Determining density function theory using a quantum computing system

Abstract

A technique is provided to facilitate the theoretical determination of density functions using a quantum computing system. The system may include a first computing processor and a second computing processor. The first computing processor generates the theoretical determination of the density function. The second computing processor can input quantum density into the theoretical determination of the density function. The first computing processor is operatively coupled to the second computing processor. Further, the first computing processor may be a classical computer, and the second computing processor may be a quantum computer.

Description

Background Technology

[0001] This invention relates to quantum computing, and more specifically, to using quantum computing systems to facilitate the theoretical determination of density functions. Simulation of large molecules using classical computers (e.g., non-quantum computers) is intractable due to the exponential growth of Hilbert space. Quantum simulation of large molecules is a possible solution because it can efficiently represent the exponential Hilbert space using qubits. However, quantum simulation of molecular systems is limited to very small sizes due to finite coherence time, gate noise, and other complexities.

[0002] For example, Yonezawa et al. (US Patent Application Publication No. 2007 / 0043545) discussed “dividing the molecule or a portion of the molecule to be simulated into a [quantum mechanical] QM space and a [molecular mechanical] MM [space] and applying an initial molecular orbital method to the QM space.” See abstract. However, Yonezawa et al. only used classical processors and were therefore limited in the size of the molecular systems that could be analyzed.

[0003] In another example, Rubin (U.S. Patent Application Publication No. 2018 / 0096085) discusses “quantum computation performed on one or more quantum processor units (QPUs) that can operate in parallel for density matrix embedding computation.” See paragraph

[0012] . In Rubin, “quantum processor units (QPUs) are used to compute density-reduced matrices (RDMs).” See paragraph

[0055] . Rubin discusses “segment-based embedded Hamiltonian operators for computing 1-reduced density matrices (1-RDMs) and 2-reduced density matrices (2-RDMs) for each segment.” See id. However, Rubin’s reduced density matrices lack the ability to provide a rigorous embedding based on iterative density function theory for quantum computation. Summary of the Invention

[0004] The following overview is presented to provide a basic understanding of one or more embodiments of the invention. This overview is not intended to identify key or essential elements or to define any scope of a particular embodiment 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 follows. In one or more embodiments described herein, systems, computer-implemented methods, apparatuses, circuits, and / or computer program products are provided that utilize quantum computing systems to assist in the determination of density function theory.

[0005] According to an embodiment, the circuit may include a first computational processor that generates a density function theoretical determination. The circuit may also include a second computational processor that inputs the quantum density into the density function theoretical determination generated by the first computational processor. The first computational processor is operatively coupled to the second computational processor. An advantage of this circuit is that it reduces the number of qubits used by the circuit.

[0006] According to another embodiment, a computer-implemented method may include generating a density function theoretical determination by a first computational processor of the system. The method may further include inputting the quantum density into the density function theoretical determination via a second computational processor of the system. The first computational processor is operatively coupled to the second computational processor. An advantage of this computer-implemented method is that the number of required qubits can be reduced because the first computational processor performing the density function theoretical determination replaces a portion of the active electrons (e.g., valence electrons).

[0007] Another embodiment relates to a system that may include a first computational processor for generating the density function theoretical determination. The system may also include a second computational processor for inputting quantum density into the density function theoretical determination. The first computational processor is operatively coupled to the second computational processor. An advantage of this system is that the number of qubits used in the circuit can be reduced by utilizing the first computational processor to generate the density function theoretical determination.

[0008] According to another embodiment, a computer-implemented method is provided, which may include employing a first computational processor via a means operatively coupled to a processor to perform a density function theoretical determination. The method may further include having the means employ a second computational processor to update the density function theoretical determination, thereby producing an updated density function theoretical determination. Further, the method may include having the means employ the first computational processor to re-optimize the updated density function theoretical determination based on an iterative density function theory-based embedding for quantum computing determination. An advantage of this computer-implemented method is the rigorous iterative density function theory-based embedding used for quantum computing computation.

[0009] Another embodiment relates to an apparatus that may include a first computational processor for implementing density function theory determination and a second computational processor for updating the density function theory determination and obtaining the updated density function theory determination. The first computational processor re-optimizes the updated density function theory determination based on an iterative density function theory-based embedding for quantum computing determination. The advantage of this apparatus is that it enables rigorous iterative density function theory-based embedding for quantum computing computations. Attached Figure Description

[0010] This patent or application document contains at least one color drawing. A copy of this patent or patent application publication with color drawings will be provided by the office upon request and payment of the necessary fees.

[0011] Figure 1 A block diagram of an example non-limiting system that facilitates the theoretical determination of density functions using a hybrid quantum and classical computing processor, according to one or more embodiments described herein, is shown.

[0012] Figure 2 Exemplary, non-limiting symbols for molecular orbitals according to one or more embodiments described herein are shown and their associated types are indicated.

[0013] Figure 3 Example non-limiting representations of molecular orbitals according to one or more embodiments described herein are shown, and their associated types and the use of iterative density function-based embeddings for hybrid classical and quantum processor systems are indicated.

[0014] Figure 4 An example non-limiting system comprising an iterative hybrid quantum and classical protocol is shown according to one or more embodiments described herein.

[0015] Figure 5 Examples of non-limiting representations of molecules of interest that become tractable using the disclosed embedding procedure according to one or more embodiments described herein are shown.

[0016] Figures 6A-6D Graphs showing different results obtained for pyridine molecules according to one or more embodiments described herein.

[0017] Figure 7 A flowchart is shown of an example, non-limiting computer implementation of a method for facilitating the theoretical determination of density functions using a quantum computing system, according to one or more embodiments described herein.

[0018] Figure 8 A flowchart is shown illustrating an example non-limiting computer implementation of a method for facilitating the mitigation of determining the number of qubits using density function theory with a quantum computing system, according to one or more embodiments described herein.

[0019] Figure 9 A flowchart is shown of an example, non-limiting computer implementation of a method for facilitating the theoretical determination of density functions using a quantum computing system, according to one or more embodiments described herein.

[0020] Figure 10 A block diagram is shown that illustrates an example non-limiting operating environment that may facilitate one or more embodiments described herein. Detailed Implementation

[0021] The following detailed description is illustrative only and is not intended to limit the embodiments and / or their application or use. Furthermore, it is not intended to be construed as being limited by any express or implied information presented in the prior art or invention description or detailed description sections.

[0022] One or more embodiments will now be described with reference to the accompanying drawings, wherein like reference numerals are used throughout to refer to like elements. In the following description, numerous specific details are set forth for purposes of explanation in order to provide a more thorough understanding of one or more embodiments. However, it will be apparent that one or more embodiments may be practiced without these specific details in various circumstances.

[0023] Figure 1 A block diagram is shown illustrating an example non-limiting system 100 that facilitates the determination of density function theory using hybrid quantum and classical computing processors according to one or more embodiments described herein. Aspects of the systems (e.g., system 100, etc.), devices, or processes explained in this disclosure may constitute multiple machine-executable components embodied within (e.g., embodied in one or more computer-readable media (or media) associated with one or more machines). When executed by one or more machines (e.g., multiple computers, multiple computing devices, multiple virtual machines, etc.), the multiple components may cause the multiple machines to perform the described operations.

[0024] In various embodiments, system 100 may be and / or may include any type of component, machine, apparatus, facility, device, and / or instrument that includes a processor and / or is capable of effectively and / or operatively communicating with wired and / or wireless networks. Components, machines, devices, facilities, and / or instruments that may include system 100 may include tablet computing devices, handheld devices, server-type computing machines and / or databases, laptop computers, notebook computers, desktop computers, cellular phones, smartphones, consumer appliances and / or instruments, industrial and / or commercial devices, handheld devices, digital assistants, multimedia internet-enabled phones, multimedia players, etc.

[0025] In various embodiments, system 100 may be a computing system associated with technologies such as, but not limited to, quantum computing, classical computing, circuitry, processor technology, computing technology, artificial intelligence, chemical technology, simulation technology, pharmaceutical and materials technology, supply chain and logistics technology, financial services technology, and / or other digital technologies. System 100 may employ hardware and / or software to solve inherently highly technical problems (e.g., these parts of the simulation are executed on a classical processor due to the less complex nature of the first part, and on a quantum processor due to the complex nature of the second part). Therefore, not all parts of the simulation need to be executed on a quantum processor, which is advantageous because it reduces the number of qubits required for the simulation.

[0026] Furthermore, in some embodiments, some of the processes performed may be executed by one or more dedicated computers (e.g., one or more dedicated processing units, dedicated computers with coupling components, feedback components, etc.) to use the quantum computing system to perform tasks related to the determination of the definition of the density function theory.

[0027] System 100 and / or components of System 100 can be used to solve new problems arising from advancements in technology, computer architecture, etc. System 100 (and other embodiments discussed herein) can perform simulations of macromolecules or other projects using iterative hybrid classical and quantum computing methods. One or more embodiments of System 100 can provide technological improvements to computing systems, classical computing systems, quantum computing systems, circuit systems, processor systems, artificial intelligence systems, deep learning computing systems, and / or other systems.

[0028] exist Figure 1 In the illustrated embodiment, system 100 may include a classical computer 102 and a quantum computer 104. Classical computer 102 may include a first computing processor 106, a first memory 108, and a first storage device 110. Quantum computer 104 may include a second computing processor 112, a second memory 114, and a second storage device 116. The memory (e.g., first memory 108, second memory 114) may store computer-executable components and instructions. These processors (e.g., first computing processor 106, second computing processor 112) may facilitate the execution of instructions (e.g., computer-executable components and corresponding instructions) via classical computer 102 and quantum computer 104. Classical computer 102 and quantum computer 104 may be electrically connected, communicatively connected, and / or operatively connected to each other to perform one or more functions of system 100.

[0029] The various embodiments presented herein can facilitate the theoretical determination of density functions using quantum computing systems coupled to classical computing systems. A problem associated with the simulation of macromolecules using classical computers (e.g., non-quantum computers) is that such simulations are intractable due to the exponential growth of Hilbert spaces. A Hilbert space is a mathematical concept or abstract vector space that can have a structure that allows for the measurement of inner products of lengths and angles. Quantum simulation of macromolecules is a possible solution because they can efficiently represent this exponential Hilbert space using qubits. However, quantum simulation of molecular systems is typically limited to very small sizes due to finite coherence time, gate noise, and other complexities. The problems associated with the size limitations of the molecular systems that can be simulated can be addressed through the aspects disclosed herein, and large-sized molecular systems can be simulated as discussed herein.

[0030] The first computational processor 106 can be used to perform density function theoretical determination. For example, input data 118 can be provided to the first computational processor 106. Input data 118 can be, for example, at least a portion of the molecular system being analyzed. The first computational processor 106 can perform density function theoretical determination on one or more portions of the input data 118 and can output the result of density function theoretical determination 120 (e.g., as output data).

[0031] The result of density function theory determination 120 can be input data received at the second computational processor 112. For example, based on the result of density function theory determination 120, the second computational processor 112 can update the result of density function theory determination. This can produce an updated density function theory determination 122, which is output by the second computational processor 112 as output data. The updated density function theory determination 122 is returned to the first computational processor 106 (as input data) (via, for example, a feedback component, not shown).

[0032] Therefore, the first computing processor 106 can be used to re-optimize the updated density function theory determination 122 from the second computing processor 112 based on the embedding of the density function theory for the iterative determination of quantum computing. The re-optimized updated density function theory determination is passed to the second computing processor. The second computing processor receives the re-optimized updated density function theory determination and performs another update. It is understood that the density function theory determination performed by the first computing processor 106 and the update of the density function theory determination performed by the second computing processor 112 can be recursive or iterative. For example, the density function theory determination can be updated (by the second computing processor 112) and iteratively re-optimized (by the first computing processor 106) until a final determination or final result is reached and output as output data 124. Note that the input data 118 is shown to be received from outside the classical computer 102. However, the disclosed aspects are not limited to this implementation, and the input data 118 can be provided by the classical computer 102.

[0033] The first computing processor 106 can be a classical computing processor and the second computing processor 112 can be a quantum computing processor. By utilizing a classical computing processor to implement (and / or reimplement) the density function theoretical determination, the number of qubits used by the system 100 can be reduced.

[0034] Understandably, System 100 (and other embodiments discussed herein) provides a technological improvement in the size of the molecular systems that cannot be simulated on classical computers at the same level of accuracy. To accommodate the current limitations of quantum computing, as discussed herein, the number of qubits and the depth of the circuits can be minimized. However, the number of qubits and the depth of the circuits can be increased based on the increasing power of quantum computing. For example, the effective core potential (ECP) allows the removal of the core electrons of atoms. ECP is a useful way to replace core electrons in computation with an effective potential, thereby eliminating the need for core basis functions, which typically require a large set of Gaussians to describe them. Through active space embedding, it is possible to freeze a subset of the molecular orbitals of the system; the remaining (unfrozen) set is called the active space.

[0035] Therefore, the disclosed aspects can help processors determine and deliver results more quickly and with less computational resources based on a hybrid approach using both classical and quantum processors, as discussed herein. Furthermore, System 100 (and other embodiments discussed herein) provides practical applications related to simulating molecular systems with sizes that could not previously be evaluated using only classical processors. Previously, embedding was achieved using purely classical iterative density matrix renormalization group-density-function theory (DMRG-DFT), and there are processes, such as density-function theory, for classical computation to embed high-precision (and therefore very expensive) methods into low-precision methods. Further, previously, quantum processors were used, neglecting the core electrons through an effective core potential. Furthermore, the electrons were frozen and excitations of their variations were ignored. Moreover, prior techniques could improve the accuracy of active space embedding by utilizing qubit space expansion. However, previous active space computations were inaccurate due to the loss of the correlation of the frozen electrons. Furthermore, the freezing of electrons does not necessarily reduce the number of qubits. However, large-scale qubit reduction can be achieved through the different embodiments discussed herein. Furthermore, the active space can be iteratively embedded into classical methods (e.g., classical processors). Therefore, these disclosed aspects use density function theory to generate subspace Hamiltonian operators used in quantum computing. Furthermore, the subsystem's 'quantum' density is fed back into density function theory and classically re-optimizes the orbits of the entire system.

[0036] Furthermore, the disclosed aspects are driven by new technologies (e.g., quantum) to address problems associated with molecular systems that only provide simulations of finite sizes. Additionally, the disclosed aspects can recover approximately one-third of the errors generated by previous methods. System 100 can also be made fully operational while performing one or more other functions (e.g., full power-on, full execution, etc.) and the aforementioned computational processes.

[0037] In more detail, Figure 2 Exemplary, non-limiting symbols 200 for molecular orbitals are shown according to one or more embodiments described herein, and their related types are indicated. For the sake of brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted.

[0038] Symbol 200 includes symbols for the quantum part, density-function theory or DFT 204 part, and the effective core potential or ECP part 206. As discussed above, ECP replaces the core electron with an effective potential in calculations, thus eliminating the need for core basis functions, which typically require a large set of Gaussians to describe the core basis functions. Through active space embedding, it is possible to freeze a subset of the molecular orbitals of the system; the remaining (unfrozen) set is called the active space.

[0039] The annotations on the right ("Virtual", "Valence", and "Core") indicate the various orbitals. Virtual 208 refers to the orbital represented by a dashed line, or a dashed orbital (Quantum Part 202). Valence 210 refers to the orbital represented by a solid line, or a solid orbital (DFT 204). Core 212 refers to the orbital represented by a solid line, or a solid orbital (ECP Part 206).

[0040] Valence state 210 can be mechanically treated as a quantum and corresponds to horizontal lines, where one horizontal line represents a single qubit. Therefore, many qubits are needed to embed this space in a quantum computer. Using the disclosed aspects, the quantum portion 202 can be reduced to a smaller orbital sub-segment. Thus, valence state 210 can represent a qubit that can be frozen. Because density function theory can be used to replace a portion of the activated electron (valence electron), classical computation (e.g., a first computational processor 106) can be used instead of valence state 210. Therefore, the number of required qubits can be dynamically reduced, as indicated by virtual 208, which represents a quantum processor (e.g., a second computational processor 112).

[0041] Figure 3 Exemplary, non-limiting representations of molecular orbitals according to one or more embodiments described herein are shown, along with their related types and the use of density function-based embeddings for iterations in hybrid classical and quantum processor systems. For brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted.

[0042] The determination using density function theory (DFT 204) can be performed in the frozen portion of the quantum processor (e.g., valence state 210). DFT 204 can be performed using a classical computing processor (e.g., first computing processor 106). The result of DFT 204 can be transferred to the unfrozen portion of the quantum processor (e.g., second computing processor 112), as indicated by the first arrow 302. The first arrow 302 represents the result of the density function theory determination. Processing using a variable quantum feature solver (VQE) can be performed while or after the result of the density function theory is transferred to the quantum processor. The result can be returned to the classical computing processor for further processing, as indicated by the second arrow 304.

[0043] More specifically, for active-space embedding, these frozen electrons can be manipulated outside of quantum hardware using classical methods such as density function theory. The energy (E) becomes:

[0044] Equation 1.

[0045] Where E is the electron energy, D is the 1-electron density matrix, d is the 2-electron density matrix, F is the Fock operator matrix, h is the 1-electron integral, and g is the 2-electron integral. Further, the superscript I indicates inactivity, the superscript A indicates activity, the subscripts i, j, k, l, m, and n indicate inactive indices, the subscripts u, v, x, and y indicate active indices, the subscripts a, b, c, and d indicate dummy indices, and the subscripts p, q, r, and s indicate general (e.g., any) indices. Additionally, the inactive Fock operator F... I Add the effective potential of the unactivated (frozen) electrons to the 1-electron integral:

[0046] Equation 2.

[0047] For range separation, the Coulomb operator can be divided into long-range and short-range parts:

[0048] Equation 3.

[0049] Where, r 12 It is the distance between two ordinary electrons, 1 and 2, erf is the error function, and µ is the unit au. (-1) The range of the separation parameters makes the independent variable of the error function dimensionless, and au is an atomic unit.

[0050] Figure 4 An example, non-limiting system 400 comprising an iterative hybrid quantum and classical protocol, according to one or more embodiments described herein, is shown. For the sake of brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted.

[0051] A CPU portion 402 (e.g., a first computational processor 106) and a CPU and QPU portion 404 (e.g., a second computational processor 112) are shown. Initialization 406 can be performed at the CPU portion 402. For example, initialization can be performed on a classical computer using Kohn-Sham density function theory (DFT) calculations, such as:

[0052] Equation 4.

[0053] Where ρ is the electron density, and the superscript (i) is the i-th iteration step (where i equals 0 for initialization).

[0054] For example, density can be divided into activity spaces as follows:

[0055] Activity Space Equation 5.

[0056] Furthermore, the electron repulsion integral can be separated by range.

[0057] Scope separation Equation 6.

[0058] In this context, the superscript LR stands for "long range" and the superscript SR stands for "short range".

[0059] The inactive long-range energy can be calculated once:

[0060] Calculate once:

[0061] Equation 7.

[0062] Where j is the 2-electron coulomb matrix and K is the 2-electron exchange matrix.

[0063] Furthermore, in the CPU section 402, density function theory 408 can be calculated. For example, the short-range contribution of inactive functions can be determined. This determination can be performed based on the following:

[0064] Equation 8.

[0065] Where the subscript "xc" indicates commutative correlation, and ρ A,(i) This is the active density matrix, which can be passed to the CPU and QPU section 404, as indicated at 412. Within the CPU and QPU section 404, VQE410 can be performed, where long-range contributions can be determined. Furthermore, the active density matrix can be updated.

[0066] Equation 9.

[0067] New density ρ A,(i+1) It can be returned to density function theory 408, as shown in 414, for further processing.

[0068] On classical computers, the various aspects related to the improved density function theoretical calculations presented in this paper are impossible. Furthermore, the type of calculations provided by classically employing the embedding mechanism will have unfavorable scaling, and therefore, the size of the molecular systems that can be analyzed is limited. Thus, accurate classical calculations can be extracted into smaller quantum systems, and this can be achieved using recent quantum computers. Quantum computers can take all degrees of freedom and perform this process at advantageous scaling. In the near term, with the disclosed aspects, it is possible to reduce the number of electrons to a minimum set of orbitals. Due to the orbitals existing in active space, it is possible to realize the disclosed aspects using quantum computers in the near term.

[0069] As discussed, quantum algorithms can be coupled to density function theory simulations via an iterative process. This also enables the initialization of quantum computations with density function theory instead of the previously performed HF orbitals. Furthermore, based on advancements in quantum processors, many other advanced classical methods can also be coupled to density function theory simulations. Therefore, it is possible to simulate increasingly larger molecular systems. An upper bound can be defined, through which low-level approximation methods can be used to treat any system on a classical computer.

[0070] Figure 5 Exemplary, non-limiting representations of molecules of interest that become processable with the disclosed embedding procedure according to one or more embodiments described herein are shown. For the sake of brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted.

[0071] As mentioned, the disclosed aspects allow molecular systems to be processed to be as large (if not larger) as those that can be processed on classical hardware. For example, processing the iron metal within heme structures of the Fe-porphyrin-like class. Heme is a coordination complex comprising a porphyrin acting as a tetradentate ligand and an iron ion coordinated to one or two axial ligands.

[0072] Figure 5 On the right is succinate dehydrogenase (SDH), represented by heme group 502, which is an electron carrier in the mitochondrial electron transfer chain and binds to two histidine residues. Large, translucent spheres indicate the location of iron ions. The porphyrin portion in box 504 is shown in atomic detail in magnified portion 506, which represents the structure of the iron-porphyrin subunit of heme B.

[0073] The molecular structure depicted in magnified portion 506 is an example of how the disclosed aspects can become visible. The disclosed aspects can be processed using a quantum processor as discussed here, specifically in portion 508 (e.g., iron atoms). This is the ionic core embedded in a protein. Other atoms in the environment of the molecular structure depicted in magnified portion 506 can be processed using a classical processor as density function theory. Furthermore, the molecular structure can be surrounded by other atoms, such as those formed by… Figure 5 The right-hand side indicates what 502 indicates, which can also be processed as discussed herein.

[0074] Figures 6A-6D Graphs showing different results obtained for the pyridine molecule according to one or more embodiments described herein are presented. For the sake of brevity, repeated descriptions of similar elements used in other embodiments described herein are omitted.

[0075] Pyridine molecules include the following structures:

[0076]

[0077] Figures 6A-6D The results show how much energy can be harvested using the disclosed aspects. Figure 6A The first curve 600 showing the two activated electrons is shown; Figure 6B The second curve 602, showing four activated electrons, is shown. Figure 6C The third curve 604 shows the six activated electrons; Figure 6D The fourth graph 606, showing eight activated electrons, is illustrated. Legend 608 is shown below each graph.

[0078] The energy (E[H]) of Hartee is shown on the left vertical axis 610. The range separation parameter µ is shown on the horizontal axis 612. The energy change (ΔE[H]) is shown on the right vertical axis 614. Thus, these graphs show E[H] relative to the range separation parameter µ. Furthermore, the results are grouped by the activity space.

[0079] Line 616 represents the HF orbital; line 618 represents the density function theory; and line 620 represents the coupled cluster single-double (CCSD). The line symbols indicate the number of active molecular orbitals. A line with an upward-facing triangle represents two orbitals; a line with a circle represents three orbitals; a line with an inverted triangle represents four orbitals; a line with a circle represents five orbitals; and a line with a square represents six orbitals.

[0080] The initial calculation for this graph is RHF (relative energy on the right y-axis). The sign 𝜇 approaching zero (𝜇→0) indicates that the energy converges toward the density function theory (XC: lda, vwn). The sign 𝜇 approaching infinity (𝜇→∞) indicates convergence to a non-iterative embedding (bound by a fully active space self-consistent domain (CASSCF) with the same active space). Furthermore, the CCSD (computation of coupled clusters with all single and dual excitations) energy serves as a nearly exact reference.

[0081] like Figures 6A to 6D As shown in the graph, the disclosed aspects can be applied to achieve the desired results. Furthermore, the disclosed aspects can be applied to simulate systems of increasingly larger sizes. An upper limit can be defined, by which low-level approximation methods can be used to treat any system on a classical computer.

[0082] Furthermore, a long-term impact of the disclosed aspects is that the system can be simulated with a modest number of qubits, as these computations can be focused on the parts of the system that are difficult to implement or process classically (e.g., via a classical processor). Moreover, the entire computing system or device can be smaller because a classical processor is embedded within a quantum processor. Furthermore, not everything needs to be brought to the quantum level; rather, these difficult parts can be implemented by a quantum processor, while other less difficult parts can be implemented by a classical processor.

[0083] Figure 7 A flowchart is shown of an exemplary, non-limiting, computer-implemented method 700 that facilitates the determination of density function theory using a quantum computing system according to one or more embodiments described herein. For brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted.

[0084] At 702 of the computer-implemented method 700, a first computational processor of the system can generate a density function theoretical determination (e.g., via first computational processor 106). According to some embodiments, the density function theoretical determination may be an active density matrix. Further, at 704 of the computer-implemented method 700, a second computational processor of the system can input quantum density into the density function theoretical determination (e.g., via second computational processor 112). The first computational processor is operatively coupled to the second computational processor. In the example, the second computational processor may be a quantum computing processor and the first computational processor may be a classical computing processor.

[0085] Figure 8A flowchart illustrating an example, non-limiting, computer-implemented method 800 for facilitating the reduction of the number of qubits determined by density function theory using a quantum computing system, according to one or more embodiments described herein, is shown. For brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted.

[0086] In method 802 of the computer implementation 800, the system's first computational processor generates the density function theoretical determination (e.g., via the first computational processor 106). The density function theoretical determination may be an active density matrix. Depending on some implementations, the first computational processor may determine the inactive short-range contributions that lead to the density function theoretical determination.

[0087] In method 800 of the computer implementation at 804, the system's second computational processor inputs the quantum density into the density function theoretical determination (e.g., via second computational processor 112). The first and second computational processors are operatively coupled. For example, by operatively coupling the first and second computational processors, the number of qubits used by the second computational processor to update the active density matrix can be reduced.

[0088] Furthermore, at 806 of the computer-implemented method 800, the second computing processor provides an updated activity density matrix based on quantum density (e.g., via the second computing processor 112 or a feedback component (not shown)). For example, the updated activity density matrix can be provided or fed back to the first computing processor. Thus, the second computing processor can transmit the updated activity density matrix to the first computing processor. Communication is performed iteratively according to some implementations.

[0089] Figure 9 A flowchart illustrating an example, non-limiting computer implementation of a method 900 for facilitating and utilizing density function theory to determine relevant feedback loops in a quantum computing system according to one or more embodiments described herein is shown. For brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted.

[0090] In method 900 implemented in a computer at 902, the means operatively coupled to the processor may employ a first computing processor to perform the density function theoretical determination (e.g., via first computing processor 106 or a coupling component (not shown)). Further, in method 900 implemented in a computer at 904, the means may employ a second computing processor to update the density function theoretical determination, resulting in an updated density function theoretical determination (e.g., via second computing processor 112). According to some implementations, the first computing processor may include a classical processor, and the second computing processor may include a quantum processor.

[0091] When or after the updated density function theory determination is made by the second computational processor, at 906 of the computer-implemented method 900, the apparatus may employ the first computational processor to re-optimize the updated density function theory determination based on the embedding of the density function theory based on the iterations used for quantum computing determination (e.g., via the first computational processor 106 or a feedback component). Employing the first computational processor may include electrons that are frozen in the second computational processor.

[0092] For simplicity of explanation, the computer-implemented method is depicted and described as a series of actions. It is understood and appreciated that the subject matter innovation is not limited to the actions shown and / or the order of actions; for example, actions may occur in different orders and / or simultaneously, and may occur with other actions not presented and described herein. Furthermore, not all actions shown are necessary to implement the computer-implemented method according to the disclosed subject matter. Moreover, those skilled in the art will understand and appreciate that the computer-implemented method may alternatively be represented as a series of interrelated states via state diagrams or events. Furthermore, it is understood that the computer-implemented method disclosed below and throughout this specification can be stored on an article of art to facilitate the transfer and assignment of the computer-implemented method to a computer. As used herein, the term article of art is intended to encompass a computer program accessible from any computer-readable device or storage medium.

[0093] In order to provide context for the various aspects of the disclosed subject, Figure 10 The following discussion is intended to provide a general description of the suitable environment in which the various aspects of the disclosed subject matter can be realized. Figure 10 A block diagram illustrating an example non-limiting operating environment that can facilitate one or more embodiments described herein is shown. For brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted. References Figure 10The suitable operating environment 1000 for implementing various aspects of this disclosure may also include a computer 1012. The computer 1012 may further include a processing unit 1014, system memory 1016, and a system bus 1018. The system bus 1018 couples system components, including but not limited to system memory 1016, to the processing unit 1014. The processing unit 1014 may be any of a variety of available processors. Dual microprocessors and other multiprocessor architectures may also be used as the processing unit 1014. The system bus 1018 may be any of several types of bus architectures, including memory buses or memory controllers, peripheral buses or external buses, and / or local buses using any of the various available bus architectures, 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 (IEEE 1394), and Small Computer System Interface (SCSI). System memory 1016 may also include volatile memory 1020 and non-volatile memory 1022. The Basic Input / Output System (BIOS) is stored in the non-volatile memory 1022, which contains basic routines for transferring information between components within the computer 1012, such as during startup. By way of example and not limitation, non-volatile memory 1022 may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, or non-volatile random access memory (RAM) (e.g., ferroelectric RAM (FeRAM)). Volatile memory 1020 may also include random access memory (RAM) that acts as an external cache memory. As an illustration and not a limitation, RAM can be obtained in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM.

[0094] Computer 1012 may also include removable / non-removable, volatile / non-volatile computer storage media. Figure 10Disk storage 1024 is illustrated, for example. Disk storage 1024 may also include, but is not limited to, devices such as disk drives, floppy disk drives, magnetic tape drives, Jaz drives, Zip drives, LS-100 drives, flash memory cards, or Memory Sticks. Disk storage 1024 may also include storage media, either alone or in combination with other storage media, including but not limited to optical disc drives, such as optical disc ROM devices (CD-ROM), CD recordable drives (CD-R drives), CD rewritable drives (CD-RW drives), or digital universal disk ROM drives (DVD-ROM). To facilitate connection of disk storage 1024 to system bus 1018, a removable or non-removable interface, such as interface 1026, is typically used. Figure 10 Software acting as an intermediary between the user and the basic computer resources described in the suitable operating environment 1000 is also described. This software may also include, for example, an operating system 1028. The operating system 1028, which may be stored on a disk storage device 1024, is used to control and allocate the resources of the computer 1012. System application 1030 utilizes the management of resources by the operating system 1028 through program modules 1032 and program data 1034, for example, stored on system memory 1016 or disk storage 1024. It is understood that this disclosure can be implemented using various operating systems or combinations of operating systems. The user inputs commands or information into the computer 1012 via input devices 1036. Input devices 1036 include, but are not limited to, pointing devices such as a mouse, trackball, pen, touchpad, keyboard, microphone, joystick, gamepad, disc satellite dish, scanner, TV tuner card, digital camera, digital camcorder, webcam, etc. These and other input devices are connected to the processing unit 1014 via interface ports(s) 1038 through a system bus 1018. Interface port 1038 includes, for example, a serial port, a parallel port, a gaming port, and a Universal Serial Bus (USB). Output device 1040 uses some of the same type of ports as input device 1036. Thus, for example, a USB port can be used to provide input to computer 1012 and to output information from computer 1012 to output device 1040. Output adapter 1042 is provided to illustrate the presence of some output devices 1040, such as monitors, speakers, and printers, as well as other output devices 1040 that require special adapters. By way of illustration and not limitation, output adapter 1042 includes video and sound cards that provide a method of connection between output device 1040 and system bus 1018. It should be noted that other devices and / or systems of devices provide both input and output capabilities, such as remote computer 1044.

[0095] Computer 1012 can operate in a networked environment using logical connections to one or more remote computers (such as remote computers 1044). Remote computer 1044 can be a computer, server, router, network PC, workstation, microprocessor-based appliance, peer-to-peer device, or other public network node, and typically may also include many or all of the elements described relative to computer 1012. For simplicity, memory storage device 1046 is described using only remote computer 1044 as an example. Remote computer 1044 is logically connected to computer 1012 via network interface 1048 and then physically connected via communication connection 1050. Network interface 1048 includes 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 Wire Distributed Data Interface (CDDI), Ethernet, Token Ring, etc. WAN technologies include, but are not limited to, point-to-point links, circuit-switched networks (such as Integrated Services Digital Network (ISDN)) and its variants, packet-switched networks, and Digital Subscriber Line (DSL). Communication connection 1050 refers to the hardware / software used to connect network interface 1048 to system bus 1018. Although communication connection 1050 is shown inside computer 1012 for clarity, it can also be outside computer 1012. For illustrative purposes only, the hardware / software used to connect to network interface 1048 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.

[0096] This invention can be a system, method, apparatus, and / or computer program product at any possible level of technical detail integration. The computer program product may include a computer-readable storage medium (or media) having computer-readable program instructions thereon for causing a processor to execute aspects of the invention. The computer-readable storage medium may be a tangible means for retaining and storing instructions for use by an instruction execution device. The computer-readable storage medium may be, for example, but not limited to, electronic storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination thereof. A non-exhaustive list of more specific examples of computer-readable storage media may also include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disk read-only memory (CD-ROM), digital universal disk (DVD), memory sticks, floppy disks, mechanical encoding devices such as punched cards, or protrusions in slots having instructions recorded thereon, and any suitable combination thereof. As used herein, computer-readable storage media should not be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses passing through fiber optic cables), or electrical signals transmitted through wires.

[0097] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to a corresponding computing / processing device via a network (e.g., the Internet, a local area network, a wide area network, and / or a wireless network), or downloaded to an external computer or external storage device. The network may include copper transmission cables, optical transmission fibers, wireless transmissions, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to a computer-readable storage medium within the corresponding computing / processing device. The computer-readable program instructions used to perform the operations of this invention may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status 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 the "C" programming language or similar programming languages). Computer-readable program instructions may execute entirely on a user's computer, partially on a user's computer, as a standalone software package, partially on a user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter case, 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., via the Internet using an Internet service provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, a field-programmable gate array (FPGA), or a programmable logic array (PLA) may be personalized to execute computer-readable program instructions by utilizing state information of the computer-readable program instructions in order to perform aspects of the present invention.

[0098] The present invention will now be described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions. These computer-readable program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a method for implementing the functions / actions specified in the blocks or blocks of the flowchart illustrations and / or block diagrams. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner, such that the computer-readable storage medium storing the instructions includes an article of manufacture containing instructions that implement aspects of the functions / actions specified in the blocks or blocks of the flowchart illustrations and / or block diagrams. Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operations to be performed on the computer, other programmable apparatus, or other device to produce computer-implemented processing, such that the instructions executed on the computer, other programmable apparatus, or other device perform the functions / actions specified in the boxes or blocks of the flowchart and / or block diagram.

[0099] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. Each block in a flowchart or block diagram may represent a module, segment, or portion of instructions, including one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than indicated in the figures. For example, depending on the functions involved, two consecutively shown blocks may actually be executed substantially simultaneously, or these blocks may sometimes be executed in reverse order. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action or executes a combination of dedicated hardware and computer instructions.

[0100] While the subject matter has been described above in the general context of computer-executable instructions running on a computer and / or a computer program product on a computer, those skilled in the art will recognize that this disclosure can also be implemented in combination 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. Furthermore, those skilled in the art will recognize that the computer implementation methods of the present invention can 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, telephones), microprocessor-based or programmable consumer or industrial electronic products, etc. The aspects shown can also be implemented in a distributed computing environment, where tasks are performed by remote processing devices linked via a communication network. However, some (if not all) aspects of the present invention can be practiced on a standalone computer. In a distributed computing environment, program modules can reside in both local and remote memory storage devices.

[0101] As used herein, the terms “component,” “system,” “platform,” “interface,” etc., may refer to and / or include computer-related entities or entities associated with an operating machine having one or more specific functions. 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 running on a processor, a processor, an object, an executable file, a thread of execution, a program, and / or a computer. As an illustration, both an application running on a server and the server itself can be components. One or more components may reside within a process and / or a thread of execution, and components may reside on a single computer and / or be distributed across two or more computers. In another instance, a corresponding component may execute from a different computer-readable medium having different data structures stored thereon. Components may communicate via local and / or remote processes, such as according to signals having one or more data packets (e.g., data from a component interacting with another component in a local system, a distributed system, and / or data from a component interacting with other systems across a network such as the Internet via that signal). As another example, a component may be a device having specific functions provided by mechanical parts operated by electrical or electronic circuitry, which is operated by a software or firmware application executed by a processor. In such a case, the processor can be internal or external to the device and can execute at least a portion of the software or firmware application. As another example, the component can be a device that provides a specific function through electronic components without mechanical parts, wherein the electronic components can include a processor or other methods to execute software or firmware that at least partially endows the electronic components with the functions. In one aspect, the component can be emulated via a virtual machine, for example, within a cloud computing system.

[0102] Furthermore, the term "or" is intended to mean an inclusive "or" rather than an exclusive "or". That is, unless otherwise specified or clear from the context, "X adopts A or B" is intended to mean any natural inclusive permutation. That is, if X adopts A; X adopts B; or X adopts both A and B, then "X adopts A or B" is satisfied in any of the foregoing cases. Additionally, the articles "a" and "an" as used in the subject matter specification and figures should generally be interpreted as meaning "one or more" unless otherwise specified or clearly indicated from the context to the singular form. As used herein, the terms "example" and / or "exemplary" are used to indicate that something is used as an example, instance, or illustration. For the avoidance of doubt, the subject matter disclosed herein is not limited to such examples. Furthermore, any aspect or design described herein as "example" and / or "exemplary" is not necessarily to be construed as superior to or superior to other aspects or designs, nor does it imply the exclusion of equivalent exemplary structures and techniques known to those skilled in the art.

[0103] As used herein, 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 multithreading capabilities; a multi-core processor; a multi-core processor with software multithreading capabilities; a multi-core processor with hardware multithreading technology; a parallel platform; and a parallel platform with distributed shared memory. Additionally, "processor" can refer to an integrated circuit, application-specific integrated circuit (ASIC), digital signal processor (DSP), field-programmable gate array (FPGA), programmable logic controller (PLC), complex programmable logic device (CPLD), discrete gate or transistor logic, discrete hardware components, or any combination thereof, designed to perform the functions described herein. Furthermore, processors can utilize nanoscale architectures, such as, but not limited to, molecular and quantum dot-based transistors, switches, and gates, to optimize space utilization or enhance the performance of user equipment. Processors can also be implemented as a combination of computing processing units. In this disclosure, terms such as “storage,” “storage device,” “data storage,” “database,” “database,” and substantially any other information storage component, in relation to the operation and function of a component, are used to refer to a “memory component,” an entity embodied in “memory,” or a component that includes memory. It should be understood that the memory and / or memory components described herein can be volatile or non-volatile memory, or may include both volatile and non-volatile memory. By way of example 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, for example, RAM that can act as an external cache memory. By way of illustration and not limitation, RAM may be available in many forms, such as synchronous RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), direct Rambus, etc. RAM (DRRAM), Direct Rambus Dynamic RAM (DRDRAM), and Rambus Dynamic RAM (RDRAM). Additionally, the memory components of the systems or computer-implemented methods disclosed herein inherently include (but are not limited to) these and any other suitable types of memory.

[0104] The above description includes only examples of systems and computer-implemented methods. Of course, for the purposes of describing this disclosure, it is impossible to describe every conceivable combination of components or computer-implemented method; however, those skilled in the art will recognize that many further combinations and substitutions of this disclosure are possible. Furthermore, the terms “comprising,” “having,” “possessing,” etc., used in the detailed description, claims, appendices, and drawings are intended to be inclusive in a manner similar to the term “comprising,” and when “comprising” is used as a transitional word in a claim, it is interpreted as “comprising.” Descriptions of different embodiments are presented for illustrative purposes but are not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein has been chosen to best explain the principles of the embodiments, their practical application, or technical improvements to technologies found in the market, or to enable those skilled in the art to understand the embodiments disclosed herein.

Claims

1. A circuit for quantum computing, comprising: Classical computational processors, which are based on the theory of density functions generated from input data related to molecular systems, include: Determine the long-range contribution of the frozen electrons in the molecular system to the inactive state determined by the density function theory, and Determine the short-range contribution of the frozen electrons to the inactive state determined by the density function theory; and A quantum computing processor that updates the density function theoretical determination by inputting the quantum density into the density function theoretical determination generated by the classical computing processor, wherein the quantum density is based on the long-range contribution of unfrozen electrons in the molecular system, wherein the classical computing processor is operatively coupled to the quantum computing processor. The inactive long-range contribution is determined once, and the inactive short-range contribution is updated iteratively with the quantum density.

2. The circuit of claim 1, wherein, The classical computing processor separates the electrons in the molecular system into the frozen electrons and the unfrozen electrons.

3. The circuit of claim 1, wherein, The density function theory determines an active density matrix, and the quantum computing processor generates an updated active density matrix based on the quantum density.

4. The circuit according to claim 1, wherein, The quantum computing processor communicates the updated density function theory determination to the classical computing processor to execute the optimization determined by the updated density function theory.

5. The circuit according to claim 4, wherein, The optimization determined by the updated density function theory optimizes the electronic orbitals of the molecular system.

6. The circuit according to any one of claims 1 to 5, wherein, The quantum computing processor employs a variable quantum feature solver.

7. The circuit according to any one of claims 1 to 5, wherein, The classical computing processor separates the electron repulsion integral associated with electrons in the molecular system into short-range and long-range components.

8. The circuit according to any one of claims 1 to 5, wherein, The density function theory generated by the classical computing processor provides the subspace Hamiltonian operator used by the quantum computing processor.

9. A method for computer implementation of quantum computing, comprising: The density function is determined by the system's classical computational processor based on the input data related to the molecular system, including: Determine the long-range contribution of the frozen electrons in the molecular system to the inactive state determined by the density function theory, and Determine the short-range contribution of the frozen electrons to the inactive state determined by the density function theory; and The quantum computing processor of the system updates the density function theoretical determination by inputting the quantum density into the density function theoretical determination, wherein the quantum density is based on the long-range contribution of unfrozen electrons in the molecular system, wherein the classical computing processor is operatively coupled to the quantum computing processor. The inactive long-range contribution is determined once, and the inactive short-range contribution is updated iteratively with the quantum density.

10. The computer-implemented method according to claim 9, wherein, The classical computing processor separates the electrons in the molecular system into the frozen electrons and the unfrozen electrons.

11. The computer-implemented method according to any one of claims 9 to 10, wherein, The density function theory determines an active density matrix, and the computer-implemented method further includes: The quantum computing processor provides an updated activity density matrix based on the quantum density.

12. The computer-implemented method according to claim 11, further comprising: The classical computing processor is operatively coupled to the quantum computing processor to reduce the number of qubits required by the quantum computing processor to update the activity density matrix.

13. The computer-implemented method according to claim 11, further comprising: The quantum computing processor communicates the updated density function theoretical determination to the classical computing processor to perform the optimization determined by the updated density function theoretical determination.

14. The computer-implemented method according to any one of claims 9, 10, 12, and 13, further comprising: The classical computing processor separates the electron repulsion integral associated with electrons in the molecular system into short-range and long-range components.

15. A quantum computing system, comprising: Classical computational processors, which are based on the theory of density functions generated from input data related to molecular systems, include: Determine the long-range contribution of the frozen electrons in the molecular system to the inactive state determined by the density function theory, and Determine the short-range contribution of the frozen electrons to the inactive state determined by the density function theory; and A quantum computing processor updates the density function theoretical determination by inputting a quantum density into the density function theoretical determination, wherein the quantum density is based on the long-range contribution of the unfrozen electrons of the molecular system, wherein the classical computing processor is operatively coupled to the quantum computing processor. The inactive long-range contribution is determined once, and the inactive short-range contribution is updated iteratively with the quantum density.

16. The quantum computing system according to claim 15, wherein, The quantum computing processor communicates the updated density function theory determination to the classical computing processor to execute the optimization determined by the updated density function theory.

17. The quantum computing system according to any one of claims 15 to 16, wherein, The classical computing processor separates the electrons in the molecular system into the frozen electrons and the unfrozen electrons.

18. A method for computer implementation of quantum computing, comprising: The density function is theoretically determined using a device operatively coupled to a processor and employing a classical computing processor, including: Determine the long-range contribution of frozen electrons in the molecular system to the inactive state determined by the density function theory, and Determine the short-range contribution of the frozen electrons to the inactive state determined by the density function theory; The device employs a quantum computing processor to update the density function theoretical determination by inputting the quantum density into the density function theoretical determination generated by the classical computing processor, resulting in an updated density function theoretical determination, wherein the quantum density is based on the long-range contribution of unfrozen electrons in the molecular system; and The device employs the classical computing processor to optimize the updated density function theory determination based on an iterative embedding of density function theory used for quantum computing determination. The inactive long-range contribution is determined once, and the inactive short-range contribution is updated iteratively with the quantum density.

19. The computer-implemented method of claim 18, further comprising using the device with the classical computing processor to separate electrons in the molecular system into frozen electrons and unfrozen electrons.

20. The computer-implemented method according to any one of claims 18 to 19, wherein, The density function theory determines that this includes the activity density matrix.

21. The computer-implemented method according to any one of claims 18 to 19, further comprising: The electron repulsion integral associated with electrons in the molecular system is separated into short-range and long-range components.

22. A quantum computing device, comprising: Classical computational processors, which determine density functions theoretically based on input data related to molecular systems, include: Determine the long-range contribution of the frozen electrons in the molecular system to the inactive state determined by the density function theory, and Determine the short-range contribution of the frozen electrons to the inactive state determined by the density function theory, and A quantum computing processor updates the density function theoretical determination by inputting the quantum density into the density function theoretical determination generated by the classical computing processor, resulting in an updated density function theoretical determination, wherein the quantum density is based on the long-range contribution of unfrozen electrons in the molecular system. The classical computing processor optimizes the updated density function theory determination based on an iterative embedding of density function theory used for quantum computing determination. The inactive long-range contribution is determined once, and the inactive short-range contribution is updated iteratively with the quantum density.

23. The quantum computing device according to claim 22, wherein, The classical computing processor separates the electrons in the molecular system into the frozen electrons and the unfrozen electrons.

24. The quantum computing device according to any one of claims 22 to 23, wherein, Reduce the amount of qubits used by the quantum computing processor.

25. The quantum computing device according to any one of claims 22 to 23, wherein, The classical computing processor separates the electron repulsion integral associated with electrons in the molecular system into short-range and long-range components.

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