle management 1048; virtual classroom teaching provision 1050; data analysis processing 1052; transaction processing 1054; and EoM calculation 1056. The service-assisted functions will be described in the following embodiments of the present disclosure. Various embodiments of the present invention may utilize reference Fig. 9 and Fig.10The cloud computing environment described herein is used to compute one or more features of an EoM method (e.g., one or more EoM matrices and / or commutators) to determine molecular excited states. For example, one or more components of the system 100 (e.g., initialization component 112 and / or matrix component 114) can be executed on a quantum computer, while one or more other components of the system 100 (e.g., computation component 402) can be executed on a classical computer, wherein the cloud computing environment can facilitate communication between the quantum computer and the classical computer and / or performance efficiency of the quantum computer and / or the classical computer.

[0105] At any possible level of technical detail combination, the present invention may be a system, method and / or computer program product. The computer program product may include a computer-readable storage medium on which are loaded computer-readable program instructions for causing a processor to implement various aspects of the present invention. A computer-readable storage medium may be a tangible device that can hold and store instructions used by an instruction execution device. The computer-readable storage medium may be, for example, - but not limited to - an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the above. More specific examples (a non-exhaustive list) of computer-readable storage media include: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disk read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device, such as a punch card or a protruding structure in a groove on which instructions are stored, and any suitable combination of the above. The computer-readable storage medium used herein is not to be construed as a transient signal per se, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagating through a waveguide or other transmission medium (e.g., light pulses through a fiber optic cable), or an electrical signal transmitted through wires.

[0106] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to each computing / processing device, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, optical fiber transmissions, wireless transmissions, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in the computer-readable storage medium in each computing / processing device.

[0107] The computer program instructions for performing the operation of the present invention may be assembler instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, integrated circuit configuration data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages, such as Smalltalk, C++, etc., and procedural programming languages, such as "C" language or similar programming languages. Computer-readable program instructions may be executed entirely on a user's computer, partially on a user's computer, as an independent software package, partially on a user's computer, partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., using an Internet service provider to connect via the Internet). In some embodiments, an electronic circuit, such as a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA), may be personalized by utilizing the state information of the computer-readable program instructions, and the electronic circuit may execute the computer-readable program instructions, thereby realizing various aspects of the present invention.

[0108] Various aspects of the present invention are described herein with reference to the flow charts and / or block diagrams of the methods, devices (systems) and computer program products according to embodiments of the present invention. It should be understood that each box of the flow chart and / or block diagram and the combination of each box in the flow chart and / or block diagram can be implemented by computer-readable program instructions.

[0109] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, thereby producing a machine, so that when these instructions are executed by the processor of the computer or other programmable data processing device, a device that implements the functions / actions specified in one or more boxes in the flowchart and / or block diagram is generated. These computer-readable program instructions can also be stored in a computer-readable storage medium, and these instructions cause the computer, programmable data processing device, and / or other equipment to work in a specific manner, so that the computer-readable medium storing the instructions includes a manufactured product, which includes instructions for implementing various aspects of the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0110] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device so that a series of operating steps are performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to implement the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0111] The flow chart and block diagram in the accompanying drawings show the possible architecture, function and operation of the system, method and computer program product according to multiple embodiments of the present invention. In this regard, each square box in the flow chart or block diagram can represent a part of a module, program segment or instruction, and a part of the module, program segment or instruction includes one or more executable instructions for realizing the specified logical function. In some alternative implementations, the function marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two continuous square boxes can actually be executed substantially in parallel, and they can sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs the specified function or action, or can be implemented with a combination of special hardware and computer instructions.

[0112] To provide context for various aspects of the disclosed subject matter, Fig.11 The following discussion is intended to provide a general description of a suitable environment in which various aspects of the disclosed subject matter can be implemented. Fig.11 A block diagram of an example non-limiting operating environment is shown in which one or more embodiments described herein may be facilitated. For the sake of brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted. Fig.11A suitable operating environment 1100 for implementing various aspects of the present disclosure may include a computer 1112. The computer 1112 may also include a processing unit 1114, a system memory 1116, and a system bus 1118. The system bus 1118 may operably couple system components including, but not limited to, the system memory 1116 to the processing unit 1114. The processing unit 1114 may be any of a variety of available processors. Dual microprocessors and other multiprocessor architectures may also be used as the processing unit 1114. The system bus 1118 may be any of several types of bus structures including a memory bus or memory controller, a peripheral bus or external bus, and / or a local bus using any available bus architecture including, but not limited to, Industry Standard Architecture (ISA), Micro Channel Architecture (MSA), Extended ISA (EISA), Intelligent Drive Electronics (IDE), VESA Local Bus (VLB), Peripheral Component Interconnect (PCI), Card Bus, Universal Serial Bus (USB), Advanced Graphics Port (AGP), FireWire, and Small Computer System Interface (SCSI). The system memory 1116 may also include volatile memory 1120 and nonvolatile memory 1122. A basic input / output system (BIOS), containing the basic routines that transfer information between elements within the computer 1112, such as during start-up, may be stored in the nonvolatile memory 1122. By way of illustration and not limitation, nonvolatile memory 1122 may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, or nonvolatile random access memory (RAM) (e.g., ferroelectric RAM (FeRAM). Volatile memory 1120 may also include random access memory (RAM) used as external cache memory. By way of illustration and not limitation, RAM comes in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM.

[0113] Computer 1112 may also include removable / non-removable, volatile / nonvolatile computer storage media. Fig.11For example, disk storage 1124 is shown. Disk storage 1124 may also include, but is not limited to, such as a disk drive, a floppy disk drive, a tape drive, a Jaz drive, a Zip drive, an LS-100 drive, a flash memory card, or a memory stick. Disk storage 1124 may also include other media, alone or in combination with other storage media, including, but not limited to, optical drives such as a compact disk ROM device (CD-ROM), a CD recordable drive (CD-R drive), a CD rewritable drive (CD-RW drive), or a digital versatile disk ROM drive (DVD-ROM). To facilitate connection of disk storage 1124 to system bus 1118, a removable or non-removable interface, such as interface 1126, may be used. Fig.11 Also depicted is software that can act as an intermediary between a user and the basic computer resources described in the appropriate operating environment 1100. Such software can also include, for example, an operating system 1128. The operating system 1128 can be stored on disk storage 1124 and is used to control and allocate resources of the computer 1112. System applications 1130 can utilize the operating system 1128 to manage resources through program modules 1132 and program data 1134 (e.g., programs stored in system memory 1116 or disk storage 1124). It should be understood that the present disclosure can be implemented with various operating systems or combinations of operating systems. A user enters commands or information into the computer 1112 through one or more input devices 1136. The input device 1136 can include, but is not limited to, a pointing device such as a mouse, a trackball, a stylus, a touchpad, a keyboard, a microphone, a joystick, a game pad, a satellite dish, a scanner, a TV tuner card, a digital camera, a digital video camera, a webcam. These and other input devices can be connected to the processing unit 1114 through the system bus 1118 via one or more interface ports 1138. The one or more interface ports 1138 may include, for example, a serial port, a parallel port, a game port, and a universal serial bus (USB). The one or more output devices 1140 may use some of the same types of ports as the input devices 1136. Thus, for example, a USB port may be used to provide input to the computer 1112 and output information from the computer 1112 to the output device 1140. An output adapter 1142 may be provided to illustrate that some output devices 1140, such as monitors, speakers, and printers, may require special adapters in addition to other output devices 1140. By way of example and not limitation, the output adapter 1142 may include a video and sound card that provides a connection between the output device 1140 and the system bus 1118. It should be noted that other devices and / or device systems provide input and output functionality, such as one or more remote computers 1144.

[0114] The computer 1112 can operate in a networked environment using logical connections to one or more remote computers, such as the remote computer 1144. The remote computer 1144 can be a computer, server, router, network PC, workstation, microprocessor-based device, peer device or other public network node, etc., and can generally also include many or all of the elements described relative to the computer 1112.

[0115] For simplicity, only a memory storage device 1146 with a remote computer 1144 is shown. The remote computer 1144 can be logically connected to the computer 1112 through a network interface 1148 and then physically connected through a communication connection 1150. Moreover, operations can be distributed over multiple (local and remote) systems. The network interface 1148 can include wired and / or wireless communication networks, such as local area networks (LANs), wide area networks (WANs), cellular networks, etc. LAN technologies include fiber distributed data interface (FDDI), copper distributed data interface (CDDI), Ethernet, token ring, etc. WAN technologies include, but are not limited to, point-to-point links, circuit switching networks (such as integrated services digital networks (ISDN)) and variations thereon, packet switching networks, and digital subscriber lines (DSL). One or more communication connections 1150 refer to the hardware / software used to connect the network interface 1148 to the system bus 1118. Although the communication connection 1150 is shown inside the computer 1112 for clarity of illustration, the communication connection 1150 can also be external to the computer 1112. For exemplary purposes only, software for connecting to the network interface 1148 may also include internal and external technologies such as modems including conventional telephone grade modems, cable modems and DSL modems, ISDN adapters and Ethernet cards.

[0116] At any possible level of technical detail combination, embodiments of the present invention may be systems, methods and / or computer program products. A computer program product may include a computer-readable storage medium on which are loaded computer-readable program instructions for causing a processor to implement various aspects of the present invention. A computer-readable storage medium may be a tangible device that can hold and store instructions used by an instruction execution device. A computer-readable storage medium may be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the above. More specific examples (a non-exhaustive list) of computer-readable storage media include: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disk read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device, such as a punch card or a protruding structure in a groove on which instructions are stored, and any suitable combination of the above. The computer-readable storage medium used herein is not to be construed as a transient signal per se, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagating through a waveguide or other transmission medium (e.g., light pulses through a fiber optic cable), or an electrical signal transmitted through wires.

[0117] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to each computing / processing device, or downloaded to an external computer or external storage device through a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, optical fiber transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network, and forwards the computer-readable program instructions for storage in the computer-readable storage medium in each computing / processing device. The computer program instructions for performing the operation of the present invention can be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-related instructions, microcodes, firmware instructions, state setting data, integrated circuit configuration data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages, such as Smalltalk, C++, etc., and procedural programming languages, such as "C" language or similar programming languages. The computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer, as an independent software package, partially on the user's computer, partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., using an Internet service provider to connect via the Internet). In some embodiments, an electronic circuit, such as a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA), may be personalized using the state information of the computer-readable program instructions, and the electronic circuit may execute the computer-readable program instructions, thereby realizing various aspects of the present invention.

[0118] Here, various aspects of the present invention are described with reference to the flowchart and / or block diagram of the method, device (system) and computer program product according to the embodiment of the present invention. It should be understood that each square frame of the flowchart and / or block diagram and the combination of each square frame in the flowchart and / or block diagram can be realized by computer-readable program instructions. These computer-readable program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer or other programmable data processing device, so as to produce a machine, so that these instructions, when executed by the processor of the computer or other programmable data processing device, produce a device for realizing the function / action specified in one or more square frames in the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium, and these instructions make the computer, programmable data processing device and / or other equipment work in a specific manner, so that the computer-readable medium storing the instructions includes a product of manufacture, which includes instructions for realizing various aspects of the function / action specified in one or more square frames in the flowchart and / or block diagram. Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device so that a series of operating steps are performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to implement the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0119] The flow chart and block diagram in the accompanying drawings show the possible architecture, function and operation of the system, method and computer program product according to multiple embodiments of the present invention. In this regard, each square box in the flow chart or block diagram can represent a part of a module, program segment or instruction, and a part of the module, program segment or instruction includes one or more executable instructions for realizing the specified logical function. In some alternative implementations, the function marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two continuous square boxes can actually be executed substantially in parallel, and they can sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs the specified function or action, or can be implemented with a combination of special hardware and computer instructions.

[0120] Although the subject matter has been described above in the general context of computer executable instructions of a computer program product running on one or more computers, those skilled in the art will recognize that the present disclosure may also or may be implemented in conjunction with other program modules. Typically, program modules include routines, programs, components, data structures, etc. that perform specific tasks and / or implement specific abstract data types. In addition, those skilled in the art will appreciate that the computer-implemented methods of the present invention may be practiced with other computer system configurations, including single-processor or multi-processor computer systems, small computing devices, mainframe computers and computers, handheld computing devices (e.g., PDAs, phones), microprocessor-based or programmable consumer or industrial electronics, etc. The described aspects may also be practiced in a distributed computing environment in which tasks are performed by remote processing devices linked through a communications network.

[0121] However, some (if not all) aspects of the present disclosure can be practiced on stand-alone computers.In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

[0122] As used in this application, the terms "component", "system", "platform", "interface", etc. may refer to and / or may include computer-related entities or entities related to an operable machine computer having one or more specific functions. The entities disclosed herein may be hardware, a combination of hardware and software, software, or software in execution. For example, a component may be, but is not limited to, a process, an executable file, an execution thread, a program, and / or a computer running on a processor, a processor, an object. As an illustration, both an application running on a server and a server may be a component. One or more components may reside in an executed process and / or thread, and a component may be located on a computer and / or distributed between two or more computers. In another example, each component may be executed from various computer-readable media having various data structures stored thereon. A component may, for example, communicate via a local and / or remote process according to a signal having one or more data packets (e.g., data from a component interacts with another component in a local system, a distributed system, and / or interacts with other systems across a network (e.g., the Internet) via a signal). As another example, a component may be a device having a specific function provided by a mechanical component operated by an electrical or electronic circuit, and the mechanical component is operated by a software or firmware application executed by a processor. In this case, the processor may be internal or external to the device and may execute at least a portion of a software or firmware application. As yet another example, the component may be a device that provides a specific functionality through electronic components without mechanical components, where the electronic components may include a processor or other means to execute software or firmware that at least partially imparts the functionality to the electronic components. In one aspect, the component may emulate the electronic component, for example, via a virtual machine within a cloud computing system.

[0123] In addition, the term "or" is intended to mean an inclusive "or" rather than an exclusive "or".

[0124] That is, unless otherwise specified or clear from the context, "X employs A or B" refers to any of the natural inclusive permutations. That is, if X employs A; X employs B; or X employs both A and B, then "X employs A or B" is satisfied in all cases. In addition, the articles "a" and "an" used in the subject specification and drawings should generally be interpreted to mean "one or more" unless otherwise specified or clear from the context to point to the singular form. The terms "example" and / or "exemplary" are used to mean serving as an example, instance, or illustration. For the avoidance of doubt, the subject matter disclosed herein is not limited to such examples. In addition, any aspect or design described herein as "example" and / or "exemplary" is not necessarily to be construed as preferred or advantageous over other example aspects or designs, nor is it meant to exclude equivalent exemplary structures and techniques known to those of ordinary skill in the art.

[0125] As used in this specification, the term "processor" can refer to substantially any computing processing unit or device, including but not limited to a single-core processor, a single processor with software multithreaded execution capability, a multi-core processor, a multi-core processor with software multithreaded execution capability, a multi-core processor with hardware multithreading technology, a parallel platform, and a parallel platform with distributed shared memory. In addition, a processor can refer to an integrated circuit, an application-specific integrated circuit (ASIC), a digital signal processor (DSP), a field programmable gate array (FPGA), a programmable logic controller (PLC), a complex programmable logic device (CPLD), a discrete gate or transistor logic, a discrete hardware component, or any combination thereof designed to perform the functions described herein. In addition, the processor can utilize nanoscale architectures, such as, but not limited to, transistors, switches, and gates based on molecules and quantum dots, to optimize space usage or enhance the performance of user devices. The processor can also be implemented as a combination of computing processing units. In the present disclosure, terms such as "storage", "data storage", "database", and substantially any other component related to the operation and function of an information storage component are used to refer to a "memory component", an entity embodied in a "memory", or a component including a memory. It should be understood that the memory and / or memory components described herein may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. As an illustration and not limitation, non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable ROM (EEPROM), flash memory, or non-volatile random access memory (RAM) (e.g., ferroelectric RAM (FeRAM). Volatile memory may include RAM, for example, RAM may be used as an external cache. As an illustration and not limitation, RAM has many forms, such as synchronous RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM). In addition, the memory components of the system or computer-implemented method disclosed herein are intended to include, but are not limited to, including these and any other suitable types of memory.

[0126] What has been described above only includes examples of systems, computer program products, and computer-implemented methods. Of course, for the purpose of describing the present disclosure, it is not possible to describe every possible combination of components, products, and / or computer-implemented methods, but those of ordinary skill in the art will recognize that many further combinations and permutations of the present disclosure are possible. Where the terms "including," "having," and the like are used in the specific embodiments, claims, appendices, and drawings, these terms are intended to be interpreted in a manner similar to the term "including" when used as a transitional word in the claims. Descriptions of various embodiments have been given for illustrative purposes, but these descriptions are not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terms used herein are selected to best explain the principles of the embodiments, the practical application of technologies found on the market, or improvements to the technologies, or to enable other persons of ordinary skill in the art to understand the patterns disclosed herein.

Claims

1. A system for quantum computing of molecular excited states in the presence of Hamiltonian symmetry in a cloud computing environment, wherein: One or more features of an equation of motion method are calculated to determine molecular excited states, wherein one or more components of the system are executed on a quantum computer and one or more components of the system are executed on a classical computer, wherein a cloud computing environment facilitates communication between the quantum computer and the classical computer, the system comprising: a memory storing computer executable components; A processor operatively coupled to the memory and executing computer executable components stored in the memory, wherein the computer executable components include: an initialization component executed on the quantum computer, the initialization component, when executed on the quantum computer, causing the quantum computer to classify a plurality of excitation operators of the mapped qubit Hamiltonian into sectors, wherein the classification is based on commutation properties of the plurality of excitation operators with a symmetry of the mapped qubit Hamiltonian; a matrix component executed on the quantum computer, the matrix component, when executed on the quantum computer, causing the quantum computer to generate one or more equation of motion matrices from only one or more excitation operators of the plurality of excitation operators based on the sectors classified by the initialization component, wherein a first sector of the sectors comprises a first pair of excitation operators of the plurality of excitation operators, wherein the first pair of excitation operators are commutated with the symmetry, wherein a second sector of the sectors comprises a second pair of excitation operators of the plurality of excitation operators, and wherein the second pair of excitation operators are anti-commutated with the symmetry, wherein the matrix component, when executed on the quantum computer, causes the quantum computer to generate a matrix of equations of motion in a first sector based on the first pair of excitation operators, and wherein the matrix component, when executed on the quantum computer, causes the quantum computer to generate another matrix of equations of motion in a second sector based on the second pair of excitation operators; The system further comprises: a commutator assembly that generates a first commutator based on a matrix of equations of motion and generates a second commutator based on another matrix of equations of motion; a decrementing component that decrements the number of qubits that perform a first commutator based on a decrementing value of a position of a reference state of a qubit Hamiltonian that takes into account the mapping relative to the symmetry; A computing component executed on a classical computer, when executed on the classical computer, causes the classical computer to solve an eigenvalue equation based on the first commutator and the second commutator using the equation of motion matrix to determine a molecular excited state.

2. The system according to claim 1, in, The decrement component further decrements the number of second qubits of the second commutator based on the decrement value.

3. The system according to claim 1, wherein: The matrix component, when executed on the quantum computer, causes the quantum computer to further generate the one or more equation of motion matrices only from the one or more excitation operators, wherein the one or more excitation operators have indices in the sectors sorted by the initialization component.

4. A computer-implemented method executed in a system in a cloud computing environment for quantum computing of molecular excited states in the presence of Hamiltonian symmetry, wherein: One or more features of an equation of motion method are calculated to determine a molecular excited state, wherein one or more components of the system are executed on a quantum computer and one or more components of the system are executed on a classical computer, wherein a cloud computing environment facilitates communication between the quantum computer and the classical computer, the method comprising: By an initialization component of the system operably coupled to the processor, when the initialization component is executed on the quantum computer, classifying a plurality of excitation operators of the mapped qubit Hamiltonian into sectors, wherein the classification is based on commutation properties of the plurality of excitation operators with a symmetry of the mapped qubit Hamiltonian; generating, by a matrix component of the system, one or more equations of motion matrices from only one or more excitation operators of the plurality of excitation operators based on the classification when the matrix component is executed on a quantum computer, wherein a first sector of the sectors comprises a first pair of excitation operators of the plurality of excitation operators, wherein the first pair of excitation operators are commutated with the symmetry, wherein a second sector of the sectors comprises a second pair of excitation operators of the plurality of excitation operators, and wherein the second pair of excitation operators are anti-commutated with the symmetry, generating, by a matrix component of the system, another equation of motion matrix in a second sector based on a second pair of excitation operators when the matrix component is executed on a quantum computer, wherein generating the equation of motion matrix is ​​based on the first pair of excitation operators; The method further comprises: generating a commutator based on a matrix of equations of motion by a commutator component of the system; decrementing, by a decrementing component of the system, the number of qubits performing a commutator based on a decrementing value of a position of a reference state of a qubit Hamiltonian that takes into account the mapping relative to the symmetry; and By means of the computing component of the system, an eigenvalue equation is solved based on the commutator when the computing component is executed on a classical computer.

5. A computer program product for performing quantum computation on molecular excited states in the presence of Hamiltonian symmetry in a system in a cloud computing environment, the computer program product comprising: A computer readable storage medium having program instructions embodied therewith, which when executed by a processor causes the processor to perform the method according to claim 4.

6. A computer program product for performing quantum computation on molecular excited states in the presence of Hamiltonian symmetry in a system in a cloud computing environment, wherein: One or more features of an equation of motion method are calculated to determine molecular excited states, wherein one or more components of the system are executed on a quantum computer and one or more components of the system are executed on a classical computer, wherein a cloud computing environment facilitates communication between the quantum computer and the classical computer, and the computer program product includes a computer program stored on a computer-readable medium and loadable into an internal memory of a digital computer, the computer program including software code portions for performing the method according to claim 4 when the program is run on a computer.

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