Estimation of expected energy value of hamiltonian

Abstract

To provide systems, methods and programs to facilitate estimation of an expected energy value of a Hamiltonian based on data of the Hamiltonian.SOLUTION: A system 200 in which a quantum state is produced by a quantum device and / or entangled measurements includes an expected energy estimation system 102. The expected energy estimation system comprise a memory that stores computer-executable components, and a processor that executes the computer-executable components stored in the memory. The computer executable components include: a selection component that selects a quantum state measurement basis having a probability defined on the basis of a ratio of a Pauli operator in a Hamiltonian of a quantum system; and a measurement component that captures quantum state measurement of a qubit in the quantum system on the basis of the quantum state measurement basis.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The subject disclosure relates to estimating expected energy values ​​of a Hamiltonian, and more particularly, to estimating expected energy values ​​of a Hamiltonian based on data and / or entangled measurements of the Hamiltonian. Summary of the Invention

[0002] The following presents a summary to provide a basic understanding of one or more embodiments of the invention. This summary is not intended to identify key or critical elements or to limit the scope of particular embodiments or the claims. Its sole purpose is to present ideas in a simplified form as a prelude to the more detailed description that is presented later. In one or more embodiments described herein, a system, device, computer-implemented method, or computer program product, or combination thereof, that facilitates estimating a Hamiltonian expected energy value based on Hamiltonian data or entangled measurements or both, is described.

[0003] According to one embodiment, a system may include a quantum device that generates quantum states used to calculate an expected energy of a Hamiltonian of a quantum system, a memory storing computer-executable components, and a processor that executes the computer-executable components stored in the memory. The computer-executable components may include a selection component that selects a quantum state measurement basis having a defined probability based on a ratio of Pauli operators in the Hamiltonian of the quantum system. The computer-executable components may further include a measurement component that captures quantum state measurements of qubits in the quantum system based on the quantum state measurement basis.

[0004] According to another embodiment, the computer-implemented method can include selecting, by a system operatively coupled to the processor, a quantum state measurement basis having a defined probability based on a ratio of Pauli operators in a Hamiltonian of the quantum system. The computer-implemented method can further include capturing, by the system, quantum state measurements of qubits in the quantum system based on the quantum state measurement basis.

[0005] According to another embodiment, a computer program product is provided that facilitates a process of estimating an expected energy value of a Hamiltonian. The computer program product includes a computer readable storage medium having program instructions embodied therein, the program instructions being executable by the processor to cause the processor to select a quantum state measurement basis having a defined probability based on a ratio of Pauli operators in a Hamiltonian of the quantum system. The program instructions are further executable by the processor to cause the processor to capture quantum state measurements of qubits in the quantum system based on the quantum state measurement basis.

[0006] According to one embodiment, a system may include a quantum device that generates quantum states used to calculate an expected energy of a Hamiltonian of a quantum system, a memory storing computer-executable components, and a processor that executes the computer-executable components stored in the memory. The computer-executable components may include a measurement component that captures entangled quantum state measurements of qubits in the quantum system based on an entangled quantum state measurement basis. The computer-executable components may further include a computation component that calculates an expected energy value of the Hamiltonian of the quantum system based on the entangled quantum state measurements.

[0007] According to another embodiment, a computer-implemented method can include capturing, by a system operatively coupled to a processor, entangled quantum state measurements of qubits in a quantum system based on the entangled quantum state measurement basis. The computer-implemented method can further include calculating, by the system, an expected energy value of a Hamiltonian of the quantum system based on the entangled quantum state measurements. [Brief description of the drawings]

[0008] [Figure 1] FIG. 1 is a block diagram of an example, non-limiting system that can facilitate estimating the expected energy value of a Hamiltonian based on data of a Hamiltonian, a quantum state produced by a quantum device, or an entangled measurement, or a combination thereof, in accordance with one or more embodiments described herein. [Diagram 2] FIG. 1 is a block diagram of an example, non-limiting system that can facilitate estimating the expected energy value of a Hamiltonian based on data of a Hamiltonian, a quantum state produced by a quantum device, or an entangled measurement, or a combination thereof, in accordance with one or more embodiments described herein. [Diagram 3] FIG. 1 is a block diagram of an example, non-limiting system that can facilitate estimating the expected energy value of a Hamiltonian based on data of a Hamiltonian, a quantum state produced by a quantum device, or an entangled measurement, or a combination thereof, in accordance with one or more embodiments described herein. [Figure 4A] FIG. 1 illustrates an example, non-limiting algorithm that can facilitate estimating the expected energy value of a Hamiltonian based on data of the Hamiltonian, quantum states produced by a quantum device, or entangled measurements, or a combination thereof, in accordance with one or more embodiments described herein. [Figure 4B]FIG. 1 illustrates an example, non-limiting algorithm that can facilitate estimating the expected energy value of a Hamiltonian based on data of the Hamiltonian, quantum states produced by a quantum device, or entangled measurements, or a combination thereof, in accordance with one or more embodiments described herein. [Figure 4C] FIG. 1 illustrates an example, non-limiting algorithm that can facilitate estimating the expected energy value of a Hamiltonian based on data of the Hamiltonian, quantum states produced by a quantum device, or entangled measurements, or a combination thereof, in accordance with one or more embodiments described herein. [Diagram 5] FIG. 1 is a flow chart of an example, non-limiting computer-implemented method that can facilitate estimating an expected energy value of a Hamiltonian based on data of a Hamiltonian, a quantum state produced by a quantum device, or an entangled measurement, or a combination thereof, in accordance with one or more embodiments described herein. [Figure 6] FIG. 1 is a flow chart of an example, non-limiting computer-implemented method that can facilitate estimating an expected energy value of a Hamiltonian based on data of a Hamiltonian, a quantum state produced by a quantum device, or an entangled measurement, or a combination thereof, in accordance with one or more embodiments described herein. [Figure 7] FIG. 1 is a flow chart of an example, non-limiting computer-implemented method that can facilitate estimating an expected energy value of a Hamiltonian based on data of a Hamiltonian, a quantum state produced by a quantum device, or an entangled measurement, or a combination thereof, in accordance with one or more embodiments described herein. [Figure 8] FIG. 1 is a block diagram of an exemplary non-limiting operating environment capable of facilitating one or more embodiments described herein. [Figure 9] FIG. 1 is a block diagram of an exemplary, non-limiting cloud computing environment in accordance with one or more embodiments of the subject disclosure. [Figure 10] FIG. 2 is a block diagram of an exemplary, non-limiting abstraction model layer, in accordance with one or more embodiments of the subject disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] The following detailed description is for illustrative purposes only, and is not intended to limit the embodiments or the application or uses of the embodiments, or both, nor is it intended to be bound by any express or implied information presented in the Background or Summary or Detailed Description above.

[0010] One or more embodiments will now be described with reference to the drawings. The same reference numerals are used to refer to the same elements throughout. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a more thorough understanding of one or more embodiments. However, it will be apparent that in various cases one or more embodiments may be practiced without these specific details.

[0011] Quantum computing is generally the use of quantum-mechanical phenomena to perform computing and information processing functions. Quantum computing can be viewed in contrast to classical computing, which generally uses transistors to perform operations on binary values. That is, while classical computers can perform operations on bit values ​​that are either 0 or 1, quantum computers perform operations on quantum bits (qubits) that contain superpositions of both 0 and 1, can entangle multiple quantum bits, and use interference.

[0012] Quantum computing has the potential to solve problems that cannot be solved at all or practically on classical computers due to their computational complexity. However, quantum computing requires that the problem be formulated in a form that quantum computing can operate on using the set of quantum operations that quantum computing has. Almost all such problems can be turned into a formula that finds the lowest energy with respect to a Hamiltonian that describes a given problem. To find the lowest energy, one must perform an iteration of expected energy values ​​of the Hamiltonian with respect to a quantum state that ultimately corresponds to the lowest energy or an approximation thereof.

[0013] The Variational Quantum Eigensolver (VQE) is a hybrid classical-quantum algorithm that utilizes near-term quantum devices to approximate the lowest eigensystem, eigenvalues ​​and eigenvectors of a given Hamiltonian H. By converting a Hamiltonian, e.g., that of a quantum chemistry or optimization problem, into a qubit Hamiltonian H, VQE is used to find the parameters θ that minimize the expected energy. min θ 〈ψ(θ)|H|ψ(θ)〉

[0014] The parameter θ is used to prepare a quantum circuit that generates the quantum state |ψ(θ)〉. For each such quantum state |ψ(θ)〉, the expected energy is evaluated by the expectation value of a weighted sum of the Pauli strings involving H. Their values ​​are obtained by measuring the quantum state in a standard computational basis (often as the limit for near-term quantum devices). A simple approach is to measure the expectation values ​​of each term of the Pauli string of H, but in a typical quantum chemistry problem, n 4 This measurement can take a long time, since there can be n Pauli strings (where n is the number of qubits).

[0015] Each iteration of VQE to evaluate the expectation value of the Hamiltonian with respect to a fixed parameter θ requires many measurements. To utilize VQE to solve problems, such as those in quantum chemistry and optimization, it is important to reduce the number of measurements, since this directly translates into faster execution of various quantum algorithms that promise quantum advantage.

[0016] Currently, many prior art approaches have been proposed to reduce the number of VQE measurements. However, a challenge with some of such prior art approaches is that they rely on solving graph problems (e.g., node coloring, independent sets, etc.) that are known to be non-deterministic polynomial-time hard (NP-hard) problems, and their approximation algorithms can be expensive (e.g., computationally expensive) to implement with classical algorithms. Another challenge with some of such prior art approaches is that they do not provide theoretical guarantees of the expected error and variance, and do not provide bounds on the sufficient number of iterations to approximate the expected value.

[0017] 1 illustrates a block diagram of an exemplary, non-limiting system 100 that can facilitate estimating an expected energy value of a Hamiltonian based on data of a Hamiltonian, a quantum device that generates a quantum state used to calculate the expected energy of the Hamiltonian of a quantum system, or an entangled measurement, or a combination thereof, according to one or more embodiments described herein. The system 100 can include an expected energy estimation system 102, which can be associated with a cloud computing environment. For example, the expected energy estimation system 102 can be associated with a cloud computing environment 950, which will be described later with reference to FIG. 9, or with one or more functional abstraction layers (e.g., a hardware and software layer 1060, a virtualization layer 1070, a management layer 1080, or a workload layer 1090, or a combination thereof), which will be described later with reference to FIG. 10, or both.

[0018] The expected energy estimation system 102 or components thereof (e.g., selection component 108, measurement component 110, state generation component 202, computation component 302, etc.), or both, can use one or more computing resources of a cloud computing environment 950, described below with reference to FIG. 9, and / or one or more functional abstraction layers (e.g., quantum software, etc.), described below with reference to FIG. 10, to perform one or more operations according to one or more embodiments of the subject disclosure described herein. For example, the cloud computing environment 950, and / or such one or more functional abstraction layers can include one or more classical computing devices (e.g., classical computers, classical processors, virtual machines, servers, etc.), quantum hardware, or quantum software (e.g., quantum computing devices, quantum computers, quantum processors, quantum circuit simulation software, superconducting circuits, etc.), or combinations thereof, that can be used by the expected energy estimation system 102 or components thereof, or both, to perform one or more operations according to one or more embodiments of the subject disclosure described herein. For example, the expected energy estimation system 102 or components thereof may use such one or more classical and / or quantum: mathematical functions, calculations and / or formulas; computing and / or processing scripts; algorithms; models (e.g., artificial intelligence (AI) models, machine learning (ML) models, etc.); and / or another operation based on one or more embodiments of the subject disclosure described herein.

[0019] Although this disclosure includes detailed descriptions of cloud computing, it should be understood that implementations of the teachings described herein are not limited to cloud computing environments alone, rather, embodiments of the invention may be practiced in connection with any other type of computing environment now known or later developed.

[0020] Cloud computing is a service delivery model that enables convenient, on-demand network access to a shared pool of configurable computing resources (e.g., networks, network bandwidth, servers, processing, memory, storage, applications, virtual machines, and services) that can be rapidly provisioned and released with minimal management effort or interaction with the provider of the service. The cloud model can include at least five characteristics, at least three service models, and at least four deployment models.

[0021] Its features are as follows:

[0022] On-Demand Self-Service: Cloud consumers can provision computing capacity, such as server time and network storage, automatically and unilaterally as needed without the need for human interaction with the provider of this service.

[0023] Broad Network Access: The functionality is available over the network and is accessed through standard mechanisms that facilitate use by heterogeneous thin or thick client platforms (eg, mobile phones, laptops, and PDAs).

[0024] Resource pooling: To serve a large number of consumers using a multi-tenant model, the provider's computing resources are pooled, and different physical and virtual resources are dynamically allocated and reallocated on demand. Consumers generally have no control over or knowledge of the exact location of the provided resources, but there is a sense of location independence in the sense that they can specify the location at a higher level of abstraction (e.g. country, state, or data center).

[0025] Rapid elasticity: Features can be provisioned quickly and elastically, sometimes automatically, to scale out quickly, and can be released quickly to scale in quickly. To the consumer, the features available for provisioning often appear infinite, and they can buy as much or as little as they want, at any time.

[0026] Measured service: Cloud systems automatically control and optimize resource usage by intervening in metering at a level of abstraction appropriate to the type of service (e.g., storage, processing, bandwidth, and user accounts in use). Resource usage can be monitored, controlled, and reported, providing transparency to both providers and consumers of the services being utilized.

[0027] The service model is as follows:

[0028] Software as a Service (SaaS): This functionality offered to consumers is the ability to use a provider's applications running on a cloud infrastructure. Those applications are accessible from a variety of client devices through thin-client interfaces such as web browsers (e.g., web-based email). Except for possibly limited user-specific application configuration settings, the consumer does not manage or control the underlying cloud infrastructure, including the network, servers, operating systems, storage, or individual application functions.

[0029] Platform as a Service (PaaS): This capability offered to consumers is the ability to deploy consumer-created or acquired applications written using provider-supported programming languages ​​and tools on a cloud infrastructure. The consumer does not manage or control the underlying cloud infrastructure, including networks, servers, operating systems, or storage, but does have control over the deployed applications and possibly the application hosting environment configuration.

[0030] Infrastructure as a Service (IaaS): This facility provided to consumers supplies processing, storage, network and other basic computing resources on which the consumer can deploy and run any software, which may include operating systems and applications. The consumer does not manage or control the underlying cloud infrastructure, but does have control over the operating systems, storage and deployed applications, and in some cases, limited control over selected network components (e.g., host firewalls).

[0031] The deployment models are:

[0032] Private Cloud: The cloud infrastructure is operated solely for an organization. The infrastructure can be managed by the organization or a third party and can exist on-premises or off-premises.

[0033] Community Cloud: The cloud infrastructure is shared by several organizations to support a specific community with shared interests (e.g., mission, security requirements, policies and compliance concerns). The infrastructure can be managed by the organizations or a third party and can exist on-premise or off-premise.

[0034] Public Cloud: The cloud infrastructure is available to the general public or large industry groups and is owned by an organization that sells cloud services.

[0035] Hybrid cloud: This cloud infrastructure is a composite of two or more clouds (private, community, or public) that maintain their own unique entities but are joined together by standardized or proprietary technologies that enable data and application portability (e.g., cloud bursting for load balancing between clouds).

[0036] A cloud computing environment is a service-oriented environment that emphasizes statelessness, low coupling, modularity and semantic interoperability. At the heart of cloud computing is an infrastructure that includes a network of interconnected nodes.

[0037] The expected energy estimation system 102 may include a memory 104, a processor 106, a selection component 108, a measurement component 110, or a bus 112, or a combination thereof.

[0038] It should be appreciated that the embodiments of the subject disclosure illustrated in the various figures disclosed herein are for illustrative purposes only, and thus the architecture of such embodiments is not limited to the systems, devices, or components or combinations thereof illustrated in those figures. For example, in some embodiments, the system 100 and / or expected energy estimation system 102 may further include various computer and / or computing-based elements described herein with respect to the operating environment 800 and FIG. 8. In some embodiments, such computer and / or computing-based elements may be used in connection with the implementation of one or more of the systems, devices, components, or computer-implemented operations illustrated and described with respect to FIG. 1 or with respect to other figures disclosed herein.

[0039] The memory 104 may store one or more components and / or instructions that can be read, written or executed, or a combination thereof, by a computer and / or machine, which when executed by the processor 106 (e.g., a classical processor, a quantum processor, etc.), can facilitate the performance of operations defined by the executable components and / or instructions. For example, the memory 104 may store one or more components and / or instructions that can be read, written or executed, or a combination thereof, by a computer and / or machine, which when executed by the processor 106 can facilitate the performance of various functions described herein related to the expected energy estimation system 102, the selection component 108, the measurement component 110, or other components (e.g., state generation component 202, computation component 302, etc.) associated with the expected energy estimation system 102, or combinations thereof, as described herein with or without reference to various figures of the subject disclosure.

[0040] The memory 104 may include volatile memory (e.g., random access memory (RAM), static RAM (SRAM), dynamic RAM (DRAM), etc.) and / or non-volatile memory (e.g., read-only memory (ROM), programmable ROM (PROM), erasable programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), etc.), which may use one or more memory architectures. Further examples of memory 104 are described below with reference to system memory 816 and FIG. 8. Such examples of memory 104 may be used to implement any embodiment of the subject disclosure.

[0041] The processor 106 may include one or more types of processors and / or electronic circuits (e.g., classical processors, quantum processors, etc.) that may implement one or more components and / or instructions that may be read, written or executed or a combination thereof by a computer and / or machine and that may be stored in the memory 104. For example, the processor 106 may perform various operations that may be specified by such components and / or instructions that may be read, written or executed or a combination thereof by a computer and / or machine, including, but not limited to, logic, control, input / output (I / O), arithmetic or other operations or combinations thereof. In some embodiments, the processor 106 may include one or more central processing units, multi-core processors, microprocessors, dual microprocessors, microcontrollers, systems on a chip (SOC), array processors, vector processors, quantum processors or other types of processors, or combinations thereof. Further examples of the processor 106 are described below with respect to the processing unit 814 and FIG. 8. Any such example of the processor 106 may be used to implement any embodiment of the subject disclosure.

[0042] To perform the functions of the system 100, the expected energy estimation system 102, the memory 104, the processor 106, the selection component 108, the measurement component 110, or other components of the expected energy estimation system 102 described herein (e.g., the state generation component 202, the computation component 302, etc.), or combinations thereof, may be communicatively, electrically, operatively, or optically coupled to one another, or combinations thereof, via a bus 112. The bus 112 may include one or more memory buses, memory controllers, peripheral buses, external buses, local buses, quantum buses, or other types of buses, or combinations thereof, and these buses may use a variety of bus architectures. Further examples of the bus 112 are described below with reference to the system bus 818 and FIG. 8. Any embodiment of the subject disclosure may be implemented using such examples of the bus 112.

[0043] The expected energy estimation system 102 can include any type of component, machine, device, facility, apparatus, and / or equipment including a processor, and / or capable of validly and / or operatively communicating with a wired network and / or a wireless network. All such embodiments are contemplated. For example, the expected energy estimation system 102 can include a server device, a computing device, a general purpose computer, a special purpose computer, a quantum computing device (e.g., a quantum computer), a tablet computing device, a handheld device, a server class computing machine and / or database, a laptop computer, a notebook computer, a desktop computer, a mobile phone, a smart phone, a consumer device and / or appliance, an industrial and / or commercial device, a digital assistant, a multimedia Internet enabled phone, a multimedia player, and / or other types of devices.

[0044] The expected energy estimation system 102 may be communicatively coupled (e.g., communicatively, electrically, operatively, optically) to one or more external systems, sources or devices (e.g., classical computing devices, communications devices, etc., or quantum computing devices, communications devices, etc., or both) or combinations thereof via a data cable (e.g., High-Definition Multimedia Interface (HDMI®), recommended standard (RS) 232, Ethernet® cable, etc.). In some embodiments, the expected energy estimation system 102 may be communicatively coupled (e.g., communicatively, electrically, operatively, optically) to one or more external systems, sources or devices (e.g., classical computing devices, communications devices, etc., or quantum computing devices, communications devices, etc., or both) or combinations thereof via a network.

[0045] In some embodiments, such networks may include wired and wireless networks, including, but not limited to, a cellular network, a wide area network (WAN) (e.g., the Internet), or a local area network (LAN). For example, the expected energy estimation system 102 may communicate with one or more external systems, sources or devices, such as computing devices, or combinations thereof (and vice versa) using substantially any desired wired or wireless technology, including, but not limited to, wireless fidelity (Wi-Fi), global system for mobile communications (GSM), universal mobile telecommunications system (UMTS), worldwide interoperability for microwave access (WiMAX), enhanced general packet radio service (enhanced GPRS), third generation partnership project (3GPP) long term evolution (LOEV), or any other technology. Mobile Broadband (LTE), Third Generation Partnership Project 2 (3GPP2), ultra mobile broadband (UMB), high speed packet access (HSPA), Zigbee and other 802.XX wireless technologies and / or conventional telecommunications technologies, BLUETOOTH®, Session Initiation Protocol (SIP), ZIGBEE®, RF4CE protocol, WirelessHART protocol, 6LoWPAN (IPv6 over Low power Wireless Area Networks), Z-Wave, ANT, ultra-wideband (UWB) standard protocols, and / or other proprietary and non-proprietary communication protocols. Thus, in such examples, the expected energy estimation system 102 may include hardware (e.g., a central processing unit (CPU), transceiver, decoder, quantum hardware, quantum processor, etc.), software (e.g., a set of threads, a set of processes, running software, quantum pulse schedules, quantum circuits, quantum gates, etc.), or a combination of hardware and software that facilitates communication between the expected energy estimation system 102 and an external system, source or device (e.g., a computing device, a communication device, etc.), or a combination thereof.

[0046] The expected energy estimation system 102 may include one or more components and / or instructions that can be read, written or executed, or a combination thereof, by a computer and / or machine, which when executed by the processor 106 (e.g., a classical processor, a quantum processor, etc.) can facilitate performance of an operation defined by such components and / or instructions. Additionally, in numerous embodiments, any components described herein with or without reference to the various figures of the subject disclosure related to the expected energy estimation system 102 may include one or more components and / or instructions that can be read, written or executed, or a combination thereof, by a computer and / or machine, which when executed by the processor 106 can facilitate performance of an operation defined by such components and / or instructions. For example, selection component 108, measurement component 110, and / or other components disclosed herein associated with expected energy estimation system 102 (e.g., communicatively, electronically, operatively, and / or optically coupled to and / or communicatively, electronically, operatively, and / or optically used by expected energy estimation system 102) may include components and / or instructions that can be read, written, and / or executed by a computer and / or machine.As a result, according to numerous embodiments, the expected energy estimation system 102 and / or any components disclosed herein related to the expected energy estimation system 102 may use the processor 106 to execute such components and / or instructions that can be read, written and / or executed or a combination thereof by a computer and / or machine to facilitate performance of one or more operations described herein with respect to the expected energy estimation system 102 and / or any components related to the expected energy estimation system 102.

[0047] The expected energy estimation system 102 (e.g., via the processor 106) can facilitate the execution of operations performed by and / or associated with the selection component 108 and / or the measurement component 110. For example, in an embodiment where Hamiltonian data (e.g., Hamiltonian data defined below) is given and the ratio of the Pauli bases is fixed, the expected energy estimation system 102 can use the selection component 108 to select a quantum state measurement basis with a defined probability based on the ratio of the Pauli operators in the Hamiltonian of the quantum system and / or the measurement component 110 to capture quantum state measurements of qubits in the quantum system based on the quantum state measurement basis. If the ratio of the Pauli bases is not fixed, the selection expected energy estimation system 102 can use the selection component 108 to select a quantum state measurement basis with a uniform probability at random and / or the measurement component 110 to capture quantum state measurements of qubits in the quantum system based on the quantum state measurement basis. Measurement component 110 may include, for example, a vector network analyzer (VNA) capable of capturing one or more quantum state measurements of one or more qubits of a quantum system.

[0048] In such embodiments described above where the Hamiltonian data (e.g., Hamiltonian data defined below) is known, in order to reduce at least one of the number of qubit quantum state measurements used to calculate the Hamiltonian expected energy value or the run time of the quantum system to execute a variational quantum eigensolver (VQE) algorithm, the expected energy estimation system 102 can use measurement component 110 to capture the qubit quantum state measurements based on a quantum state measurement basis. In these embodiments, the quantum state measurement basis can include basis states of stabilizer states, single-qubit stabilizer states, or multi-qubit quantum states spanning quantum states with a defined number of non-identity Pauli matrices, or combinations thereof, and the Hamiltonian can include a sum of weighted Pauli strings with a defined number of non-identity Pauli matrices.

[0049] In embodiments where the Hamiltonian is in the form of a Heisenberg model, the expected energy estimation system 102 can use the measurement component 110 to capture entangled quantum state measurements of qubits in the quantum system based on an entangled quantum state measurement basis. For example, when the Hamiltonian is in the form of a Heisenberg model, the expected energy estimation system 102 can use the measurement component 110 to capture entangled quantum state measurements of qubits (e.g., entangled qubits) in a quantum system (e.g., a two-qubit quantum system) based on an entangled quantum state measurement basis (e.g., a two-qubit quantum state). In these embodiments, the expected energy estimation system 102 can use the measurement component 110 to capture entangled quantum state measurements of qubits based on an entangled quantum state measurement basis to reduce at least one of the number of qubit quantum state measurements used to calculate the expected energy value of the Hamiltonian or the run time of the quantum system to execute a variational quantum eigensolver (VQE) algorithm. In these embodiments, the entangled quantum state measurement basis can include two-qubit quantum states and the Hamiltonian can include a sum of successive weighted Pauli strings that include a defined number of non-identity Pauli matrices. In these embodiments, the expected energy estimation system 102 can use the measurement component 110 to capture the entangled quantum state measurement of a qubit based on an even or odd outcome of a flipped fair coin, as described below with reference to algorithm 400b shown in FIG.

[0050] The expected energy estimation system 102 may further (e.g., via the processor 106) facilitate the execution of operations performed by and / or associated with one or more other components of the expected energy estimation system 102. For example, the expected energy estimation system 102 may further facilitate the execution of operations performed by and / or associated with the state generation component 202, described below with reference to FIG.

[0051] 2 illustrates a block diagram of an exemplary, non-limiting system 200 that can facilitate estimating an expected energy value of a Hamiltonian based on Hamiltonian data and / or entangled measurements in accordance with one or more embodiments described herein. The system 200 can include an expected energy estimation system 102. In some embodiments, the expected energy estimation system 102 can include a state generation component 202. For the sake of brevity, repeated descriptions of the same elements and / or processes used in each corresponding embodiment are omitted.

[0052] In such embodiments described above in which Hamiltonian data (e.g., Hamiltonian data defined below) is known, the expected energy estimation system 102 can use state generation component 202 to generate a product quantum state based on quantum state measurements of qubits captured based on multiple quantum state measurement bases. For example, in these embodiments, the expected energy estimation system 102 can use state generation component 202 to generate a product quantum state based on quantum state measurements of qubits that can be captured by measurement component 110 described above, and such measurements can be captured based on (e.g., using) multiple quantum state measurement bases that can be selected by selection component 108 described above.

[0053] In such embodiments described above in which the Hamiltonian is in the form of the Heisenberg model, the expected energy estimation system 102 may use state generation component 202 to generate quantum states based on multiple entangled quantum state measurements of qubits captured based on multiple entangled quantum state measurement bases. For example, in these embodiments, the expected energy estimation system 102 may use state generation component 202 to generate quantum states based on multiple entangled quantum state measurements of qubits that may be captured by measurement component 110 described above, where such measurements may be captured based on (e.g., using) multiple entangled quantum state measurement bases (e.g., multiple two-qubit quantum states).

[0054] The expected energy estimation system 102 may further (e.g., via processor 106) facilitate the execution of operations performed by and / or associated with one or more other components of the expected energy estimation system 102. For example, the expected energy estimation system 102 may further facilitate the execution of operations performed by and / or associated with a computational component 302, described below with reference to FIG.

[0055] 3 illustrates a block diagram of an exemplary, non-limiting system 300 that can facilitate estimating an expected energy value of a Hamiltonian based on Hamiltonian data and / or entangled measurements, according to one or more embodiments described herein. The system 300 can include an expected energy estimation system 102. In some embodiments, the expected energy estimation system 102 can include a computational component 302. The computational component 302 can include a classical computer (e.g., a desktop computer, a laptop computer, etc.). For the sake of brevity, repeated descriptions of the same elements and / or processes used in each corresponding embodiment are omitted.

[0056] In such embodiments described above where Hamiltonian data (e.g., Hamiltonian data defined below) is known, expected energy estimation system 102 may use computation component 302 to calculate expected energy values ​​of the Hamiltonian based on product quantum states generated based on quantum state measurements of qubits captured based on multiple quantum state measurement bases. For example, in these embodiments, expected energy estimation system 102 may use computation component 302 to calculate expected energy values ​​of the Hamiltonian based on product quantum states that may be generated by state generation component 202 based on quantum state measurements of qubits that may be captured by measurement component 110 based on multiple quantum state measurement bases (e.g., using multiple quantum state measurement bases) that may be selected by selection component 108 described above.

[0057] In such embodiments described above in which the Hamiltonian is in the form of the Heisenberg model, the expected energy estimation system 102 may use the computation component 302 to calculate an expected energy value of the Hamiltonian of the quantum system based on the entangled quantum state measurements. For example, in these embodiments, calculating the expected energy value of the Hamiltonian of the quantum system based on the entangled quantum state measurements of qubits (e.g., entangled qubits) that may be captured by the measurement component 110 described above.

[0058] Unbiased Estimation Using Entangled Measurements To facilitate the execution of one or more of the exemplary operations defined above, thereby enabling the estimation of the expected energy value of the Hamiltonian based on the data of the Hamiltonian and / or the entangled measurement, the expected energy estimation system 102 and / or its components (e.g., the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) can use one or more of the quantum states, formulas, algorithms, or lemmas, or combinations thereof, described below. For example, the expected energy estimation system 102 and / or its components (e.g., the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) can use one or more of the quantum states, formulas, algorithms, or lemmas, or combinations thereof, described below, to obtain an unbiased estimation of 〈ψ|H|ψ〉 for a Hamiltonian H and any quantum state |ψ〉.

[0059] If data for the Hamiltonian is known, the expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) can obtain an estimate of an expected energy value for the Hamiltonian based on such data for the Hamiltonian. For example, if data for the Hamiltonian is known, the expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) can obtain an estimate of an expected energy value for the Hamiltonian based on such data for the Hamiltonian by performing a process described below with reference to Section 2.0 (e.g., by performing one or more quantum states, formulas, algorithms, or lemmas, or combinations thereof, defined below in Section 2.0).

[0060] In one example, such data for a Hamiltonian may be that the Hamiltonian H for an n-qubit system is a sum of Pauli strings of weight at most k. For example, the following is the Hamiltonian H for a 4-qubit system that has a Pauli string of weight exactly 3 because the number of all terms that are not the identity Pauli matrix (denoted as I) is exactly 3: H=a1IXYZ+a2XIXZ+a3XZYI+a4ZXYI

[0061] In another example, such data for a Hamiltonian may be that there is at least one Pauli matrix where the ratio of the Pauli matrices is the same for each term. For example, in the Hamiltonian above, Z always appears once in each term, and therefore the ratio is 1 / 3 (e.g., generally 1 / k for k>3). If there is no such ratio in the Hamiltonian, e.g., when H=XX+YY+ZZ, the expected energy estimation system 102 may use that the ratio of X:Y:Z is 1:1:1.

[0062] In another example, such a datum for a Hamiltonian may be that the Hamiltonian H is a sum of successive Pauli strings of weight 2k, e.g., H=XX+YY+ZZ is the Hamiltonian for successive Pauli strings of weight 2, H=XXXX+YYYY+ZZZZ is the Hamiltonian for weight 4, and so on.

[0063] If the Hamiltonian is in the form of a Heisenberg model, the expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) may use an entangled measurement process described below with reference to Sections 1.0-1.6 to obtain an unbiased estimate, since such a process may be more efficient than individual qubit measurements. For example, if the Hamiltonian is in the form of a Heisenberg model, the expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) may implement one or more quantum states, formulas, algorithms, or lemmas, or combinations thereof, defined below in Sections 1.0-1.6.

[0064] 1.0 Quantum State The expected energy estimation system 102 or its components (e.g., selection component 108, measurement component 110, state generation component 202, computation component 302, etc.) or both can simultaneously measure a two-qubit system using the following two-qubit quantum state:

[0065] 1.1 Ω condition The expected energy estimation system 102 can use the Ω state to obtain the coefficients of II, XZ, YY and ZX, which are as follows:

[0066]

number

[0067] The corresponding density matrix of the above quantum state is:

[0068]

number

[0069] 1.2 Σ state The expected energy estimation system 102 allows the Σ state to be used to obtain the coefficients of II, XY, YX and ZZ.

[0070]

number

[0071] The corresponding density matrix of the above quantum state is:

[0072]

number

[0073] 1.3 Ξ state The expected energy estimation system 102 can use the Ξ state to obtain the coefficients of II, XX, YZ and ZY.

[0074]

number

[0075] The corresponding density matrix of the above quantum state is:

[0076]

number

[0077] 1.4 Unbiased estimation of two-qubit systems using entangled measurements The expected energy estimation system 102 or its components (e.g., selection component 108, measurement component 110, state generation component 202, computation component 302, etc.) or both may perform one or more of the operations of the subject disclosure according to one or more embodiments described herein based on the assumption that the Hamiltonian H is a two-qubit Hamiltonian of the form: H=a1XX+a2XY+a3XZ+a4YX+a5YY+a6YZ+a7ZX+a8ZY+a9ZZ

[0078] Based on such a two-qubit Hamiltonian H, the expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) can execute the algorithm 400a shown in FIG. 4A (algorithm 400a is shown as Algorithm 1 in FIG. 4A ) to calculate an unbiased estimate of 〈ψ|H|ψ〉 by sampling

[0079] Let 0<η<1.

[0080] Lemma 1. For any ε>0,

number

[0081] where max and min span all two-qubit states that can be computed using the simpler Variational Quantum Eigensolver (VQE) method.

[0082] 4A illustrates an example, non-limiting algorithm 400a that can facilitate estimating a Hamiltonian's expected energy value based on Hamiltonian data, quantum devices generating quantum states used to calculate the Hamiltonian's expected energy of a quantum system, or entangled measurements, or a combination thereof, according to one or more embodiments described herein. For the sake of brevity, repeated descriptions of the same elements and / or processes used in each corresponding embodiment are omitted.

[0083] See algorithm 400a shown in FIG. 4A. For all t=1, 2, ..., S, the expected energy estimation system 102 can use a quantum computer to prepare |ψ〉. For example, one or more cloud computing nodes 910 of a cloud computing environment 950 shown in FIG. 9 described later can include a quantum computer that can be used by the expected energy estimation system 102 to prepare |ψ〉. The expected energy estimation system 102 can use a selection component 108 to uniformly randomly choose a basis b to be either Ω, Σ, or Ξ. The expected energy estimation system 102 can use a measurement component 110 to measure |ψ〉 in basis b and record the result ν∈{00, 01, 10, 11}. The expected energy estimation system 102 (e.g., via state generation component 202) can select |ψ〉 in basis b and record the result ν∈{00, 01, 10, 11}. b 〉 can be a state in basis b with measurement result ν, and further, a computation component 302, which can include a classical computer, can be used to compute w t =〈ν b |H|ν b Based on the execution of the algorithm 400a described above, the expected energy estimation system 102 can calculate

number

[0084] Proof.wt Let be a random variable that can be obtained at each t=1, 2, ..., S, such that the expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) determines E[w t ]=〈ψ|H|ψ〉 It can be shown that

[0085] Additionally, the expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) computes min for min and max over all entangled measurements that can be computed from a simpler form of variational quantum eigensolver (VQE). ψ 〈ψ|H|ψ〉≦w t ≦max ψ We can determine that 〈ψ|H|ψ〉 holds. Recalling the Chernoff-Hoeffding bound,

number

[0086]

number

[0087] From the Chernoff-Hoeffding bound above, the expected energy estimation system 102 further (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.)

number

[0088] In the above equation, b ≡ maxψ 〈ψ|H|ψ〉, a≡min ψ Therefore, the expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the calculation component 302, etc.) determines whether the number of iterations S is

number

[0089] 1.5 Hamiltonian of the Heisenberg model The expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) can generalize the above lemma to obtain an unbiased estimate for the Hamiltonian H of a 2n qubit system, which is a sum of successive weight 2k Pauli operators. The Heisenberg model is one such successive weight 2k Pauli operators. For example, the standard Heisenberg model is:

number

[0090] In the above formula, σ j is the Pauli spin 1 / 2 matrix.

[0091] To obtain an unbiased estimate of the sum of successive Pauli operators of weight 2k, the expected energy estimation system 102 can use state generation component 202 to represent (e.g., generate) the following quantum state, which is a tensor product of two-qubit states:

[0092]

number

[0093] As defined above

number

number

[0094] Similar to the two-qubit system case, the expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) can obtain the following lemma:

[0095] Lemma 2. Let H be a 2n qubit Hamiltonian that is a sum of Pauli operators of weight 2k. Then, for any ε>0, expected energy estimation system 102 (e.g., via selection component 108, measurement component 110, state generation component 202, computation component 302, etc.) performs algorithm 400b shown in FIG. 4B (algorithm 400b is shown as Algorithm 2 in FIG. 4B) to obtain

number

[0096] 4B illustrates an example, non-limiting algorithm 400b that can facilitate estimating the expected energy value of a Hamiltonian based on data of the Hamiltonian, a quantum device that generates a quantum state used to calculate the expected energy of the Hamiltonian of a quantum system, or an entangled measurement, or a combination thereof, according to one or more embodiments described herein. For the sake of brevity, repeated descriptions of the same elements and / or processes used in each corresponding embodiment are omitted.

[0097] See algorithm 400b shown in FIG. 4B. For all t=1, 2, ..., S, the expected energy estimation system 102 can use one or more quantum devices (e.g., quantum computers) to prepare |ψ〉. For example, one or more cloud computing nodes 910 of a cloud computing environment 950 shown in FIG. 9 described later can include a quantum computer that can be used by the expected energy estimation system 102 to prepare |ψ〉. The expected energy estimation system 102 can implement a script to flip a fair coin C to obtain EVEN or ODD. For all i=1, 2, ..., n, the expected energy estimation system 102 can use selection component 108 to uniformly randomly pick a basis b that is either Ω, Σ, or Ξ. If C is EVEN, the expected energy estimation system 102 can use measurement component 110 to measure the 2(i-1) and 2i-1 qubits. Otherwise, if C is ODD, then expected energy estimation system 102 uses measurement component 110 to measure the 2i-1 and 2i qubits of |ψ〉 in basis b and obtain the results

number

number

number

number

[0098] Proof.,The proof follows similarly to the proof explained in the previous,lemma by making use of the Chernoff-Höffding bound.

[0099] 1.6 Special cases of the Heisenberg model For a limited type of Heisenberg model described below, the expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) can use more convenient entangled measurements.

number

[0100] In the above formula,

number

[0101] The expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) can use Bell states as a basis for measurements, where the Bell states are as follows:

[0102]

number

[0103] The corresponding density matrix of the above quantum state is:

[0104]

number

[0105] For a Heisenberg model with only XX, YY, and ZZ interactions, the expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) selects the Bell state

number

number

number

[0106] 2.0 Using Partial Knowledge to Estimate Observables Using a Hamiltonian H of an n-qubit system that is a sum of Pauli operators with arbitrary coefficient weight k, where the distribution of the Pauli bases containing H is fixed for all terms in the Hamiltonian (e.g., the ratio of the Pauli bases {x,y,z} is known to be fixed), and where the ratio of x:y:z is α:(1-α) / 2:(1-α / 2) for 0≦a≦1, the expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) can obtain an estimate of f(ψ)≡〈ψ|H|ψ〉 for the quantum state |ψ. The expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) can

number

number

[0107] The expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) can perform the following steps and / or algorithm 400c shown in FIG. 4C (algorithm 400c is shown as Algorithm 3 in FIG. 4C) to estimate f(ψ) (e.g., to estimate f(|ψ〉)).

[0108] 4C illustrates an example, non-limiting algorithm 400c that can facilitate estimating the expected energy value of a Hamiltonian based on data of the Hamiltonian, a quantum device that generates a quantum state used to calculate the expected energy of the Hamiltonian of a quantum system, or an entangled measurement, or a combination thereof, according to one or more embodiments described herein. For the sake of brevity, repeated descriptions of the same elements and / or processes used in each corresponding embodiment are omitted.

[0109] See algorithm 400c shown in FIG. 4C. For all t=1, 2, ..., S, the expected energy estimation system 102 can use one or more quantum devices (e.g., quantum computers) to prepare |ψ〉. For example, one or more cloud computing nodes 910 of a cloud computing environment 950 shown in FIG. 9 described below can include a quantum computer that can be used by the expected energy estimation system 102 to prepare |ψ〉. For all i=1, 2, ..., n, the expected energy estimation system 102 can use selection component 108 to select a basis b that is either x, y, or z with probabilities α, (1-α) / 2, (1-α) / 2, respectively. i The expected energy estimation system 102 can use the measurement component 110 to select the basis b i Measure |ψ〉 at i ∈{0,1}. The expected energy estimation system 102 (e.g., via the state generation component 202)

number

number

[0110] In addition, for 0≦α≦1

number

[0111] Lemma 3. With high probability, |w-〈ψ|H|ψ〉|≦ε, and in this formula,

number

[0112] Proof. The idea of ​​the proof is as follows. Here, we consider a basis b = b1, b2, ..., b n is calculated by the expected energy estimation system 102 or its components (e.g., the selection component 108, the measurement component 110, the state generation component 202, the calculation component 302, etc.) or both with a probability

number

[0113]

number

[0114] For the summation above, the non-zero values ​​are in the basis b=b1...b n occurs when coincides with a Pauli operator of weight k. In the Pauli operator of weight k, there exists an α fraction of x, a (1-α) / 2 fraction of y, and a (1-α) / 2 fraction of z. This gives us

[0115]

number

[0116] In the above formula, n' x +n' y +n' z = nk, which corresponds to a Pauli operator of non-matching weight k. Thus,

number

[0117]

number

[0118] Similarly, the expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the calculation component 302, etc.) determines that the standard deviation of w is

number

[0119] α x +α y +α z For all terms in the Hamiltonian such that α = 1, x , α y , α z If the ratio {x,y,z} is known to be fixed for x , α y , α z Following the same arguments as above, the expected energy estimation system 102 and / or its components (e.g., the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) may choose a basis having the terms

number

number

[0120] The expected energy estimation system 102 may be associated with various technologies, such as quantum computing technologies, quantum hardware and / or software technologies, quantum algorithm technologies, machine learning technologies, artificial intelligence technologies, cloud computing technologies, and / or other technologies.

[0121] The expected energy estimation system 102 may provide technical improvements to systems, devices, components, operational or processing steps, or combinations thereof associated with the various techniques identified above. For example, the expected energy estimation system 102 may reduce the number of quantum state measurements captured to estimate the expected energy value of a Hamiltonian in a variational quantum eigensolver (VQE) algorithm within an error threshold ε based on Hamiltonian data or entangled measurements, or both. In another example, based on such reduction in the number of quantum state measurements, the expected energy estimation system 102 may reduce the execution time of a quantum system (e.g., a quantum computer, a quantum processor, etc.) that executes the variational quantum eigensolver (VQE) algorithm.

[0122] The expected energy estimation system 102 may provide a technological improvement to a processing unit (e.g., processor 106) associated with a classical computing device or a quantum computing device (e.g., quantum processor, quantum hardware, superconducting circuit, etc.) or both associated with the expected energy estimation system 102. For example, by reducing the number of quantum state measurements that estimate the expected energy value of a Hamiltonian in the VQE algorithm, or by reducing the execution time of a quantum system that executes the VQE algorithm described above, or both, the expected energy estimation system 102 may reduce the computational cost of a processor (e.g., processor 106, quantum processor, etc.) that executes such quantum state measurements and / or the VQE algorithm.

[0123] Based on this reduction in computational cost as described above, a practical application of the expected energy estimation system 102 is that the expected energy estimation system 102 may be implemented by quantum computing systems, or by operators (e.g., vendors) operating such systems, or both, to perform VQE algorithms in a variety of domains and / or for a variety of problems of varying complexity.

[0124] It should be appreciated that the expected energy estimation system 102 provides a new approach driven by relatively new quantum computing techniques, for example, the expected energy estimation system 102 provides a new approach for efficiently estimating expected energy values ​​of Hamiltonians for implementing VQE algorithms on quantum computing devices that are currently driven by lengthy and computationally expensive methods used to estimate such expected energy values ​​of Hamiltonians.

[0125] The expected energy estimation system 102 may use hardware or software to solve problems that are highly technical in nature, not abstract, and cannot be performed as a set of mental acts by a human. In some embodiments, one or more of the processes described herein may be performed by one or more special-purpose computers (e.g., special-purpose processing units, special-purpose classical computers, special-purpose quantum computers, etc.) to perform the stated tasks for the various technologies identified above. The expected energy estimation system 102 or components thereof or both may be used to solve new problems that arise due to the advancements in the technologies discussed above, the use of quantum computing systems, cloud computing systems, computer architectures or other technologies, or combinations thereof.

[0126] It should be appreciated that the various operations that may be performed by the expected energy estimation system 102 and / or its components described herein are operations beyond the capabilities of human intelligence, and therefore the expected energy estimation system 102 may utilize various combinations of electrical components, mechanical components, and circuitry that cannot be replicated or performed by the human intelligence. For example, the amount of data processed by the expected energy estimation system 102 in a given period of time, the rate at which such data is processed, or the types of data may be greater than, faster than, or different types of data than the human intelligence can process in the same period of time.

[0127] According to some embodiments, the expected energy estimation system 102 may further be fully operable to perform one or more other functions (e.g., fully powered on, fully running, etc.) while also performing various operations described herein. It should be appreciated that such simultaneous multi-operation execution is beyond the capabilities of the human mind. It should also be appreciated that the expected energy estimation system 102 may include information that is impossible for an entity, such as a human user, to manually obtain. For example, the type, amount, or variety of information included in the expected energy estimation system 102, the selection component 108, the measurement component 110, the state generation component 202, or the computation component 302, or combinations thereof, may be more complex than information manually obtained by a human user.

[0128] 5 illustrates a flow diagram of an exemplary non-limiting computer-implemented method 500 that can facilitate estimating expected energy values ​​of a Hamiltonian based on Hamiltonian data and / or entangled measurements in accordance with one or more embodiments described herein. For the sake of brevity, repeated descriptions of the same elements and / or processes used in each corresponding embodiment are omitted.

[0129] At 502, the computer-implemented method 500 may include selecting, by a system operatively coupled to a processor (e.g., processor 106, quantum processor, etc.) (e.g., via expected energy estimation system 102 or selection component 108, or both), a quantum state measurement basis having a defined probability based on a ratio of Pauli operators in a Hamiltonian of the quantum system.

[0130] At 504, the computer-implemented method 500 may include capturing, by the system (e.g., via the expected energy estimation system 102 or the measurement component 110, or both), quantum state measurements of qubits in the quantum system based on the quantum state measurement basis.

[0131] 6 illustrates a flow diagram of an exemplary non-limiting computer-implemented method 600 that can facilitate estimating an expected energy value of a Hamiltonian based on Hamiltonian data and / or entangled measurements, according to one or more embodiments described herein. For the sake of brevity, repeated descriptions of the same elements and / or processes used in each corresponding embodiment are omitted.

[0132] At 602, the computer-implemented method 600 may include capturing, by a system operatively coupled to a processor (e.g., processor 106, quantum processor, etc.) (e.g., via expected energy estimation system 102 or measurement component 110, or both), an entangled quantum state measurement of a qubit in a quantum system based on an entangled quantum state measurement basis.

[0133] At 604, the computer-implemented method 600 may include calculating, by the system (e.g., via the expected energy estimation system 102 or the computational component 302, or both), an expected energy value of the Hamiltonian of the quantum system based on the entangled quantum state measurement.

[0134] 7 illustrates a flow diagram of an exemplary non-limiting computer-implemented method 700 that can facilitate estimating expected energy values ​​of a Hamiltonian based on Hamiltonian data and / or entangled measurements, according to one or more embodiments described herein. For the sake of brevity, repeated descriptions of the same elements and / or processes used in each corresponding embodiment are omitted.

[0135] At 702, the computer-implemented method 700 may include obtaining a Hamiltonian for the quantum system. For example, the expected energy estimation system 102 may obtain (e.g., receive) a Hamiltonian for a quantum system, including but not limited to an n-qubit quantum system, a 2n-qubit quantum system, or another quantum system, or a combination thereof. For example, the expected energy estimation system 102 may include an interface component (e.g., an application programming interface (API), a graphical user interface (GUI), etc.) through which such a Hamiltonian for the quantum system defined above may be received.

[0136] At 704a, 704b, 704c, the computer-implemented method 700 can include determining whether the data of the ratios of the Pauli basis of the Hamiltonian is found to satisfy some property. For example, the expected energy estimation system 102 (e.g., via read and / or write operations performed by the processor 106) can determine at 704a whether the Hamiltonian is an n-qubit system that is a sum of Pauli strings of weight at most k (e.g., for some small k, are all terms in the Hamiltonian of weight at most k?). In another example, the expected energy estimation system 102 (e.g., via read and / or write operations performed by the processor 106) can determine at 704b whether the Hamiltonian is a sum of successive Pauli strings of weight 2k (e.g., is it a Heisenberg model Hamiltonian?). In another example, the expected energy estimation system 102 (e.g., via read and / or write operations performed by the processor 106) may determine, at 704c, whether the ratio of Pauli bases for each term in the Hamiltonian is the same (e.g., is the ratio of Pauli bases known to be the same for all terms in the Hamiltonian?).

[0137] If, at 704a, 704b, or 704c, or a combination thereof, it is determined that the data for the Hamiltonian satisfies some of the properties described above, the computer-implemented method 700 may include estimating (e.g., via the expected energy estimation system 102, the selection component 108, the measurement component 110, the state generation component 202, or the computation component 302) an expected energy value for the Hamiltonian based on the known data for the Hamiltonian. For example, if the data for the Hamiltonian is known to satisfy all of these properties, then, at 706a, 706b, 706c, the expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) may estimate (e.g., by implementing one or more quantum states, formulas, algorithms, or lemmas, or combinations thereof, defined in Section 2.0 above) an expected energy value for the Hamiltonian based on such data for the Hamiltonian.

[0138] If it is determined at 704a, 704b, or 704c, or any combination thereof, that the Hamiltonian data does not conform to the above-mentioned properties, then the computer-implemented method 700 may include estimating an expected energy value of the Hamiltonian at 708a, 708b, or both, using one or more of the methods described herein. For example, if it is determined at 704a that not all of the terms of the Hamiltonian are terms of at most weight k for some small k, then at 708a, the computer-implemented method 700 may include estimating an expected energy value of the Hamiltonian using a conventional method.

[0139] In another example, if it is determined at 704b that the data for the Hamiltonian does not conform to the above-mentioned properties, the computer-implemented method 700 can include determining whether the Hamiltonian is a Heisenberg model Hamiltonian. For example, at 704b, the expected energy estimation system 102 (e.g., via read and / or write operations performed by the processor 106) can determine whether the Hamiltonian includes a Hamiltonian for a 2n qubit system that is a sum of successive weight 2k Pauli operators. If it is determined at 704b that the Hamiltonian is of the Heisenberg model form, then at 708b, the computer-implemented method 700 can include (e.g., via the expected energy estimation system 102, the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) estimating an expected energy value for the Hamiltonian based on the entangled measurements. For example, if the Hamiltonian is in the form of the Heisenberg model, the expected energy estimation system 102 (e.g., via the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) may implement one or more quantum states, formulas, algorithms or lemmas defined in Sections 1.0-1.6 above, or a combination thereof.

[0140] If, at 704b, it is determined that the Hamiltonian is not in the form of the Heisenberg model, the computer-implemented method 700 may include terminating, or continuing to use partial or full tomography on the qubit system, or both.

[0141] For simplicity of explanation, the computer-implemented methods are depicted and described as a series of operations. It should be understood and appreciated that the subject innovation is not limited by the operations depicted and / or by the order of operations, e.g., operations can be performed in various orders or simultaneously, or both, and can be performed with other operations not depicted and described herein. Moreover, not all depicted operations are required to implement a computer-implemented method in accordance with the disclosed subject matter. Moreover, those skilled in the art will understand and appreciate that a computer-implemented method can alternatively be represented as a series of interrelated states, such as by a state diagram or events. It should also be appreciated that the computer-implemented methods disclosed below and throughout this specification can be stored on an article of manufacture to facilitate transporting and transferring such computer-implemented methods to a computer. As used herein, the term article of manufacture is intended to encompass a computer program accessible from a computer-readable device or storage medium.

[0142] To provide a context for various aspects of the disclosed subject matter, Fig. 8 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. 8 illustrates a block diagram of an exemplary, non-limiting operating environment that may facilitate one or more embodiments described herein. For the sake of brevity, repeated descriptions of the same elements and / or processes used in each corresponding embodiment are omitted.

[0143] 8, a suitable operating environment 800 for implementing various aspects of the present disclosure may further include a computer 812. The computer 812 may further include a processing unit 814, a system memory 816, and a system bus 818. The system bus 818 couples system components including, but not limited to, the system memory 816 to the processing unit 814. The processing unit 814 may be any of a variety of processors available. Dual microprocessors and other multi-processor architectures may also be used as the processing unit 814. The system bus 818 may be any of several types of bus structures including a memory bus or memory controller, a peripheral or external bus, and / or a local bus using any of a variety of available bus architectures including, but not limited to, Industrial Standard Architecture (ISA), MicroChannel Architecture (MCA), 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).

[0144] The system memory 816 may further include a volatile memory 820 and a non-volatile memory 822. The non-volatile memory 822 stores a basic input / output system (BIOS), which contains the basic routines for transferring information between elements within the computer 812, such as during start-up. The computer 812 may further include removable / non-removable volatile / non-volatile computer storage media. FIG. 8 illustrates, for example, a disk storage 824. The disk storage 824 may further 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 824 may further include storage media separate from or in combination with other storage media. To facilitate connection of the disk storage 824 to the system bus 818, a removable or non-removable interface, such as an interface 826, is typically used. 8 further illustrates software that acts as an intermediary between users and the basic computer resources described within suitable operating environment 800. Such software may further include, for example, an operating system 828. The operating system 828, which may be stored on disk storage 824, serves to control and allocate resources of the computer 812.

[0145] System applications 830 utilize management of resources by operating system 828 via program modules 832 and program data 834 stored, for example, in system memory 816 or disk storage 824. 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 computer 812 through input devices 836. Input devices 836 include, but are not limited to, pointing devices such as a mouse, a trackball, a stylus, a touch pad, a keyboard, a microphone, a joystick, a game pad, a satellite dish, a scanner, a TV tuner card, a digital camera, a digital video camera, a web camera, and the like. These and other input devices connect to processing unit 814 through system bus 818 via interface ports 838. Interface ports 838 include, for example, serial ports, parallel ports, game ports, and a universal serial bus (USB). Output devices 840 use some of the same types of ports as input devices 836. Thus, for example, a USB port can be used to provide input to computer 812 and to output information from computer 812 to output device 840. Output adapter 842 is provided to illustrate that there are some output devices 840, such as monitors, speakers, and printers, among others, that require dedicated adapters. By way of example, output adapter 842 includes, but is not limited to, video cards and sound cards that provide a means of connection between output device 840 and system bus 818. It should be noted that other devices and / or device systems, such as remote computer 844, provide both input and output capabilities.

[0146] The computer 812 can operate in a networked environment using logical connections to one or more remote computers, such as a remote computer 844. The remote computer 844 can be a computer, a server, a router, a network PC, a workstation, a microprocessor-based device, a peer device or other common network node, and typically further includes many or all of the elements described with respect to the computer 812. For simplicity, only a memory storage device 846 is shown in the remote computer 844. The remote computer 844 is logically connected to the computer 812 through a network interface 848, which is then physically connected through a communication connection 850. The network interface 848 encompasses wired and / or wireless communication networks, such as a local area network (LAN), a wide area network (WAN), and a cellular network. 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 variations thereon, packet-switched networks, and Digital Subscriber Lines (DSL). Communications connection 850 refers to the hardware / software used to connect network interface 848 to system bus 818. For ease of illustration, communications connection 850 is shown internal to computer 812, but communications connection 850 can also be external to computer 812. For purposes of illustration only, the hardware / software for connecting to network interface 848 can further include internal and external technologies such as modems, including regular telephone grade modems, cable modems and DSL modems, ISDN adapters, and Ethernet® cards.

[0147] Referring now to FIG. 9, an exemplary cloud computing environment 950 is shown. As shown, the cloud computing environment 950 includes one or more cloud computing nodes 910 with which local computing devices used by cloud consumers, such as a personal digital assistant (PDA) or mobile phone 954A, a desktop computer 954B, a laptop computer 954C, or an automobile computer system 954N, or combinations thereof, can communicate. Although not shown in FIG. 9, the cloud computing node 910 may further include a quantum platform (e.g., quantum computer, quantum hardware, quantum software, etc.) with which the local computing devices used by the cloud consumers can communicate. The nodes 910 can communicate with each other. The nodes may be physically or virtually grouped (not shown) into one or more networks, such as a private, community, public, or hybrid cloud, or combinations thereof, as described above. This allows the cloud computing environment 950 to provide infrastructure, platform, or software, or a combination thereof, as a service, so that cloud consumers do not need to maintain resources on local computing devices. It is understood that the types of computing devices 954A-N illustrated in Figure 9 are intended to be examples only, and that the computing nodes 910 and the cloud computing environment 950 can communicate with any type of computerized device over any type of network or addressable network connection, or both (e.g., using a web browser).

[0148] Referring now to Figure 10, a set of functional abstraction layers provided by cloud computing environment 950 (Figure 9) is shown. It should be understood in advance that the components, layers, and functions shown in Figure 10 are intended to be examples only, and embodiments of the present invention are not limited thereto. As shown, the following layers and corresponding functions are provided:

[0149] Hardware and software layer 1060 includes hardware and software components. Examples of hardware components include mainframe 1061, RISC (reduced instruction set computer) architecture based servers 1062, servers 1063, blade servers 1064, storage devices 1065, and networks and networking components 1066. In some embodiments, software components include network application server software 1067, quantum platform routing software 1068, or quantum software (not shown in FIG. 10), or combinations thereof.

[0150] The virtualization layer 1070 provides an abstraction layer that can provide the following instances of virtual entities: virtual servers 1071, virtual storage 1072, virtual networks including virtual private networks 1073, virtual applications and operating systems 1074, and virtual clients 1075.

[0151] In one example, the management layer 1080 may provide the following functions: Resource provisioning 1081 provides dynamic procurement of computing and other resources utilized to execute tasks within the cloud computing environment. Metering and pricing 1082 provides cost tracking as resources are utilized within the cloud computing environment and charging or billing for the consumption of these resources. In one example, these resources may include application software licenses. Security provides identity verification of cloud consumers and tasks and protection of data and other resources. User portal 1083 provides consumers and system administrators with access to the cloud computing environment. Service level management 1084 provides allocation and management of cloud computing resources such that required service levels are achieved. Service Level Agreement (SLA) planning and fulfillment 1085 provides proactive coordination and procurement of anticipated future needs for cloud computing resources according to SLAs.

[0152] The workload tier 1090 provides examples of functionality that can utilize a cloud computing environment. Non-limiting examples of workloads and functionality that can be provided from this tier include mapping and navigation 1091, software development and lifecycle management 1092, virtual classroom instructional delivery 1093, data analytics processing 1094, transaction processing 1095, and expected energy estimation software 1096.

[0153] The present invention may be a system, method, apparatus, or computer program product, or combinations thereof, at any level of technical detail capable of integration. The computer program product may include a computer readable storage medium having computer readable program instructions thereon for causing a processor to execute 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 thereof. A non-exhaustive list of more specific examples of computer readable storage media may include 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 disk (DVD), memory stick, floppy disk, mechanically encoded devices such as punch cards or raised structures in grooves on which instructions are recorded, and suitable combinations of these. As used herein, computer readable storage media should not be construed as being, in itself, a transitory signal, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating in a wave guide or other transmission body (e.g., light pulses traveling in a fiber optic cable), or electrical signals transmitted through electrical wires.

[0154] The computer readable program instructions described herein may be downloaded from a computer readable storage medium into the respective computing / processing device or may be downloaded to an external computer or 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 may include copper transmission cables, optical transmission fiber, wireless transmission, 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 transfers the computer readable program instructions to a computer readable storage medium in the respective computing / processing device for storage. The computer readable program instructions for carrying out the operations of the present invention may be assembler instructions, instruction set architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state setting data, or configuration data for an integrated circuit, or may be source or object code written in any combination of one or more programming languages, including object oriented programming languages ​​such as Smalltalk®, C++, and procedural programming languages ​​such as the “C” programming language or the like. 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 remote server.In the last scenario above, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or wide area network (WAN), or the connection may be made 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), may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry to carry out aspects of the invention.

[0155] Aspects of the present invention are described herein with reference to flowchart and / or block diagram illustrations of methods, apparatus (systems) and computer program products according to embodiments of the present invention. It will be understood that each block of the flowchart and / or block diagram illustrations, and combinations of blocks in the flowchart and / or block diagram illustrations, 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 device forming a machine such that the instructions, executed by the processor of the computer or other programmable data processing device, generate means for implementing the functions / operations specified in the blocks of the flowchart and / or block diagram illustrations. These computer readable program instructions can further be stored on a computer readable storage medium capable of directing a computer, programmable data processing device, or other device, or combination thereof, to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises a product including instructions for implementing aspects of the functions / operations specified in the blocks of the flowchart and / or block diagram illustrations. These computer readable program instructions can further be loaded onto a computer, other programmable data processing apparatus or other device to cause the computer, other programmable apparatus or other device to perform a series of operational steps to generate a computer-implemented process, in a manner such that the instructions executed on the computer, other programmable apparatus or other device perform the functions / operations specified in the blocks of these flowcharts and / or block diagrams.

[0156] The flowcharts and block diagrams in the accompanying 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, including one or more executable instructions for implementing specified logical functions. In some alternative implementations, the functions shown in the blocks may be implemented in an order different from that shown in the figures. For example, two blocks shown in succession may in fact be executed substantially simultaneously, or the blocks may be executed in the reverse order depending on the functionality involved. It should also be noted that each block of the block diagrams and / or flowcharts, as well as combinations of blocks in the block diagrams and / or flowcharts, may be implemented by a hardware-based dedicated system that performs the specified functions or operations or implements a combination of dedicated hardware and computer instructions.

[0157] Although 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, or both, those skilled in the art will recognize that the disclosure may 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. Furthermore, those skilled in the art will recognize that the computer-implemented methods of the present invention may also be implemented with other computer system configurations, including single-processor or multi-processor computer systems, minicomputing devices, mainframe computers, computers, handheld computing devices (e.g., PDAs, telephones), microprocessor-based or programmable home or industrial electronic devices, and the like. The illustrated aspects may also be implemented 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 disclosure may also be implemented on stand-alone computers. In a distributed computing environment, program modules may be located in both local and remote memory storage devices. For example, in one or more embodiments, computer-executable components may be executed from a memory that may include or consist of one or more distributed memory units. As used herein, the terms "memory" and "memory unit" are interchangeable. Furthermore, one or more embodiments described herein may execute code of the computer-executable components in a distributed manner, e.g., execute code of the computer-executable components in multiple processors that act in conjunction or cooperation to execute code from one or more distributed memory units.As used herein, the term "memory" may encompass a single memory or memory unit in one location or multiple memories or memory units in one or more locations.

[0158] As used in this application, the terms "component," "system," "platform," "interface," and the like, may refer to or include a computer-related or operational machine-related entity having one or more specific functions, or both. The entities disclosed herein may be hardware, a combination of hardware and software, software, or software in execution. For example, a component may be, but is not limited to, a process running on a processor, a processor, an object, an executable, a thread of execution, a program, or a computer, or combinations thereof. As an example, both an application running on a server and the server may be a component. Within a process or thread of execution, or both, one or more components may be localized on one computer or distributed between two or more computers, or both. In other examples, corresponding respective components may be executed from various computer-readable media having various data structures stored thereon. A component may communicate via local or remote processes or both, e.g., according to a signal having one or more data packets (e.g., data from one component interacting with another component via a signal, whether within a local system, within a distributed system, or across a network such as the Internet, or with other systems, or a combination thereof). As another example, a component may be a device having a particular function 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 may be located within or outside the device and may execute at least a portion of the software or firmware application.As another example, a component may be a device that provides a particular functionality through electronic components that do not include mechanical parts, and those electronic components may include a processor or other means for executing software or firmware that provides at least part of the functionality of the electronic component. In one aspect, a component may emulate an electronic component through a virtual machine, for example, in a cloud computing system.

[0159] Furthermore, the term "or" is intended to mean an inclusive "or" rather than an exclusive "or". That is, unless otherwise stated or clear from the context, "X uses A or B" is intended to mean any of the natural inclusive permutations. That is, if X uses A, if X uses B, or if X uses both A and B, "X uses A or B" is satisfied under any of the above cases. Furthermore, unless otherwise stated or clear from the context to indicate the singular form, the articles "a" and "an" used in this specification and the accompanying drawings should generally be construed to mean "one or more". As used herein, the terms "example" and / or "exemplary" are utilized 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. Moreover, 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, or to be meant to exclude equivalent exemplary structures and techniques known to those skilled in the art.

[0160] As used herein, the term "processor" may refer to substantially any computing processing unit or device, including, but not limited to, a single-core processor, a single-core 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 techniques, a parallel platform, and a parallel platform with distributed shared memory. Additionally, a processor may refer to an integrated circuit designed to perform the functions described herein, 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. Additionally, a processor may utilize nanoscale architectures, such as, but not limited to, molecular-based and quantum dot-based transistors, switches, and gates, to optimize space usage or enhance the performance of a user device. A processor may also be implemented as a combination of computing processing units. In this disclosure, terms such as "store," "storage," "data store," "data storage," "database," and substantially any other information storage component associated with the operation and functionality of the component are utilized to refer to a "memory component" that is an entity embodied as a "memory" or a component that includes memory. It should be appreciated that the memory and / or memory components described herein can be volatile or non-volatile memory, or can include both volatile and non-volatile memory.By way of example, non-volatile memory may include, but is not limited to, read only memory (ROM), programmable ROM (PROM), erasable programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, or non-volatile random access memory (RAM), such as ferroelectric RAM (FeRAM). Volatile memory may include RAM, which may function, for example, as external cache memory. Many forms of RAM may be used, including, by way of example, but not limited to, static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM). Additionally, the disclosed memory components of the systems or computer-implemented methods herein are intended to include, but are not limited to, these and other suitable types of memory.

[0161] What has been described above includes merely examples of systems and computer-implemented methods. Of course, it is not possible to describe every conceivable combination of components or computer-implemented methods in order to describe the present disclosure, but one of ordinary skill in the art can appreciate that many other combinations and permutations of the present disclosure are possible. Moreover, 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 the same manner as the term "comprising" is interpreted when used as a transitional word in the claims.

[0162] The above description of various embodiments is provided for illustrative purposes, and is not intended to be exhaustive or to be limited to only the disclosed embodiments. Many modifications and variations that do not depart from the scope and spirit of the described embodiments will be apparent to those skilled in the art. The terms used in this specification have been selected to best explain the principles of the embodiments, practical applications, or technical improvements over commercially available technology, or to enable those skilled in the art to understand the embodiments disclosed herein.

Claims

1. 1. A system comprising: A memory having computer executable components stored therein; A quantum device for generating a quantum state; a processor for executing the computer-executable components stored in the memory; the computer executable components comprising: a measurement component that captures an entangled quantum state measurement of a qubit in the quantum system based on the entangled quantum state measurement basis; and a computational component that calculates an expected energy value of a Hamiltonian of the quantum system based on the entangled quantum state measurement. Including, system.

2. 2. The system of claim 1 , wherein the entangled quantum state measurement basis comprises two-qubit quantum states and the Hamiltonian comprises a sum of successive weighted Pauli strings comprising a defined number of non-identity Pauli matrices.

3. 3. The system of claim 1 or 2, wherein the measurement component captures the entangled quantum state measurements of the qubits based on the entangled quantum state measurement basis to reduce at least one of a number of quantum state measurements of the qubits used to calculate the expected energy value of the Hamiltonian or a run-time of the quantum system to execute a variational quantum eigensolver algorithm.

4. The computer executable components further include: a state generating component that generates a quantum state based on multiple entangled quantum state measurements of the captured qubits based on multiple entangled quantum state measurement bases.

4. The system according to claim 1, further comprising:

5. 5. The system of claim 1, wherein the measurement component further captures the entangled quantum state measurement of the qubit based on an even or odd outcome of a flipped fair coin.

6. 1. A computer-implemented method comprising: capturing, by a system operatively coupled to the processor, entangled quantum state measurements of qubits in the quantum system based on the entangled quantum state measurement basis; and calculating, by the system, an expected energy value of a Hamiltonian of the quantum system based on the entangled quantum state measurement; 23. A computer-implemented method comprising:

7. 7. The computer-implemented method of claim 6, wherein the entangled quantum state measurement basis comprises two-qubit quantum states and the Hamiltonian comprises a sum of successive weighted Pauli strings comprising a defined number of non-identity Pauli matrices.

8. The capturing step comprises: capturing, by the system, the entangled quantum state measurements of the qubits in the quantum system based on the entangled quantum state measurement basis to reduce at least one of a number of quantum state measurements of the qubits used to calculate the expected energy value of the Hamiltonian or a run-time of the quantum system to execute a variational quantum eigensolver algorithm.

8. The computer-implemented method of claim 6 or 7, comprising:

9. generating a quantum state based on multiple entangled quantum state measurements of the qubits captured by the system based on multiple entangled quantum state measurement bases; 9. The computer-implemented method of claim 6, further comprising:

10. The capturing step comprises: capturing, by the system, the entangled quantum state measurement of the qubit based on an even or odd outcome of a fair coin flip; 10. The computer-implemented method of claim 6, further comprising:

11. A computer program product facilitating the process of estimating the expected energy value of a Hamiltonian, the computer program product causing a system operatively coupled to a processor to perform the method according to any of claims 6 to 10.

Images