Density Functional Theory Determination Using Quantum Computing Systems

Abstract

Techniques are provided for facilitating density functional theory determinations using a quantum computing system. The system can include a first computing processor and a second computing processor. The first computing processor can generate a density functional theory determination. The second computing processor can input a quantum density into the density functional theory determination. The first computing processor can be operably coupled to the second computing processor. Furthermore, the first computing processor can be a classical computer and the second computing processor can be a quantum computer.

Description

[Technical Field]

[0001] This disclosure relates to quantum computing, and more particularly to facilitating density functional theory determinations using quantum computing systems. Simulations of large molecules using classical computers (e.g., non-quantum computers) are intractable due to the exponential growth of Hilbert space. Quantum simulations of large molecules offer a possible solution because this exponential Hilbert space can be efficiently represented using qubits. However, quantum simulations of molecular systems are limited to extremely small sizes due to limited coherence times, gate noise, and other complexities. [Background technology]

[0002] For example, Yonezawa et al. (US Patent Application Publication No. 2007 / 0043545) consider "dividing a molecule or a part of a molecule to be simulated into a [Quantum Mechanics] QM space and an [Molecular Mechanics] MM [space] and applying an ab initio molecular orbital method to the QM space" (see Abstract). However, Yonezawa et al. use only classical processors, which limits the size of the molecular systems they can analyze.

[0003] In another example, Rubin (US Patent Application Publication No. 2018 / 0096085) discusses "quantum computations executed on one or more quantum processor units (QPUs), which may operate in parallel, are used for density matrix embedding calculations" (see paragraph

[0012] ). According to Rubin, "quantum processor units (QPUs) are used to compute reduced density matrices (RDMs)" (see paragraph

[0055] ). Rubin considers that "1-reduced density matrix (1-RDM) and 2-reduced density matrix (2-RDM) are computed for each fragment based on the embedded Hamiltonian for the fragment" (ibid.). However, Rubin's reduced density matrix lacks the ability to provide an exact, iterative density functional theory-based embedding for quantum computing calculations. Summary of the Invention

[0004] SUMMARY OF THE INVENTION

[0003] The following is a summary intended to provide a basic understanding of one or more embodiments of the present invention. This summary is not intended to identify key or critical elements or to delineate the scope of particular embodiments or 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.

[0004] In one or more embodiments described herein, a system, computer-implemented method, apparatus, circuit, or computer program product, or combination thereof, is provided that facilitates density functional theory determinations using a quantum computing system.

[0005] According to an embodiment, the circuit can include a first computing processor that generates a density functional theory determination. The circuit can also include a second computing processor that inputs a quantum density into the density functional theory determination generated by the first computing processor. The first computing processor can be operably coupled to the second computing processor. An advantage of such a circuit is a reduction in the number of qubits used by the circuit.

[0006] According to another embodiment, a computer-implemented method can include generating, by a first computing processor of the system, a density functional theory determination. The method can also include inputting, by a second computing processor of the system, a quantum density into the density functional theory determination. The first computing processor can be operably coupled to the second computing processor. An advantage of such a computer-implemented method is that the number of required qubits can be reduced because a portion of the active electrons (e.g., valences) are replaced by the first computing processor making the density functional theory determination.

[0007] Another embodiment relates to a system that can include a first computing processor that generates density functional theory determinations. The system can also include a second computing processor that inputs quantum densities into the density functional theory determinations. The first computing processor can be operatively coupled to the second computing processor. An advantage of such a system is that the number of qubits used by the circuit can be reduced by utilizing the first computing processor to generate the density functional theory determinations.

[0008] According to a further embodiment, a computer-implemented method is provided that can include, by a device operatively coupled to the processor, utilizing a first computing processor to implement the density functional theory determination. The method can also include, by the device, utilizing a second computing processor to update the density functional theory determination to obtain an updated density functional theory determination. Furthermore, the method can include, by the device, utilizing the first computing processor to reoptimize the updated density functional theory determination based on an iterative density functional theory-based embedding for the quantum computing determination. An advantage of such a computer-implemented method is the rigorous iterative density functional theory-based embedding for quantum computing calculations.

[0009] Yet another embodiment relates to a device that may include a first computing processor that implements density functional theory determination and a second computing processor that updates the density functional theory determination to obtain an updated density functional theory determination. The first computing processor reoptimizes the updated density functional theory determination based on an iterative density functional theory-based embedding for the quantum computing determination. An advantage of such a device is that it is possible to achieve an exact iterative density functional theory-based embedding for a quantum computing calculation.

[0010] The patent or patent application file contains at least one drawing in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a block diagram of an example, non-limiting system that facilitates density functional theory determinations using a hybrid quantum-classical computing processor, according to one or more embodiments described herein. [Figure 2] FIG. 1 illustrates an example, non-limiting notation for molecular orbitals and their associated types, according to one or more embodiments described herein. [Figure 3] FIG. 1 illustrates an example, non-limiting representation of molecular orbitals and their associated types and the use of iterative density functional theory-based embedding for hybrid classical and quantum processor systems, according to one or more embodiments described herein. [Figure 4] FIG. 1 is a diagram of an example, non-limiting system including an iterative hybrid quantum-classical protocol, according to one or more embodiments described herein. [Figure 5]FIG. 1 is a representation of exemplary, non-limiting molecules of interest that can be manipulated using the implantation procedures of the present disclosure, according to one or more embodiments described herein. [Figure 6A] 1 is a plot of various results obtained for pyridine molecules according to one or more embodiments described herein. [Figure 6B] 1 is a plot of various results obtained for pyridine molecules according to one or more embodiments described herein. [Figure 6C] 1 is a plot of various results obtained for pyridine molecules according to one or more embodiments described herein. [Figure 6D] 1 is a plot of various results obtained for pyridine molecules according to one or more embodiments described herein. [Figure 7] FIG. 1 is a flow diagram of an exemplary, non-limiting computer-implemented method for facilitating density functional theory determinations using a quantum computing system, according to one or more embodiments described herein. [Figure 8] FIG. 1 is a flow diagram of an example, non-limiting, computer-implemented method that facilitates reducing the number of qubits utilized to perform density functional theory determinations using a quantum computing system, in accordance with one or more embodiments described herein. [Figure 9] FIG. 1 is a flow diagram of an example, non-limiting, computer-implemented method for facilitating a feedback loop associated with density functional theory determinations using a quantum computing system, according to one or more embodiments described herein. [Figure 10] FIG. 1 is a block diagram of an example, non-limiting operating environment capable of facilitating one or more embodiments described herein. DETAILED DESCRIPTION OF THE INVENTION

[0012] The following detailed description is illustrative only and is not intended to limit the embodiments or the application and / or uses of the embodiments, nor is it intended to be bound by any stated or implied information presented in the preceding "Background" or "Summary" sections or in the "Detailed Description" section.

[0013] One or more embodiments will now be described with reference to the drawings, wherein like reference numerals are used to refer to like elements throughout. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of one or more embodiments. It will be apparent, however, that in various instances, one or more embodiments may be practiced without these specific details.

[0014] 1 is a block diagram of an example, non-limiting system 100 that facilitates density functional theory determinations using a hybrid quantum-classical computing processor, according to one or more embodiments described herein. Aspects of the systems (e.g., system 100, etc.), apparatus, or processes described in this disclosure may constitute machine-executable components embodied within a machine, e.g., embodied in one or more computer-readable media associated with one or more machines. Such components, when executed by one or more machines, e.g., computers, computing devices, virtual machines, etc., can cause the machine to perform the operations described.

[0015] In various embodiments, system 100 can be and / or include any type of component, machine, device, facility, equipment, and / or appliance that includes a processor and / or is capable of effectively and / or operatively communicating with a wired and / or wireless network. The components, machines, devices, facilities, and / or appliances that comprise system 100 can include tablet computing devices, handheld devices, server-class computing machines and / or databases, laptop computers, notebook computers, desktop computers, mobile phones, smartphones, household appliances and / or appliances, industrial and / or commercial devices, handheld devices, personal digital assistants, multimedia Internet-enabled telephones, multimedia players, etc.

[0016] In various embodiments, system 100 can be a computing system related to technologies such as, but not limited to, quantum computing, classical computing, circuit technology, processor technology, computational technology, artificial intelligence technology, chemistry technology, simulation technology, medical and materials technology, supply chain and logistics technology, financial services technology, or other digital technologies, or combinations thereof. System 100 can utilize hardware and / or software to solve problems that are highly technical in nature (e.g., a first portion of a simulation is run on a classical processor due to the less complex nature of such portion of the simulation, and a second portion of the simulation is run on a quantum processor due to the more complex nature of such portion of the simulation). Thus, not all portions of the simulation need to be run on a quantum processor, which can be beneficial because it can reduce the number of qubits required for the simulation.

[0017] Furthermore, in some embodiments, some of the processes performed may be performed by one or more specialized computers (e.g., one or more specialized processing units, specialized computers with coupling components, feedback components, etc.) to accomplish certain tasks related to density functional theory determinations using quantum computing systems.

[0018] System 100 and / or components of system 100 can be employed to solve new problems arising from advances in technology, computer architecture, etc. System 100 (and other embodiments discussed herein) can perform simulations of large molecules or other entities using iterative, hybrid classical and quantum computing techniques. One or more embodiments of system 100 can provide technological advances for computing systems, classical computing systems, quantum computing systems, circuit systems, processor systems, artificial intelligence systems, deep learning computing systems, or other systems, or combinations thereof.

[0019] In the embodiment shown in FIG. 1, 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 110. Quantum computer 104 may include a second computing processor 112, a second memory 114, and a second storage 116. The memories (e.g., first memory 108, second memory 114) may store computer-executable components and instructions. The processors (e.g., first computing processor 106, second computing processor 112) may facilitate 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, communicatively, operably, or a combination thereof, coupled to each other to perform one or more functions of system 100.

[0020] Various embodiments provided herein can facilitate density functional theory determinations using a quantum computing system coupled to a classical computing system. A problem associated with simulating macromolecules using classical computers (e.g., non-quantum computers) is that such simulations are intractable due to the exponential growth of Hilbert space. Hilbert space is a mathematical concept or abstract vector space that can have an inner product structure, allowing lengths and angles to be measured. Quantum simulation of macromolecules is a possible solution because this exponential Hilbert space can be efficiently represented using qubits. However, quantum simulation of molecular systems is typically limited to extremely small sizes due to limited coherence times, gate noise, and other complexities. Problems associated with limitations on the size of molecular systems that can be simulated are resolved by the disclosed embodiments, enabling molecular systems of enormous size to be simulated as discussed herein.

[0021] The first computing processor 106 can be utilized to perform a density functional theory determination. For example, input data 118 can be provided to the first computing processor 106. The input data 118 can be, for example, at least a portion of a molecular system being analyzed. The first computing processor 106 can perform a density functional theory determination on one or more portions of the input data 118 and can output the results of the density functional theory determination 120 (e.g., as output data).

[0022] The results of the density functional theory determination 120 may be input data received by the second computing processor 112. For example, based on the results of the density functional theory determination 120, the second computing processor 112 may update the results of the density functional theory determination, which may produce an updated density functional theory determination 122, which is output (as output data) by the second computing processor 112. The updated density functional theory determination 122 may be returned (as input data) to the first computing processor 106 (e.g., via a feedback component, not shown).

[0023] Thus, for quantum computing decisions, the first computing processor 106 can be utilized to reoptimize the updated density functional theory decisions 122 from the second computing processor 112 based on an iterative density functional theory-based embedding. The reoptimized updated density functional theory decisions are passed to the second computing processor. The second computing processor receives the reoptimized updated density functional theory decisions and performs new updates. It should be understood that the density functional theory decisions performed by the first computing processor 106 and the updates to the density functional theory decisions performed by the second computing processor 112 can be recursive or iterative. For example, the density functional theory decisions can be iteratively updated (by the second computing processor 112) and reoptimized (by the first computing processor 106) until a final decision or result is reached and output as output data 124. Note that the input data 118 is illustrated as being received from outside the classical computer 102. However, the disclosed aspects are not limited to this implementation, and the input data 118 may be provided by a classical computer 102 .

[0024] The first computing processor 106 may be a classical computing processor, and the second computing processor 112 may be a quantum computing processor. By utilizing a classical computing processor to implement (or re-implement) density functional theory determinations, it is possible to reduce the number of qubits utilized by the system 100.

[0025] It should be appreciated that system 100 (and other embodiments discussed herein) provide technical improvements for simulating molecular systems of sizes that are impossible to simulate with the same level of accuracy using classical computers. To accommodate the current limitations of quantum computing, the number of qubits and circuit depth can be minimized as discussed herein. However, the number of qubits and circuit depth may increase as quantum computing capabilities increase. For example, effective core potentials (ECPs) allow for the removal of atomic core electrons. For example, ECPs are a useful way to replace core electrons with effective potentials in calculations, thereby eliminating the need for core basis functions, which typically require a large set of Gaussians to describe them. Active space embedding allows for the freezing of a subset of the molecular orbitals of a system. The remaining (unfrozen) set is referred to as the active space.

[0026] Thus, the disclosed aspects can help processors determine and provide results faster with fewer computing resources based on the use of hybrid approaches utilizing 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 previously infeasible with classical processors alone. Previously, purely classical, iterative density matrix renormalization group-density functional theory (DMRG-DFT) embeddings were utilized, and such procedures exist for classical computing to embed highly accurate (and therefore very expensive) methods into less accurate ones, such as density functional theory. Furthermore, previously, quantum processors were used to exclude core electrons from the overall effective core potential. Furthermore, electrons were frozen, and their variational forms of excitation were ignored. Additionally, previous techniques could improve the accuracy of the active space embedding by leveraging the expansion of the quantum subspace. However, previous active space calculations were inaccurate due to the lack of correlations between the frozen electrons. Furthermore, freezing electrons does not necessarily reduce the number of qubits. However, using various embodiments discussed herein, it is possible to achieve enormous qubit reduction. Additionally, the active space can be iteratively embedded in classical methods (e.g., classical processors). Thus, the disclosed aspects use density functional theory to generate the subspace Hamiltonians used in quantum computation. Furthermore, the "quantum" densities of the subsystems are fed back into density functional theory to classically re-optimize the trajectories of the entire system.

[0027] Furthermore, the disclosed embodiments are driven by new technologies (e.g., quantum technologies) and solve problems associated with only being able to simulate molecular systems of limited size. Additionally, the disclosed embodiments are capable of correcting approximately one-third of the errors caused by previous methods. System 100 can also be fully operational (e.g., always powered on, always running, etc.) to perform one or more other functions while also executing the above-referenced computing processes.

[0028] More specifically, Figure 2 illustrates an exemplary, non-limiting representation 200 of molecular orbitals and their associated types, according to one or more embodiments described herein, with repeated descriptions of similar elements employed in other embodiments described herein omitted for brevity.

[0029] The notation 200 includes notation for a quantum portion, a density functional theory or DFT 204 portion, and an effective core potential or ECP portion 206. As discussed above, ECP is a useful way to replace core electrons with effective potentials in calculations, thereby eliminating the need for core basis functions, which typically require a large set of Gaussians to describe the core basis functions. The active space embedding allows a subset of the molecular orbitals of a system to be frozen. The remaining (unfrozen) set is referred to as the active space.

[0030] The annotations on the right ("virtual," "valence," and "core") refer to each orbital. Virtual orbitals 208 refer to orbitals represented by dotted lines, i.e., dashed orbitals (quantum portion 202). Valence 210 refer to orbitals represented by solid lines, i.e., solid orbitals (DFT 204). Core 212 refer to orbitals represented by solid lines, i.e., solid orbitals (ECP portion 206).

[0031] Valences 210 can be treated quantum mechanically and correspond to horizontal lines, with one horizontal line representing a single qubit. Therefore, many qubits are required to fill this space with a quantum computer. Using the disclosed embodiments, quantum portion 202 can be reduced to a smaller subsection of the orbital. Thus, valences 210 can represent qubits that can be frozen. Because a portion of the active electrons, the valences, can be replaced by density functional theory, valences 210 can be replaced by classical computing (e.g., first computing processor 106). Therefore, the number of required qubits can be dynamically reduced, as shown by virtual orbitals 208 representing a quantum processor (e.g., second computing processor 112).

[0032] 3 illustrates an example, non-limiting representation of molecular orbitals and their associated types and the use of iterative density functional theory-based embedding for hybrid classical and quantum processor systems, according to one or more embodiments described herein. Repeated descriptions of similar elements employed in other embodiments described herein are omitted for brevity.

[0033] A determination utilizing density functional theory (DFT204) can be performed in a frozen portion of a quantum processor (e.g., valence 210). DFT204 can be performed using a classical computing processor (e.g., first computing processor 106). The results of DFT204 can be passed to an unfrozen portion of a quantum processor (e.g., second computing processor 112), as indicated by first arrow 302. First arrow 302 represents the result of the density functional theory determination. Upon or after passing the density functional theory results to the quantum processor, processing using a variational quantum eigensolver (VQE) can be performed. The results can be returned to the classical computing processor for further processing, as indicated by second arrow 304.

[0034] More specifically, in the active spatial embedding, the frozen electrons can be treated outside of the quantum hardware by using classical methods such as density functional theory. The energy (E) is:

number

number

[0035] Due to the separation of ranges, the Coulomb operators can be divided into long-range and short-range:

number

[0036] 4 is a diagram of an example, non-limiting system 400 including an iterative hybrid quantum-classical protocol according to one or more embodiments described herein. Repetitive descriptions of similar elements employed in other embodiments described herein are omitted for brevity.

[0037] A CPU portion 402 (e.g., first computing processor 106) and a CPU and QPU portion 404 (e.g., second computing processor 112) are shown. Initialization 406 can be performed in CPU portion 402. For example, it can be performed on a classical computer using Kohn-Sham density functional theory (DFT) calculations such as:

number

[0038] For example, the density can be divided into active spaces as follows:

number

[0039] Furthermore, the electron repulsion integrals can be separated by range.

number

[0040] The inert long-range energy can be calculated once:

number

[0041] Furthermore, the CPU portion 402 can calculate density functional theory 408. For example, it is possible to determine the inert short-range contribution. Such a determination can be based on:

number

number

[0042] New density ρ A,(i+1) can be returned to density functional theory 408 for further processing, as shown at 414.

[0043] The various aspects provided herein for improving density functional theory calculations are not possible with classical computers. Furthermore, calculations of the type provided herein, which use classical embedding schemes, can result in unfavorable scaling, limiting the size of molecular systems that can be analyzed. Therefore, accurate classical calculations can be extracted to smaller quantum systems, which may be achievable with quantum computers in the near future. Quantum computers can operate with favorable scaling using all degrees of freedom. Using the disclosed aspects, it may be possible in the near future to reduce the number of electrons to a minimal set of orbitals. The orbitals reside in active space, making the disclosed aspects implementable in the near future using quantum computers.

[0044] As discussed, quantum algorithms can be coupled to density functional theory simulations through an iterative procedure. This also allows for initializing quantum calculations using density functional theory instead of HF orbitals, as previously done. In addition, with advances in quantum processors, many other advanced classical methods can also be coupled to density functional theory simulations. Thus, it is possible to simulate molecular systems of ever increasing size, with the upper limit defined by systems that can be handled on classical computers using lower-order approximation methods.

[0045] 5 is a representation of exemplary, non-limiting molecules of interest that may be manipulated using the disclosed implantation procedures, according to one or more embodiments described herein. Repetitive descriptions of similar elements employed in other embodiments described herein are omitted for brevity.

[0046] As mentioned, the disclosed embodiments are capable of handling molecular systems as large (if not larger) than those achievable with classical hardware, such as metallic iron within the iron-porphyrin-like structure heme. Heme is a coordination complex containing a porphyrin acting as a tetradentate ligand and an iron ion coordinated to monoaxial or biaxial ligands.

[0047] On the right side of Figure 5 is a representation 502 of the heme group of succinate dehydrogenase, with the electron carrier of the mitochondrial electron transport chain bound to two histidines. The large translucent sphere indicates the location of the iron ion. The porphyrin portion, box 504, is shown with atomic details in a close-up view 506, which is the structure of the iron-porphyrin subunit of heme B.

[0048] The molecular structure depicted in enlarged view 506 is an example of what can be visualized by implementing the disclosed embodiments. The disclosed embodiments can use a quantum processor as discussed herein to manipulate box 508 (e.g., an iron atom), which is an ionic core embedded in a protein. Other atoms on the periphery of the molecular structure depicted in enlarged view 506 can be treated as density functional theory by a classical processor. Furthermore, the molecular structure may be surrounded by other atoms, as shown by representation 502 on the right side of FIG. 5, which can also be treated as discussed herein.

[0049] 6A-6D are plots of various results obtained for pyridine molecules according to one or more embodiments described herein, and a repeated description of similar elements employed in other embodiments described herein is omitted for brevity.

[0050] The pyridine molecule has the following structure: [ka]

[0051] The results in Figures 6A-6D illustrate how much energy can be captured using the disclosed embodiments. Figure 6A shows a first plot 600 for two active electrons. Figure 6B shows a second plot 602 for four active electrons. Figure 6C shows a third plot 604 for six active electrons. Figure 6D shows a fourth plot 606 for eight active electrons. A legend 608 is provided below each plot.

[0052] Energy (E[H]) in Hartee units is shown on the left vertical axis 610. The range separation parameter μ is shown on the horizontal axis 612. The change in energy (ΔE[H]) is shown on the right vertical axis 614. Thus, the plot is a graphical representation of E[H] against the range separation parameter μ. Furthermore, the results are group by active space.

[0053] HF orbitals are represented by line 616. Density functional theory is represented by line 618. Coupled Cluster Single and Double (CCSD) excited states are represented by line 620. The line symbols indicate the number of active molecular orbitals. 2 orbitals are represented by a line with an up triangle. 3 orbitals are represented by a line with a circle. 4 orbitals are represented by a line with an inverted triangle. 5 orbitals are represented by a line with a circle. 6 orbitals are represented by a line with a square.

[0054] The initial calculation in the plot is the RHF (relative energy on the right y-axis). The symbol μ going to zero (μ→0) indicates that the energy converges towards density functional theory (XC:lda,vwn). The symbol μ going to infinity (μ→∞) indicates that the energy converges to a non-iterative embedding (bounded by a complete active space self-consistent field (CASSCF) in the same active space). Furthermore, CCSD (coupled cluster calculations with all single and double excitations) energies are an approximately accurate measure.

[0055] As illustrated by the plots of Figures 6A-6D, the disclosed embodiments can be applied to achieve desired results. Furthermore, the disclosed embodiments can be applied to simulate systems of increasingly larger sizes, the upper limit of which can be defined by classical computationally tractable systems using low-order approximation methods.

[0056] Furthermore, a long-term impact of the disclosed embodiments is that it becomes possible to simulate a system using a reduced number of qubits, because computations can be concentrated on portions of the system that are difficult to implement or handle classically (e.g., via a classical processor). Additionally, by embedding a quantum processor in a classical processor, the overall computing system or device can be smaller. Furthermore, it is not necessary to bring everything to the quantum level; instead, the difficult portions can be implemented by quantum processors, and other, less difficult portions can be implemented by classical processors.

[0057] 7 is a flow diagram of an exemplary, non-limiting, computer-implemented method 700 for facilitating density functional theory determinations using a quantum computing system, according to one or more embodiments described herein. Repetitive descriptions of similar elements employed in other embodiments described herein are omitted for brevity.

[0058] At 702 of the computer-implemented method 700, a first computing processor of the system can generate a density functional theory determination (e.g., via the first computing processor 106). The density functional theory determination can be an active density matrix, according to some implementations. Further, at 704 of the computer-implemented method 700, a second computing processor of the system can input a quantum density into the density functional theory determination (e.g., via the second computing processor 112). The first computing processor can be operably coupled to the second computing processor. In one example, the second computing processor can be a quantum computing processor and the first computing processor can be a classical computing processor.

[0059] 8 is a flow diagram of an exemplary, non-limiting computer-implemented method 800 that facilitates reducing the number of qubits utilized to perform density functional theory determinations using a quantum computing system, according to one or more embodiments described herein. Repeated descriptions of similar elements employed in other embodiments described herein are omitted for brevity.

[0060] At 802 of the computer-implemented method 800, a first computing processor of the system generates a density functional theory determination (e.g., via the first computing processor 106). The density functional theory determination can be an active density matrix. According to some implementations, the first computing processor can determine an inactive short-range contribution that guides the density functional theory determination.

[0061] At 804 of the computer-implemented method 800, a second computing processor of the system inputs the quantum density (e.g., via the second computing processor 112) into the density functional theory determination. The first computing processor and the second computing processor are operatively coupled. For example, operatively coupling the first computing processor and the second computing processor can reduce the number of qubits utilized by the second computing processor to update the active density matrix.

[0062] Further, at 806 of the computer-implemented method 800, the second computing processor provides an updated active density matrix based on the quantum density (e.g., via the second computing processor 112 or a feedback component (not shown)). For example, the updated active density matrix may be provided or fed back to the first computing processor. Thus, the second computing processor may communicate the updated active density matrix to the first computing processor. According to some implementations, this communication occurs iteratively.

[0063] 9 is a flow diagram of an exemplary, non-limiting, computer-implemented method 900 for facilitating a feedback loop associated with density functional theory determinations using a quantum computing system, according to one or more embodiments described herein. Repetitive descriptions of similar elements employed in other embodiments described herein are omitted for brevity.

[0064] At 902 of the computer-implemented method 900, a device operatively coupled to a processor may utilize a first computing processor to implement a density functional theory determination (e.g., via the first computing processor 106 or a coupling component (not shown)). Further, at 904 of the computer-implemented method 900, the device may utilize a second computing processor to update the density functional theory determination and obtain an updated density functional theory determination (e.g., via the 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.

[0065] At 906 of the computer-implemented method 900, once or after the updated density functional theory determination is determined by the second computing processor, the device may utilize the first computing processor (e.g., via the first computing processor 106 or a feedback component) to re-optimize the updated density functional theory determination based on an iterative density functional theory-based embedding for the quantum computing determination. Utilizing the first computing processor may include avoiding frozen electrons in the second computing processor.

[0066] For ease of explanation, computer-implemented methods are depicted and described as a series of acts. It is understood and appreciated that the subject innovation is not limited by the acts and / or the order of acts depicted; for example, acts can occur in various orders or simultaneously, and / or with other acts not shown and described herein. Furthermore, not all depicted acts may be required to implement a computer-implemented method in accordance with the disclosed subject matter. In addition, as will be understood and appreciated by those skilled in the art, a computer-implemented method can alternatively be represented as a series of interrelated states via a state diagram or events. Additionally, it should be further appreciated that the computer-implemented methods disclosed hereinafter and throughout this specification can be stored on an article of manufacture to facilitate transporting and transferring such computer-implemented methodologies to a computer. As used herein, the term article of manufacture is intended to encompass a computer program accessible from any computer-readable device or storage medium.

[0067] To provide context for various aspects of the disclosed subject matter, FIG. 10 and the following discussion are intended to provide a general description of a suitable environment in which various aspects of the disclosed subject matter may be implemented. FIG. 10 illustrates a block diagram of an exemplary, non-limiting operating environment in which one or more embodiments described herein may be facilitated. Repeated descriptions of similar elements employed in other embodiments described herein are omitted for brevity. Referring to FIG. 10, a suitable operating environment 1000 for implementing various aspects of the present disclosure may also include a computer 1012. The computer 1012 may also include a processing unit 1014, a system memory 1016, and a system bus 1018. The system bus 1018 couples system components, including but not limited to the 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 employed as the processing unit 1014. The system bus 1018 can be any of several types of bus structures, including a memory bus or memory controller, a peripheral bus or external bus, or a local bus using any of a variety of available bus architectures, including, but not limited to, Industrial Standard Architecture (ISA), MicroChannel Architecture (MSA), Enhanced 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 Systems Interface (SCSI), or a combination thereof. The system memory 1016 can also include volatile memory 1020 and non-volatile memory 1022.The Basic Input / Output System (BIOS), containing the basic routines to transfer information between elements within computer 1012, such as during start-up, is stored in non-volatile memory 1022. 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) such as ferroelectric RAM (FeRAM). Volatile memory 1020 may also include random access memory (RAM) that acts as external cache memory. By way of example and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), SyncLink DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM.

[0068] The computer 1012 may also include removable / non-removable, volatile / non-volatile computer storage media. For example, FIG. 10 illustrates disk storage 1024. The disk storage 1024 may also include devices such as, but not limited to, a magnetic 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. The disk storage 1024 may also include storage media separately or in combination with other storage media, including, but not limited to, an optical disk drive such as a compact disc read-only memory (CD-ROM), a CD-writeable drive (CD-R drive), a CD-rewriteable drive (CD-RW drive), or a digital versatile disc read-only memory (DVD-ROM). A removable or non-removable interface, such as interface 1026, is typically used to facilitate connection of the disk storage 1024 to the system bus 1018. FIG. 10 also illustrates software that acts as an intermediary between a user and the basic computer resources described within the preferred operating environment 1000. Such software may include, for example, an operating system 1028. The operating system 1028, which may be stored on disk storage 1024, acts to control and allocate resources of the computer 1012. System applications 1030 take advantage of the management of resources by the operating system 1028 through program modules 1032 and program data 1034, which are stored, for example, in either the system memory 1016 or on the disk storage 1024. It should be appreciated that the present disclosure may be implemented with various operating systems or combinations of operating systems. A user enters commands or information into the computer 1012 through input devices 1036.Input devices 1036 include, but are not limited to, pointing devices such as mice, trackballs, styluses, touch pads, keyboards, microphones, joysticks, game pads, satellite dishes, scanners, TV tuner cards, digital cameras, digital video cameras, web cameras, etc. These and other input devices connect to the processing unit 1014 through the system bus 1018 via interface ports 1038. Interface ports 1038 include, for example, serial ports, parallel ports, game ports, and universal serial buses (USBs). Output devices 1040 use some of the same types of ports as the input devices 1036. Thus, for example, a USB port can be used to provide input to the computer 1012 and to output information from the computer 1012 to the output device 1040. Output adapter 1042 is provided to illustrate that there are some output devices 1040, such as monitors, speakers, and printers, among other output devices 1040, that require special adapters. Output adapters 1042 include, by way of example and not limitation, video cards 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, such as remote computer(s) 1044, provide both input and output capabilities.

[0069] The computer 1012 can operate in a networked environment using logical connections to one or more remote computers, such as a remote computer 1044. The remote computer 1044 may be a computer, server, router, network PC, workstation, microprocessor-based appliance, peer device, or other common network node, and may include many or all of the elements typically described for the computer 1012. For simplicity, only a memory storage device 1046 is illustrated with the remote computer 1044. The remote computer 1044 is logically connected to the computer 1012 through a network interface 1048, which is then physically connected via a communication connection 1050. The network interface 1048 encompasses wired and / or wireless communication networks such as a local area network (LAN), a wide area network (WAN), a cellular network, and the like. LAN technologies include Fiber Distributed Data Interface (FDDI), Copper Distributed Data Interface (CDDI), Ethernet, Token Ring, and the like. WAN technologies include, but are not limited to, point-to-point links, circuit-switched networks such as Integrated Services Digital Networks (ISDN) and their variations, packet-switched networks, and Digital Subscriber Lines (DSL). Communications connection 1050 refers to the hardware / software employed to connect network interface 1048 to system bus 1018. While shown internal to computer 1012 for clarity of illustration, communications connection 1050 may be external to computer 1012. Hardware / software for connecting to network interface 1048 may also include, by way of example only, internal and external technologies such as modems, including telephone-grade modems, cable modems and DSL modems, ISDN adapters, and Ethernet cards.

[0070] The present invention may be a system, method, apparatus, or computer program product, or combinations thereof, at any possible level of technical detail of integration. The computer program product may include a computer-readable storage medium having computer-readable program instructions for causing a processor to perform aspects of the present invention. The computer-readable storage medium may be a tangible device capable of holding and storing instructions for use by an instruction-execution device. The computer-readable storage medium may be, for example, but not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of computer-readable storage media further includes: portable computer diskettes, 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 versatile disks (DVD), memory sticks, floppy disks, mechanically encoded devices such as punch cards or grooved structures having instructions recorded thereon, and any suitable combination of the foregoing. As used herein, computer-readable storage media should not be construed as being ephemeral signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission medium (e.g., light pulses passing through fiber optic cable), or electrical signals transmitted over electrical wires.

[0071] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to an individual computing / processing device or to an external computer or external storage device over a network, such as the Internet, a local area network, a wide area network, or a wireless network, or a combination thereof. The network can include copper transmission cables, optical fiber transmissions, wireless transmissions, routers, firewalls, switches, gateway computers, or edge servers, or a combination thereof. A 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 a computer-readable storage medium within the individual computing / processing device. The computer readable program instructions for carrying out the operations of the present invention may be either source code or object code written in any combination of one or more programming languages, including assembler instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state configuration data, configuration data for integrated circuits, or object-oriented programming languages ​​such as Smalltalk®, C++, and procedural 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 a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server.In the latter scenario, the remote computer can 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 the connection can be to an external computer (e.g., via the Internet using an Internet Service Provider). In some embodiments, electronic circuitry, including, for example, programmable logic circuits, field programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), can execute computer-readable program instructions to individualize the electronic circuitry by utilizing state information of the computer-readable program instructions to perform aspects of the present invention.

[0072] Aspects of the present invention are described herein 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 may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute on a processor of the computer or other programmable data processing apparatus, implement the functions / acts specified in one or more blocks of the flowchart illustrations and / or block diagrams. These computer-readable program instructions may also be stored on a computer-readable storage medium, directing a computer, programmable data processing apparatus, or other device, or combination thereof, to function in a particular manner, such that the computer-readable storage medium having the instructions stored thereon comprises an article of manufacture including instructions for implementing aspects of the functions / acts specified in one or more blocks of the flowchart illustrations and / or block diagrams. The computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to create a computer-implemented process, causing the computer, other programmable apparatus, or other device to perform a series of operable functions, such that the instructions, which execute on the computer, other programmable apparatus, or other device, implement the functions / acts specified in one or more blocks of the flowcharts and / or block diagrams.

[0073] The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowcharts or block diagrams may represent a module, segment, or portion of instructions, which includes one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions shown in the blocks may occur out of the order shown in the figures. For example, two blocks shown in succession may in fact be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending on the functionality involved. It should also be noted that each block in the block diagrams and / or flowchart diagrams, and combinations of blocks in the block diagrams and / or flowchart diagrams, may be implemented by special-purpose hardware-based systems that perform the specified functions or acts or execute a combination of special-purpose hardware and computer instructions.

[0074] While the subject matter has been described above in the general context of computer-executable instructions for a computer program product executing on one or more computers, those skilled in the art will appreciate that the present disclosure can also be implemented in combination with other program modules. Generally, program modules include routines, programs, components, data structures, etc. that perform particular tasks and / or implement particular abstract data types. Moreover, those skilled in the art will appreciate that the computer-implemented methods of the present invention can be practiced with other computer system configurations, including single-processor or multiprocessor computer systems, minicomputing devices, mainframe computers, as well as computers, handheld computing devices (e.g., PDAs, telephones), microprocessor-based or programmable home or business electronic devices, etc. The illustrated aspects can also be practiced in distributed computing environments where tasks are performed by remote processing devices linked through a communications network. However, some, if not all, aspects of the present disclosure can be practiced on stand-alone computers. In a distributed computing environment, program modules can be located in both local and remote memory storage devices.

[0075] As used in this application, the terms “component,” “system,” “platform,” “interface,” etc. may refer to and / or include computer-related entities or entities related to machines operable with one or more specialized functionalities. The entities disclosed herein can be hardware, a combination of hardware and software, software, or software in execution. For example, a component can be, but is not limited to, a process running on a processor, a processor, an object, an executable, a thread of execution, a program, or a computer, or any combination thereof. By way of illustration, both an application running on a server and the server can be a component. One or more components can reside within a process and / or thread of execution, and a component can be localized on one computer or distributed between two or more computers or both. In another example, individual components can execute from various computer-readable media having various data structures stored thereon. Components may communicate through local and / or remote processes, such as through signals carrying one or more data packets (e.g., data from one component may interact with another component within a local system, within a distributed system, or across networks, or a combination thereof, such as the Internet, which interacts with other systems via signals). As another example, a component may be a device having specialized functionality imparted by mechanical parts operated by electrical or electronic circuits, operated by a software or firmware application executed by a processor. In such cases, the processor may be internal or external to the device and may execute at least a portion of the software or firmware application.As yet another example, a component can be a device that provides specialized functionality through electronic components without mechanical components, in which case the electronic components can include a processor or other means for executing software or firmware that provides at least some of the functionality of the electronic components. In one aspect, a component can emulate an electronic component via a virtual machine, for example, within a cloud computing system.

[0076] Additionally, 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 utilizes A or B" is intended to mean any of the natural inclusive permutations. That is, if X utilizes A, X utilizes B, or X utilizes both A and B, then "X utilizes A or B" is satisfied under any of the foregoing cases. Moreover, as used within the specification of the present subject matter and the accompanying drawings, the articles "a" and "an" should be construed generally to mean "one or more" unless otherwise specified to cover the singular or clear from the context. As used herein, the terms "example," "illustrative," 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 by such examples. Additionally, any aspect or design described herein as "example" and / or "exemplary" is not necessarily to be construed as preferred or advantageous over other aspects or designs, and is not intended to exclude equivalent exemplary structures and techniques known to those skilled in the art.

[0077] As employed in the subject 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 capabilities, a multi-core processor, a multi-core processor with software multithreaded execution capabilities, a multi-core processor with hardware multithreading technology, a parallel platform, and a parallel platform with distributed shared memory. Additionally, 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), discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. Furthermore, a processor can utilize nanoscale architectures, such as, but not limited to, molecular and quantum dot-based transistors, switches, and gates, to optimize space usage or improve the performance of user equipment. A processor can also be implemented as a combination of computing processing units. In this disclosure, terms such as "store," "storage," "data store," "database," and substantially any other information storage component associated with the operation and functionality of a component are utilized to refer to a "memory component" entity embodied in a "memory" or a component that includes a memory. It should be appreciated that the memory and / or memory components described herein can be either volatile memory or non-volatile memory, or can 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 external cache memory. By way of example, and not limitation, RAM is available in many forms, such as synchronous RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), SyncLink DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM). Additionally, the disclosed memory components of the systems or computer-implemented methods herein are intended to include these and any other suitable types of memory, but are not intended to be limited to including such.

[0078] What has been described above includes merely exemplary systems and computer-implemented methods. Of course, for purposes of describing this disclosure, it is not possible to describe every conceivable combination of components or computer-implemented methods, but one of ordinary skill in the art will recognize that many further combinations and permutations of the present disclosure are possible. Furthermore, to the extent that the terms "includes," "has," "possesses," and the like are used in the Detailed Description, claims, appendices, and drawings, such terms are intended to be inclusive in a manner similar to the word "comprising" when interpreted as such when employed as a transitional phrase in a claim. The description of various embodiments has been presented for illustrative purposes, but is not intended to be exhaustive or to be 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, practical applications or technical improvements over techniques found in the marketplace, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A classical computing processor for generating a density functional theory determination based on input data associated with a molecular system, the classical computing processor determining a frozen electron inert long-range contribution of the molecular system and a frozen electron inert short-range contribution of the frozen electrons to the density functional theory determination; a quantum computing processor operably coupled to the classical computing processor, the quantum computing processor determining a long-range contribution of unfrozen electrons of the molecular system and updating the density functional theory determination by inputting a quantum density based on the long-range contribution of the unfrozen electrons into the density functional theory determination; and Equipped with The density functional theory determination includes an active density matrix. system.

2. 10. The system of claim 1, wherein the quantum computing processor iteratively communicates updated active density matrices to the classical computing processor.

3. The system of claim 2 , wherein the classical computing processor reoptimizes the density functional theory determination.

4. The system described in claim 1, wherein the quantum computing processor performs processing using a variational quantum eigensolver (VQE).

5. The system described in claim 1, wherein the classical computing processor separates electrons in the molecular system into frozen electrons and unfrozen electrons.

6. The system described in claim 1, wherein the classical computing processor separates electron repulsion integrals associated with electrons in the molecular system into short-range and long-range.

7. 7. The system of claim 1, wherein the density functional theory determinations generated by the classical computing processor provide subspace Hamiltonians used by the quantum computing processor.

8. 1. A computer-implemented method comprising: generating, by a classical computing processor of the system, a density functional theory determination, wherein the density functional theory determination includes determining a frozen-electron inert long-range contribution of the molecular system and a frozen-electron inert short-range contribution; obtaining, by a quantum computing processor of the system operatively coupled to the classical computing processor, an updated density functional theory determination by inputting quantum densities into the density functional theory determination, wherein the quantum densities include determining long-range contributions of unfrozen electrons of the molecular system, and obtaining an updated active density matrix based on the quantum densities; Including, The density functional theory determination includes an active density matrix. Computer-implemented methods.

9. reducing the number of qubits utilized by the quantum computing processor to update the active density matrix based on the classical computing processor being operably coupled to the quantum computing processor. The computer-implemented method of claim 8 further comprising:

10. communicating, by the quantum computing processor, the updated active density matrix to the classical computing processor, wherein said communicating is performed iteratively. The computer-implemented method of claim 8 further comprising:

11. The computer-implemented method of claim 8, further comprising separating electrons in the molecular system into the frozen electrons and the unfrozen electrons by the classical computing processor.

12. The computer-implemented method of claim 8, wherein the classical computing processor further comprises separating electron repulsion integrals associated with electrons in a molecular system into short-range and long-range integrals.

13. 1. A computer-implemented method comprising: Implementing, by a device operatively coupled to a processor, a density functional theory determination utilizing a classical computing processor, wherein the density functional theory determination includes determining a frozen electron inert long-range contribution of the molecular system and a frozen electron inert short-range contribution of the frozen electron to the density functional theory determination. updating, by the device, the density functional theory determination utilizing a quantum computing processor to obtain an updated density functional theory determination, wherein the updated density functional theory determination includes determining the long-range contribution of unfrozen electrons of the molecular system. and utilizing the classical computing processor, by the device, to reoptimize the updated density functional theory determination based on an iterative density functional theory-based embedding for the quantum computing determination. Including, The density functional theory determination includes an active density matrix. Computer-implemented methods.

14. initializing, by the device, the classical computing processor, wherein the initializing includes: Dividing density into active spaces, Separating the electron repulsion integral by range; Determining the energies of inert long-range the initializing step comprising: The computer-implemented method of claim 13 further comprising:

15. A device, a classical computing processor that implements density functional theory determinations on molecular systems; a quantum computing processor for updating the density functional theory determination to obtain an updated density functional theory determination; and Equipped with the density functional theory determination includes an active density matrix; the classical computing processor determines a frozen electron inert long-range contribution of the molecular system and a frozen electron inert short-range contribution to the density functional theory determination; the quantum computing processor determines a long-range contribution of unfrozen electrons of the molecular system and inputs a quantum density based on the long-range contribution of the unfrozen electrons into the density functional theory determination; the classical computing processor is configured to re-optimize the updated density functional theory determination based on inputs to the iterative density functional theory determination by a quantum computing processor; device.

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