Estimation of the expected energy of the Hamiltonian operator

Abstract

Systems, computer-implemented methods, and computer program products are provided for facilitating estimating the expected energy value of a Hamiltonian based on data of the Hamiltonian, quantum states generated by a quantum device, and / or measurements of entanglement. According to embodiments, the system may include a memory storing computer-executable components and a processor executing 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 probabilities defined based on ratios of Pauli operators in the Hamiltonian of the quantum system. The computer-executable components may further include a measurement component that acquires quantum state measurements of qubits in the quantum system based on the quantum state measurement basis.

Description

Background Art

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

[0002] The following is presented to provide a basic understanding of one or more embodiments of the present invention. This summary is not intended to identify key or critical elements or to delineate any scope of a particular embodiment or any scope of the claims. Its sole purpose is to present concepts in a simplified form as a prelude to the more detailed description presented later. In one or more embodiments described herein, systems, devices, computer-implemented methods, and / or computer program products are described that facilitate estimating the expected energy value of a Hamiltonian based on data and / or entangled measurements of the Hamiltonian.

[0003] According to an embodiment, a system may include: a quantum device that generates a quantum state to be used to calculate a desired energy of a Hamiltonian operator of a quantum system; a memory that stores 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 probability defined by a ratio of Pauli operators in the Hamiltonian operator of the quantum system. The computer-executable components may further include a measurement component that acquires quantum state measurements of qubits in the quantum system based on the quantum state measurement basis.

[0004] According to another embodiment, a computer-implemented method may include selecting, by a system operatively coupled to a processor, a quantum state measurement basis having a probability defined by a ratio of Pauli operators in a Hamiltonian of a quantum system. The computer-implemented method may further include acquiring, 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 for 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 a processor to cause the processor to select a quantum state measurement basis having probabilities defined by ratios of Pauli operators in a Hamiltonian of a quantum system. The program instructions are further executable by the processor to cause the processor to acquire quantum state measurements of qubits in the quantum system based on the quantum state measurement basis.

[0006] According to an embodiment, a system may include: a quantum device that generates quantum states to be used to calculate an expected energy of a Hamiltonian operator of a quantum system; a memory that stores 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 acquires entangled quantum state measurements of qubits in the quantum system based on entangled quantum state measurements. The computer-executable components may further include a computation component that computes an expected energy value of the Hamiltonian operator of the quantum system based on the entangled quantum state measurements.

[0007] According to another embodiment, a computer-implemented method may include acquiring, by a system operatively coupled to a processor, entangled quantum state measurements of qubits in a quantum system based on the entangled quantum state measurements. The computer-implemented method may 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 A block diagram is shown of an example, non-limiting system that can facilitate estimating an expected energy value of a Hamiltonian based on data of the Hamiltonian, quantum states produced by a quantum device, and / or measurements of entanglement in accordance with one or more embodiments described herein.

[0009] Figure 2 A block diagram is shown of an example, non-limiting system that can facilitate estimating an expected energy value of a Hamiltonian based on data of the Hamiltonian, quantum states produced by a quantum device, and / or measurements of entanglement in accordance with one or more embodiments described herein.

[0010] Figure 3 A block diagram is shown of an example, non-limiting system that can facilitate estimating an expected energy value of a Hamiltonian based on data of the Hamiltonian, quantum states produced by a quantum device, and / or measurements of entanglement in accordance with one or more embodiments described herein.

[0011] Figure 4A 、 Figure 4B and Figure 4C Diagrams illustrating example, non-limiting algorithms that may facilitate estimating an expected energy value of a Hamiltonian based on data of the Hamiltonian, quantum states produced by a quantum device, and / or measurements of entanglement, according to one or more embodiments described herein.

[0012] Figure 5A flow chart is shown of an example, non-limiting computer-implemented method that can facilitate estimating an expected energy value of a Hamiltonian based on data of the Hamiltonian, quantum states produced by a quantum device, and / or measurements of entanglement, according to one or more embodiments described herein.

[0013] Figure 6 A flow chart is shown of an example, non-limiting computer-implemented method that can facilitate estimating an expected energy value of a Hamiltonian based on data of the Hamiltonian, quantum states produced by a quantum device, and / or measurements of entanglement, according to one or more embodiments described herein.

[0014] Figure 7 A flow chart is shown of an example, non-limiting computer-implemented method that can facilitate estimating an expected energy value of a Hamiltonian based on data of the Hamiltonian, quantum states produced by a quantum device, and / or measurements of entanglement, according to one or more embodiments described herein.

[0015] Figure 8 A block diagram illustrating an example non-limiting operating environment that can facilitate one or more embodiments described herein is shown.

[0016] Figure 9 A block diagram illustrating an example non-limiting cloud computing environment according to one or more embodiments of the present invention is shown.

[0017] Figure 10 A block diagram illustrating example non-limiting abstract model layers in accordance with one or more embodiments of the present invention is shown. DETAILED DESCRIPTION

[0018] The following detailed description is illustrative only and is not intended to limit the embodiments and / or the application or uses of the embodiments. Furthermore, no explicit or implicit information presented in the previous background or summary sections or detailed description sections is intended to limit the embodiments.

[0019] One or more embodiments will now be described with reference to the accompanying drawings, wherein like reference numerals are used throughout to refer to like elements. In the following description, 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 circumstances, one or more embodiments may be practiced without these specific details.

[0020] Quantum computing generally refers to the use of quantum-mechanical phenomena to perform computational and information processing functions. Quantum computing can be viewed in contrast to conventional computing, which typically operates on binary values using transistors. That is, whereas conventional computers can operate on bit values of either 0 or 1, quantum computers operate on quantum bits (qubits) that contain overlapping values of both 0 and 1, can entangle multiple qubits, and utilize interference.

[0021] Quantum computing has the potential to solve problems that are simply unsolvable, or for all practical purposes, on classical computers due to their computational complexity. However, quantum computing requires formulating the problem into a form that can be manipulated using the set of quantum operations available to it. Almost all of these problems can be reduced to finding a formula for the minimum energy of the Hamiltonian that describes the given problem. To find the minimum energy, the expected energy value of the Hamiltonian must be iterated relative to the quantum state that ultimately corresponds to the minimum energy or an approximation thereof.

[0022] The Variational Quantum Eigensolver (VQE) is a traditional quantum hybrid algorithm that leverages recent quantum devices to approximate the lowest eigensystem, eigenvalues, and eigenvectors of a given Hamiltonian H. By transforming the Hamiltonian of, for example, a quantum chemistry or optimization problem into the qubit Hamiltonian H, VQE is used to find the parameter θ that minimizes the expected energy:

[0023] min θ <ψ(θ)|H|ψ(θ)>.

[0024] The parameter θ is used to prepare a quantum circuit that generates quantum states |ψ(θ)>. For each such quantum state |ψ(θ)>, the expected energy is evaluated by the expectation value of the weighted sum of the Pauli strings of H. This value is obtained by measuring quantum states in the standard computational basis (as is usually limited to recent quantum devices). A straightforward approach is to measure the expectation value of each term of the Pauli string of H, but this can be time-consuming because in a typical quantum chemistry problem there may be n 4 Pauli strings (where n is the number of qubits).

[0025] Each iteration of the VQE (to evaluate the expected value of the Hamiltonian with respect to a fixed parameter θ) requires many measurements. Reducing the number of measurements is important for using VQE to solve problems such as those in quantum chemistry and optimization, as VQE directly translates into faster execution of various quantum algorithms that promise quantum advantages.

[0026] Currently, there are many proposed prior art methods for reducing the number of measurements of VQE. However, a problem with some of these prior art methods is that they resort to solving graph problems (e.g., node coloring, independent sets, etc.) that are known to be non-deterministic polynomial-time hard (NP-hard) problems, and furthermore, their approximation algorithms can be expensive (e.g., computationally expensive) to run on traditional algorithms. Another problem with some of these prior art methods is that they do not provide theoretical guarantees on the expected error and variance, and do not provide bounds on the number of sufficient repetitions used to approximate the expected value.

[0027] Figure 1 A block diagram of an example, non-limiting system 100 is shown according to one or more embodiments described herein. The system 100 can facilitate estimating an expected energy value of a Hamiltonian based on data of the Hamiltonian, a quantum device that produces a quantum state to be used to calculate the expected energy of the Hamiltonian of a quantum system, and / or entanglement measurements. 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 the following reference: Figure 9 The cloud computing environment 950 described and / or the following references Figure 10 The depicted one or more functional abstraction layers (eg, hardware and software layer 1060, virtualization layer 1070, management layer 1080, and / or workload layer 1090) are associated.

[0028] The expected energy estimation system 102 and / or its components (eg, the selection component 108, the measurement component 110, the state generation component 202, the calculation component 302, etc.) may employ the following methods: Figure 9 One or more computing resources of the cloud computing environment 950 described and / or referred to below Figure 10The one or more functional abstraction layers (e.g., quantum software, etc.) described herein may be used 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 the one or more functional abstraction layers may include one or more traditional computing devices (e.g., traditional computers, traditional processors, virtual machines, servers, etc.), quantum hardware, and / or quantum software (e.g., quantum computing devices, quantum computers, quantum processors, quantum circuit simulation software, superconducting circuits, etc.) that can be used by the desired energy estimation system 102 and / or its components to perform one or more operations according to one or more embodiments of the subject disclosure described herein. For example, the desired energy estimation system 102 and / or its components may employ the one or more traditional and / or quantum computing resources to perform one or more traditional and / or quantum: mathematical functions, calculations, and / or equations; calculation and / or processing scripts; algorithms; models (e.g., artificial intelligence (AI) models, machine learning (ML) models, etc.); and / or another operation according to one or more embodiments of the subject disclosure described herein.

[0029] It should be understood that although the present disclosure includes detailed descriptions about cloud computing, the implementation of the teachings cited herein is not limited to cloud computing environments. Instead, embodiments of the present invention can be implemented in conjunction with any other type of computing environment now known or later developed.

[0030] 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 quickly provisioned and released with minimal management effort or interaction with the service provider. The cloud model can include at least five characteristics, at least three service models, and at least four deployment models.

[0031] Features are as follows:

[0032] On-demand self-service: Cloud consumers can unilaterally and automatically provision computing capabilities, such as server time and network storage, as needed without requiring human interaction with the service provider.

[0033] Broad Network Access: Capabilities are available over the network and accessed through standard mechanisms that facilitate the use of heterogeneous thin-client or thick-client platforms (e.g., mobile phones, laptops, and PDAs).

[0034] Resource pooling: A provider's computing resources are pooled to serve multiple consumers using a multi-tenant model, where different physical and virtual resources are dynamically allocated and reallocated based on demand. There is a sense of location independence, as consumers typically do not have control or knowledge of the exact location of the provided resources, but may be able to specify the location at a higher level of abstraction (e.g., country, state, or data center).

[0035] Rapid elasticity: The ability to quickly and elastically provision capacity, in some cases automatically scaling down and releasing capacity to scale up quickly. To the consumer, the capacity available for provisioning typically appears unlimited and can be purchased in any quantity at any time.

[0036] Metered Services: Cloud systems automatically control and optimize resource usage by leveraging metering capabilities at a level of abstraction appropriate to the type of service (e.g., storage, processing, bandwidth, and active user accounts). Resource usage can be monitored, controlled, and reported, providing transparency to both providers and consumers of the utilized services.

[0037] The service model is as follows:

[0038] Software as a Service (SaaS): The ability provided to consumers is to use the provider's applications running on a cloud infrastructure. Applications can be accessed from various client devices through a thin client interface such as a web browser (e.g., web-based email). The consumer does not manage or control the underlying cloud infrastructure, including the network, servers, operating systems, storage, or even individual application capabilities, with the possible exception of limited user-specific application configuration settings.

[0039] Platform as a Service (PaaS): The capability provided to consumers is to deploy applications created or acquired using programming languages and tools supported by the provider onto cloud infrastructure. Consumers do not manage or control the underlying cloud infrastructure, including networks, servers, operating systems, or storage, but do have control over the deployed applications and the configuration of the application hosting environment.

[0040] Infrastructure as a Service (IaaS): The capabilities provided to consumers are processing, storage, networking, and other basic computing resources on which consumers can deploy and run arbitrary software, including operating systems and applications. Consumers do not manage or control the underlying cloud infrastructure, but rather have control over the operating system, storage, deployed applications, and potentially limited control over selected networking components (e.g., host firewalls).

[0041] The deployment model is as follows:

[0042] Private cloud: Cloud infrastructure is operated solely for an organization. It can be managed by the organization or a third party and can exist on-premises or off-premises.

[0043] Community cloud: Cloud infrastructure is shared by several organizations and supports a specific community with shared concerns (e.g., mission, security requirements, policies, and compliance considerations). It can be managed by the organization or a third party and can exist on-premises or off-premises.

[0044] Public cloud: Cloud infrastructure is made available to the public or large industry groups and is owned by the organization that sells cloud services.

[0045] Hybrid cloud: A cloud infrastructure is a combination of two or more clouds (private, public, or public) that remain unique entities but are bound together by standardized or proprietary technologies that enable data and application portability (e.g., cloud bursting for load balancing between clouds).

[0046] Cloud computing environments are service-oriented and focus on statelessness, low coupling, modularity, and semantic interoperability. The core of cloud computing is the infrastructure that consists of a network of interconnected nodes.

[0047] The expected energy estimation system 102 may include a memory 104 , a processor 106 , a selection component 108 , a measurement component 110 , and / or a bus 112 .

[0048] It should be understood that the embodiments of the subject disclosure described in the various figures disclosed herein are for illustration only, and therefore, the architecture of these embodiments is not limited to the systems, devices, and / or components described herein. For example, in some embodiments, the system 100 and / or the expected energy estimation system 102 may further include the reference operating environment 800 and Figure 8 In some embodiments, the computer and / or computing-based components may be combined with the implementation of Figure 1 or used in combination with one or more of the systems, devices, components, and / or computer-implemented operations illustrated and described in other figures disclosed herein.

[0049] The memory 104 may store one or more computer and / or machine readable, writable, and / or executable components and / or instructions that, when executed by the processor 106 (e.g., a conventional processor, a quantum processor, etc.), may facilitate the performance of operations defined by the executable component(s) and / or instruction(s). For example, the memory 104 may store computer and / or machine readable, writable, and / or executable components and / or instructions that, when executed by the processor 106, may facilitate the performance of various functions described herein related to the expected energy estimation system 102, the selection component 108, the measurement component 110, and / or another component associated with the expected energy estimation system 102 (e.g., the state generation component 202, the calculation component 302, etc.), as described herein with or without reference to the various figures of the present disclosure.

[0050] 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), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), etc.) that may employ one or more memory architectures. References below to system memory 816 and Figure 8 Further examples of memory 104 are described. Such examples of memory 104 may be used to implement any embodiment of the present disclosure.

[0051] The processor 106 may include one or more types of processors and / or electronic circuits (e.g., conventional processors, quantum processors, etc.) that may implement one or more computer and / or machine readable, writable, and / or executable components and / or instructions that may be stored on the memory 104. For example, the processor 106 may perform various operations that may be specified by the computer and / or machine readable, writable, and / or executable components and / or instructions, including but not limited to logic, control, input / output (I / O), arithmetic, etc. 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 (SOCs), array processors, vector processors, quantum processors, and / or another type of processor. Reference is made below to the processing unit 814 and Figure 8 Describes further examples of processor 106. Such examples of processor 106 may be used to implement any embodiment of the present disclosure.

[0052] The expected energy estimation system 102, the memory 104, the processor 106, the selection component 108, the measurement component 110, and / or another component of the expected energy estimation system 102 as described herein (e.g., the state generation component 202, the calculation component 302, etc.) can be communicatively, electrically, operatively, and / or optically coupled to each other via a bus 112 to perform the functions of the system 100, the expected energy estimation system 102, and / or any components coupled thereto. The bus 112 may include one or more memory buses, memory controllers, peripheral buses, external buses, local buses, quantum buses, and / or another type of bus that may employ different bus architectures. Reference is made below to the system bus 818 and Figure 8 Described is a further example of bus 112. Such examples of bus 112 may be used to implement any embodiment of the present disclosure.

[0053] The expected energy estimation system 102 may include any type of component, machine, device, facility, apparatus, and / or instrument that includes a processor and / or may be capable of effectively and / or operatively communicating with a wired and / or wireless network. All such embodiments are contemplated. For example, the expected energy estimation system 102 may 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 cellular phone, a smartphone, a consumer appliance and / or instrument, an industrial and / or commercial device, a digital assistant, a multimedia internet-enabled phone, a multimedia player, and / or another type of device.

[0054] The expected energy estimation system 102 can be coupled (e.g., communicatively, electrically, operationally, optically, etc.) to one or more external systems, sources, and / or devices (e.g., traditional and / or quantum computing devices, communication devices, etc.) 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 can be coupled (e.g., communicatively, electrically, operationally, optically, etc.) to one or more external systems, sources, and / or devices (e.g., traditional and / or quantum computing devices, communication devices, etc.) via a network.

[0055] In some embodiments, the network may include wired and wireless networks, including but not limited to cellular networks, wide area networks (WANs) (e.g., the Internet), or local area networks (LANs). For example, the expected energy estimation system 102 may communicate with one or more external systems, sources, and / or devices (e.g., computing devices (and vice versa)) using virtually 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), 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE), 3rd Generation Partnership Project 2 (3GPP2) Ultra Mobile Broadband (UMB), High Speed Packet Access (HSPA), Zigbee, and other 802.XX wireless technologies and / or legacy telecommunication technologies, Session Initiation Protocol (SIP), RF4CE protocol, WirelessHART protocol, 6LoWPAN (IPv6 over Low Power Wireless Area Network), Z-Wave, ANT, Ultra-Wideband (UWB) standard protocol, and / or other proprietary and non-proprietary communication protocols. In this example, the expected energy estimation system 102 may therefore include hardware (e.g., a central processing unit (CPU), a transceiver, a decoder, quantum hardware, a quantum processor, etc.), software (e.g., a set of threads, a set of processes, software in execution, quantum pulse schedules, quantum circuits, quantum gates, etc.), or a combination of hardware and software that facilitates the transfer of information between the expected energy estimation system 102 and external systems, sources, and / or devices (e.g., computing devices, communication devices, etc.).

[0056] The expected energy estimation system 102 may include one or more computer and / or machine readable, writable, and / or executable components and / or instructions that, when executed by a processor 106 (e.g., a conventional processor, a quantum processor, etc.), may facilitate the performance of operations defined by the components and / or instructions. Further, in many embodiments, as described herein with or without reference to various figures of the present disclosure, any component associated with the expected energy estimation system 102 may include one or more computer and / or machine readable, writable, and / or executable components and / or instructions that, when executed by the processor 106, may facilitate the performance of operations defined by the components and / or instructions. For example, the selection component 108, the measurement component 110, and / or any other component associated with the expected energy estimation system 102 as disclosed herein (e.g., communicatively, electronically, operatively, and / or optically coupled to, and / or employed by, the expected energy estimation system 102) may include such computer and / or machine readable, writable, and / or executable components and / or instructions. Thus, according to various embodiments, the expected energy estimation system 102 and / or any components associated therewith as disclosed herein may employ a processor 106 to execute such computer and / or machine readable, writable, and / or executable components and / or instructions to facilitate performance of one or more operations described herein with reference to the expected energy estimation system 102 and / or any such components associated therewith.

[0057] Expected energy estimation system 102 can facilitate (e.g., via processor 106) the execution of operations performed by and / or associated with selection component 108 and / or measurement component 110. For example, in embodiments where data of a Hamiltonian operator is given and the ratio of the Pauli basis is fixed (e.g., data of a Hamiltonian operator as defined below), expected energy estimation system 102 can: employ selection component 108 to select a quantum state measurement basis having a probability defined based on the ratio of the Pauli operators in the Hamiltonian operator of the quantum system; and / or further employ measurement component 110 to acquire quantum state measurements of qubits in the quantum system based on the quantum state measurement basis. If the ratio of the Pauli basis is not fixed, then expected energy estimation system 102 can: employ selection component 108 to select a quantum state measurement basis having a random uniform probability; and / or further employ measurement component 110 to acquire quantum state measurements of qubits in the quantum system based on the quantum state measurement basis. The measurement component 110 may include, for example, a vector network analyzer (VNA) that can acquire one or more quantum state measurements of one or more qubits of a quantum system.

[0058] In the embodiments described above where the Hamiltonian data is known (e.g., as defined below), expected energy estimation system 102 can use measurement component 110 to acquire quantum state measurements of qubits based on a quantum state measurement basis to reduce at least one of: the number of quantum state measurements of the qubits used to calculate the expected energy value of the Hamiltonian; or the execution time of the quantum system to perform a variational quantum eigensolver (VQE) algorithm. In these embodiments, the quantum state measurement basis can include a basis state of stabilizer states, a single-qubit stabilizer state, and / or a multi-qubit quantum state spanning a quantum state including a defined number of non-identity Pauli matrices, and the Hamiltonian can include a sum of weighted Pauli strings including a defined number of non-identity Pauli matrices.

[0059] In embodiments where the Hamiltonian is in the form of a Heisenberg model, the expected energy estimation system 102 can employ the measurement component 110 to acquire entangled quantum state measurements of qubits in the quantum system based on an entangled quantum state measurement basis. For example, if the Hamiltonian is in the form of a Heisenberg model, the expected energy estimation system 102 can employ the measurement component 110 to acquire entangled quantum state measurements of qubits (e.g., entangled qubits) in the quantum system (e.g., a 2-qubit quantum system) based on an entangled quantum state measurement basis (e.g., a 2-qubit quantum state). In these embodiments, the expected energy estimation system 102 can employ the measurement component 110 to acquire entangled quantum state measurements of the qubits based on the entangled quantum state measurement basis to reduce at least one of: the number of quantum state measurements of the qubits used to calculate the expected energy value of the Hamiltonian; or the execution time of the quantum system to execute a variational quantum eigensolver (VQE) algorithm. In these embodiments, the entangled quantum state measurement basis may include two quantum bit (2-qubit) quantum states, and the Hamiltonian may include a sum of consecutive weighted Pauli strings, the consecutive weighted Pauli strings including a finite number of non-unit Pauli matrices. In these embodiments, as described below with reference to Figure 4B As described in algorithm 400b shown in FIG, expected energy estimation system 102 can employ measurement component 110 to acquire entangled quantum state measurements of qubits based on an even or odd outcome of a flipped fair coin.

[0060] The expected energy estimation system 102 may further facilitate (e.g., via the processor 106) 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 described below with reference to Figure 2 The state generation component 202 performs and / or the execution of operations associated with the state generation component 202.

[0061] Figure 2 A block diagram of an example, non-limiting system 200 is shown that can facilitate estimating an expected energy value of a Hamiltonian based on data and / or entangled measurements of the Hamiltonian, according to one or more embodiments described herein. The system 200 may include an expected energy estimation system 102. In some embodiments, the expected energy estimation system 102 may include a state generation component 202. For the sake of brevity, repeated descriptions of similar elements and / or processes employed in the corresponding embodiments are omitted.

[0062] In the embodiments described above where Hamiltonian data is known (e.g., Hamiltonian data as defined below), expected energy estimation system 102 can employ state generation component 202 to generate a product quantum state based on quantum state measurements of qubits acquired according to a plurality of quantum state measurement bases. For example, in these embodiments, expected energy estimation system 102 can employ state generation component 202 to generate a product quantum state based on quantum state measurements of qubits that can be acquired by measurement component 110 as described above, where the measurements can be acquired based on (e.g., using) a plurality of quantum state measurement bases that can be selected by selection component 108 as described above.

[0063] In the embodiments described above in which the Hamiltonian is in the form of a Heisenberg model, expected energy estimation system 102 can employ state generation component 202 to generate a quantum state based on a plurality of entangled quantum state measurements of qubits acquired according to a plurality of entangled quantum state measurement bases. For example, in these embodiments, expected energy estimation system 102 can employ state generation component 202 to generate a quantum state based on a plurality of entangled quantum state measurements of qubits that can be acquired by measurement component 110 as described above, where the measurements can be acquired based on (e.g., using) a plurality of entangled quantum state measurement bases (e.g., a plurality of 2-qubit quantum states).

[0064] The expected energy estimation system 102 may further facilitate (e.g., via the processor 106) 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 described below with reference to Figure 3 The computing component 302 performs and / or the execution of operations associated with the computing component 302.

[0065] Figure 3 A block diagram of an example, non-limiting system 300 is shown that can facilitate estimating an expected energy value of a Hamiltonian based on data and / or entangled measurements of the Hamiltonian according to one or more embodiments described herein. The system 300 may include an expected energy estimation system 102. In some embodiments, the expected energy estimation system 102 may include a computing component 302. The computing component 302 may include a conventional computer (e.g., a desktop computer, a laptop computer, etc.). For the sake of brevity, repeated descriptions of similar elements and / or processes employed in the corresponding embodiments are omitted.

[0066] In the embodiments described above where the data of the Hamiltonian is known (e.g., data of the Hamiltonian as defined below), expected energy estimation system 102 can use computation component 302 to compute the expected energy value of the Hamiltonian based on a product quantum state generated based on quantum state measurements of the qubits acquired according to a plurality of quantum state measurement bases. For example, in these embodiments, expected energy estimation system 102 can use computation component 302 to compute the expected energy value of the Hamiltonian based on a product quantum state generated by state generation component 202 based on quantum state measurements of the qubits acquired by measurement component 110 based on (e.g., using) a plurality of quantum state measurement bases selectable by selection component 108 as described above.

[0067] In the embodiments described above where the Hamiltonian is in the form of a Heisenberg model, the expected energy estimation system 102 can employ the computation component 302 to compute the expected energy value of the Hamiltonian of the quantum system based on the entangled quantum state measurements. For example, in these embodiments, the expected energy value of the Hamiltonian of the quantum system can be computed based on the entangled quantum state measurements of qubits (e.g., entangled qubits) that can be acquired by the measurement component 110 as described above.

[0068] Unbiased estimation of tangled measurements

[0069] To facilitate the performance of one or more of the example operations defined above and thereby enable estimation of an expected energy value of a Hamiltonian based on data and / or entangled measurements of the Hamiltonian, the expected energy estimation system 102 and / or its component(s) (e.g., the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) can employ one or more of the quantum states, equations, algorithms, and / or lemmas described below. For example, the expected energy estimation system 102 and / or its component(s) (e.g., the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) can employ one or more of the quantum states, equations, algorithms, and / or lemmas described below to obtain an unbiased estimate <ψ|H|ψ> for some Hamiltonian H and any quantum state |ψ>.

[0070] If the 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 calculation component 302, etc.) can obtain an estimate of the expected energy value of the Hamiltonian based on such data for the Hamiltonian. For example, if the 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 calculation component 302, etc.) can obtain an estimate of the expected energy value of the Hamiltonian based on such data for the Hamiltonian by implementing the process described below with reference to Section 2.0 (e.g., by implementing one or more quantum states, equations, algorithms, and / or lemmas defined below in Section 2.0).

[0071] In an example, such data for a Hamiltonian may be that the Hamiltonian H is an n-qubit system that is the sum of at most weight -k Pauli strings. For example, the following is the Hamiltonian H for a 4-qubit system with Pauli strings of exactly weight -3, since the number of non-unit Pauli matrices (denoted as I) in each entry is exactly 3.

[0072] H=a1IXYZ+a2XIXZ+a3XZYI+a4ZXYI

[0073] In another example, such data for the Hamiltonian may be that there is at least a Pauli matrix whose ratios are the same for each term. For example, in the above Hamiltonian, Z always appears once in each term, and therefore its ratio is 1 / 3 (e.g., 1 / k for k>3 in general). If this ratio does not exist in the Hamiltonian, such as when H=XX+YY+ZZ, the desired energy estimation system 102 may use a ratio of X:Y:Z of 1:1:1.

[0074] In another example, the data of the Hamiltonian operator may be that the Hamiltonian operator H is the sum of consecutive Pauli strings of weight -2k. For example, H=XX+YY+ZZ is the sum of consecutive Pauli strings of weight -2, H=XXXX+YYYY+ZZZZ is the sum of consecutive Pauli strings of weight -4, and so on.

[0075] If the Hamiltonian is in the form of a Heisenberg model, it is expected that energy estimation system 102 (e.g., via selection component 108, measurement component 110, state generation component 202, computation component 302, etc.) can use the entangled measurement process described below with reference to Sections 1.0 through 1.6 to obtain an unbiased estimate, as this process can be more efficient than individual qubit measurements. For example, if the Hamiltonian is in the form of a Heisenberg model, it is expected that energy estimation system 102 (e.g., via selection component 108, measurement component 110, state generation component 202, computation component 302, etc.) can implement one or more quantum states, equations, algorithms, and / or lemmas defined below in Sections 1.0-1.6.

[0076] 1.0 Quantum State

[0077] Desired energy estimation system 102 and / or components thereof (eg, selection component 108, measurement component 110, state generation component 202, computation component 302, etc.) can simultaneously measure a 2-qubit system using the following 2-qubit quantum state.

[0078] 1.1Ω state

[0079] The desired energy estimation system 102 may use the Ω state to obtain the coefficients of II, XZ, YY, and ZX. They are as follows.

[0080]

[0081]

[0082]

[0083]

[0084] The density matrix corresponding to the above quantum state is as follows.

[0085]

[0086]

[0087]

[0088]

[0089] 1.2Σ state

[0090] The desired energy estimation system 102 may use the Σ state to obtain coefficients for II, XY, YX, and ZZ.

[0091]

[0092]

[0093]

[0094]

[0095] The density matrix corresponding to the above quantum state is as follows.

[0096]

[0097]

[0098]

[0099]

[0100] 1.3 Ξ state

[0101] The expected energy estimation system 102 may use the Ξ state to obtain coefficients of II, XX, YZ, and ZY.

[0102]

[0103]

[0104]

[0105]

[0106] The density matrix corresponding to the above quantum state is as follows.

[0107]

[0108]

[0109]

[0110]

[0111] 1.4 Unbiased Estimation of a 2-Qubit System with Entanglement Measurements

[0112] The expected energy estimation system 102 and / or its component(s) (e.g., the selection component 108, the measurement component 110, the state generation component 202, the computation component 302, etc.) can perform one or more operations of the present disclosure in accordance with one or more embodiments described herein based on the assumption that the Hamiltonian operator H is a 2-qubit Hamiltonian operator of the following form.

[0113] H=a1XX+a2XY+a3XZ+a4YX+a5YY+a6YZ+a7ZX+a8ZY+a9ZZ

[0114] Based on the 2-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 calculation component 302, etc.) can perform Figure 4A The algorithm 400a shown in FIG. Figure 4A It is represented as Algorithm 1) in order to calculate the unbiased estimate 〈ψ|H|ψ〉 by the following sampling.

[0115] Let 0<η<1.

[0116] Lemma 1. For any ∈>0, the output w of Algorithm 400a (Algorithm 1) satisfies |w-<ψ|H|ψ>|≤∈ with probability 1-η, at any of the following times

[0117]

[0118] where the maxima and minima are all 2-qubit states that can be calculated using the simpler variational quantum eigensolver (VQE) method.

[0119] Figure 4A A diagram illustrating an example, non-limiting algorithm 400a, according to one or more embodiments described herein, that can facilitate estimating the expected energy value of a Hamiltonian based on data of the Hamiltonian, a quantum device (which produces a quantum state that is used to calculate the expected energy of the Hamiltonian of a quantum system), and / or measurements of entanglement. For the sake of brevity, repeated descriptions of similar elements and / or processes employed in corresponding embodiments are omitted.

[0120] Reference Figure 4A In the algorithm 400a shown in FIG, for all t = 1, 2, ..., S, the expected energy estimation system 102 can use a quantum computer to prepare |ψ>. For example, the following description and Figure 9One or more cloud computing nodes 910 of the cloud computing environment 950 shown in FIG. 1 may include a quantum computer that may be used by the expected energy estimation system 102 to prepare |ψ>. The expected energy estimation system 102 may employ a selection component 108 to uniformly and randomly select a basis b to be Ω, Σ, or Ξ. The expected energy estimation system 102 may employ a measurement component 110 to measure |ψ> in the basis b and record the result v∈{00,01,10,11}. The expected energy estimation system 102 (e.g., via the state generation component 202) may select |v b > is the state of the basis b with the measurement result v, and can further use the computing component 302 (which may include a conventional computer) to calculate w t = <v> b |H|v b Based on executing algorithm 400a as described above, the expected energy estimation system 102 may return

[0121] Prove that, let w t is a random variable available at each t=1, ..., S. The expected energy estimation system 102 (eg, via the selection component 108, the measurement component 110, the state generation component 202, the calculation component 302, etc.) can thus show that:

[0122] E[w t ]=〈ψ|H|ψ>.

[0123] Additionally, the expected energy estimation system 102 (eg, via the selection component 108, the measurement component 110, the state generation component 202, the calculation component 302, etc.) can determine the min ψ 〈ψ|H|ψ>≤w t ≤max ψ 〈ψ|H|ψ〉 holds at the minimum (min) and maximum (max) over all entangled measurements that can be computed from the simpler form of the variable square quantum eigensolver (VQE). i ≤b, recalling the Chernoff-Hoeffding bounds, such that And μ = E[X], which holds:

[0124]

[0125]

[0126] Based on the above Chernoff-Hoffding bound, 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.) can further determine:

[0127]

[0128] Where b≡max ψ <ψ|H|ψ>, and a≡min ψ <ψ|H|ψ>. Thus, 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.) can implement the above process, which can be repeated at least 1-n times. When successful.

[0129] 1.5 Hamiltonian operator of the Heisenberg model

[0130] 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 of the Hamiltonian H of a 2n-qubit system, which is a sum of continuous weight-2k Pauli operators. A Heisenberg model is one of such continuous weight-2k Pauli operators. For example, the standard Heisenberg model is as follows.

[0131]

[0132] Among them, σ j is the Pauli rotation-1 / 2 matrix.

[0133] To obtain an unbiased estimate of the sum of successive weight-2k Pauli operators, the expected energy estimation system 102 may employ the state generation component 202 to represent (eg, generate) the following quantum state, which is a tensor product of two-qubit states.

[0134]

[0135]

[0136] The above-defined is the product state of the 2-qubit states that entangle the 0th qubit with the 1st qubit, the 2nd and 3rd qubits, and so on, and is the product state of 2-qubit states that entangles the 1st qubit with the 2nd qubit, the 3rd and 4th qubits, etc. Each of the 2-qubit states is a labeled state in one of the previously mentioned Ω, Σ, or Ξ bases.

[0137] Similar to the case of the 2-qubit system, it is expected that energy estimation system 102 (eg, via selection component 108, measurement component 110, state generation component 202, computation component 302, etc.) can obtain the following lemma.

[0138] Lemma 2. Zero H is a 2n-qubit Hamiltonian, which is a sum of Pauli operators of weight -2k. Then, for any ∈ > 0, 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 Figure 4B The algorithm 400b shown in FIG. Figure 4B In Algorithm 2), we generate The output satisfies |w-<ψ|H|ψ>|≤∈ with probability at least 1-η, where it takes the maximum and minimum values over all two-qubit product states, each of which can be computed by a simpler form of variable-square quantum eigensolver (VQE).

[0139] Figure 4B A diagram illustrating an example, non-limiting algorithm 400b, according to one or more embodiments described herein, can facilitate estimating the expected energy value of a Hamiltonian based on data of the Hamiltonian, a quantum device (which generates a quantum state that is used to calculate the expected energy of the Hamiltonian of a quantum system), and / or measurements of entanglement. For the sake of brevity, repeated descriptions of similar elements and / or processes employed in corresponding embodiments are omitted.

[0140] Reference Figure 4B In the algorithm 400b shown in FIG, for all t = 1, 2, ..., S, the expected energy estimation system 102 can use one or more quantum devices (e.g., (multiple) quantum computers) to prepare |ψ>. For example, the following description and Figure 9 One or more cloud computing nodes 910 of the cloud computing environment 950 shown in FIG may include a quantum computer that may be used by the expected energy estimation system 102 to prepare |ψ>. The expected energy estimation system 102 may implement a script to flip a fair coin C to obtain EVEN (even) or ODD (odd). For i=1, 2, ...n, the expected energy estimation system 102 may employ a selection component 108 to randomly and uniformly pick a basis b that is Ω, Σ, or Ξ. If C is EVEN, the expected energy estimation system 102 may employ a measurement component 110 to measure the 2(i-1) qubit and the 2i-1 qubit. Otherwise, if C is ODD, the expected energy estimation system 102 may employ a measurement component 110 to measure the 2i-1 and 2i qubits of |ψ> in the basis b and record the result. The expected energy estimation system 102 (e.g., via the state generation component 202) may enable is the quantum state obtained from the measurement of n entanglement and can be further calculated using the computing component 302 Based on executing the algorithm 400b as described above, 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.) can return

[0141] Proof,The proof is similar to that described in the previous lemma by exploiting the,Chernoff–Hoffding bound.

[0142] 1.6 Special Cases of the Heisenberg Model

[0143] For a limited type of Heisenberg models as shown below, it is expected that energy estimation system 102 (eg, via selection component 108, measurement component 110, state generation component 202, computation component 302, etc.) can use a better entanglement measure.

[0144]

[0145] in, is a Pauli spin-1 / 2 matrix, and only XX, YY, and ZZ interactions exist.

[0146] 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.) can use Bell states as a basis for measurement, where a Bell state is:

[0147]

[0148]

[0149]

[0150]

[0151] The density matrix corresponding to the above quantum state is as follows.

[0152]

[0153]

[0154]

[0155]

[0156] 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 calculation component 302, etc.) can now use the Bell state As a Figure 4B Instead of randomly selecting from the Ω, Σ, or Ξ basis, the basis of the measurement at the algorithm 400b (Algorithm 2) shown in FIG. By simple calculation, 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 Lemma 2 above to show that an estimate with at least probability 1-η is sufficient to have It is 9 times smaller than using algorithm 400b (Algorithm 2) as it is.

[0157] 2.0 Exploring Partial Knowledge for Estimating Observable Forces

[0158] Using a Hamiltonian H for an n-qubit system (which is a sum of Pauli operators with weights -k of arbitrary coefficients), where the distribution of the Pauli basis including H is fixed for all terms in the Hamiltonian (e.g., the ratios of the Pauli basis {x, y, z} are known to be fixed), and using the ratios x:y:z being α:(1-α) / 2:(1-α) / 2, for 0≤α≤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 obtain an estimate of f(ψ)≡<ψ|H|ψ> from the equation obtained by The estimate is calculated by taking the weighted average of is the quantum state {|0>,|1>} of the basis {x,y,z}.

[0159] The expected energy estimation system 102 (eg, via the selection component 108, the measurement component 110, the state generation component 202, the calculation component 302, etc.) may perform the following processes and / or Figure 4C The algorithm 400c shown in Figure 4C , which is represented as Algorithm 3) to estimate f(ψ) (e.g., estimate f(|ψ>)).

[0160] Figure 4C A diagram illustrating an example, non-limiting algorithm 400c according to one or more embodiments described herein, which can facilitate estimating the expected energy value of a Hamiltonian based on data of the Hamiltonian, a quantum device (which produces a quantum state that is used to calculate the expected energy of the Hamiltonian of a quantum system), and / or measurements of entanglement. For the sake of brevity, repeated descriptions of similar elements and / or processes employed in corresponding embodiments are omitted.

[0161] refer to Figure 4C , for all t=1, 2, ..., S, the expected energy estimation system 102 may employ one or more quantum devices (e.g., quantum computers) to prepare |ψ>. For example, as described below and in Figure 9 One or more cloud computing nodes 910 of the cloud computing environment 950 shown in FIG. 1 may include a quantum computer that may be employed by the expected energy estimation system 102 to prepare |ψ>. For i=1, 2, ... n, the expected energy estimation system 102 may employ the selection component 108 to select a basis b i is x, y, or z with probabilities α, (1-α) / 2, (1-α) / 2, respectively. The expected energy estimation system 102 can use the measurement component 110 to i Measure |ψ> and record the result v i ∈{0,1}. The expected energy estimation system 102 (e.g., via the state generation component 202) may set And the calculation component 302 can be further used to calculate w t = <v b |H|v b >, the computing component 302 may include a conventional computer. Based on the execution algorithm 400c as described above, the expected energy estimation system 102 may return

[0162] Notice, For 0≤α≤1.

[0163] Lemma 3. With high probability |w-<ψ|H|ψ>|≤∈, where And the maximum value covers all separable states.

[0164] Proof,The proof described below is the proof idea, where, the basis b=b1,b2,…,b n 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 calculation component 302, etc.) may be configured with probability To select, where n x +n y +n z =n, and n x ,n y ,n z is the number of basis x, y, z. The expected energy estimation system 102 (eg, via the selection component 108, the measurement component 110, the state generation component 202, the calculation component 302, etc.) can probabilistically | <v b |ψ>| 2 Get v∈{0,1} n Expected energy estimation system 102 (eg, via selection component 108, measurement component 110, state generation component 202, calculation component 302, etc.) can evaluate E[wl] (defined below).

[0165]

[0166] Regarding the summation above, when the basis b=b1…b n A non-zero value occurs when it is consistent with the Pauli operator of weight -k. In the Pauli operator of weight -k, there exists an α score of x, a (1-α) / 2 score of y, and a (1-α) / 2 score of z. For this reason,

[0167]

[0168]

[0169] Among them, in the above n′ x +n′ y +n′ z =nk, which corresponds to the Pauli operator with mismatched weight -k. Therefore,

[0170]

[0171] because,

[0172] E[w]=<ψ|H|ψ>

[0173] Similarly, the expected energy estimation system 102 (eg, via the selection component 108, the measurement component 110, the state generation component 202, the calculation component 302, etc.) can determine the nominal deviation of w as

[0174]

[0175] If the {x,y,z} ratio is known for the Hamiltonian α x ,α y ,α z If all terms in are fixed, the expected energy estimation system 102 can use the selection component 108 to select a 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 calculation component 302, etc.) can be used Replacement For any positive α x ,α y , which is at least 1 / 3, such that 0≤α x +α y ≤ 1. If the {x, y, z} ratios are different for each term in the Hamiltonian, then by setting α x =α y =α z = 1 / 3, the expected energy estimation system 102 can use the selection component 108 to select a x ,α y ,α z basis.

[0176] The expected energy estimation system 102 can be associated with different technologies. For example, the expected energy estimation system 102 can be associated with quantum computing technology, quantum hardware and / or software technology, quantum algorithm technology, machine learning technology, artificial intelligence technology, cloud computing technology, and / or other technologies.

[0177] The expected energy estimation system 102 can provide technical improvements to the systems, devices, components, operating steps, and / or processing steps associated with the various techniques identified above. For example, the expected energy estimation system 102 can reduce the number of quantum state measurements collected to estimate the expected energy value of the Hamiltonian within an error threshold ε in a variational quantum eigensolver (VQE) algorithm based on Hamiltonian data and / or entangled measurements. In another example, based on such a reduced number of quantum state measurements, the expected energy estimation system 102 can reduce the execution time of a quantum system (e.g., a quantum computer, a quantum processor, etc.) performing the variational quantum eigensolver (VQE) algorithm.

[0178] The expected energy estimation system 102 can provide technical improvements to processing units associated with conventional computing devices (e.g., processor 106) and / or quantum computing devices (e.g., quantum processors, quantum hardware, superconducting circuits, etc.) associated with the expected energy estimation system 102. For example, by reducing the number of quantum state measurements used to estimate the expected energy value of a Hamiltonian operator in a VQE algorithm and / or reducing the execution time of a quantum system used to perform the VQE algorithm as described above, the expected energy estimation system 102 can reduce the computational cost of a processor (e.g., processor 106, quantum processor, etc.) performing such quantum state measurements and / or the VQE algorithm.

[0179] Based on the aforementioned reduced computational cost, it is expected that a practical application of the energy estimation system 102 is that it can be implemented by quantum computing systems and / or administrators (e.g., vendors) operating the systems to perform VQE algorithms on various problems in various domains and / or over a range of complexities.

[0180] It should be appreciated that the expected energy estimation system 102 provides new methods driven by relatively new quantum computing technology. For example, the expected energy estimation system 102 provides a new method for efficiently estimating the expected energy value of a Hamiltonian operator for executing a VQE algorithm on a quantum computing device that is driven by current long-standing and computationally expensive methods for estimating such expected energy values of a Hamiltonian operator.

[0181] The expected energy estimation system 102 can employ hardware or software to solve problems that are inherently highly technical, non-abstract, and not executable by a human as a set of mental activities. In some embodiments, one or more of the processes described herein can be executed by one or more special-purpose computers (e.g., special-purpose processing units, special-purpose conventional computers, special-purpose quantum computers, etc.) to perform defined tasks associated with the various technologies identified above. The expected energy estimation system 102 and / or its components can be used to solve new problems that arise through advances in the aforementioned technologies, quantum computing systems, cloud computing systems, computer architectures, and / or other technological advancements.

[0182] It should be understood that the expected energy estimation system 102 may utilize different combinations of electrical components, mechanical components, and circuits that cannot be replicated or performed by a human mind because the different operations that can be performed by the expected energy estimation system 102 and / or its components as described herein are operations that are greater than the capabilities of the human mind. For example, the amount of data processed by the expected energy estimation system 102 in a certain period of time, the speed at which the data is processed, or the type of data may be greater, faster, or different than the amount, speed, or type of data processed by the human mind in the same period of time.

[0183] According to several embodiments, the expected energy estimation system 102 may also be fully operational toward performing one or more other functions (e.g., fully powered on, fully executed, etc.) while also performing the various operations described herein. It should be understood that such simultaneous multi-operation execution is beyond the capabilities of the human brain. It should also be understood that the expected energy estimation system 102 may include information that is not manually accessible to an entity (e.g., a human user). For example, the type, amount, and / 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, and / or the calculation component 302 may be more complex than information manually accessible to a human user.

[0184] Figure 5 A flowchart illustrating an exemplary non-limiting computer-implemented method 500 that can facilitate estimating an expected energy value of a Hamiltonian based on data and / or entangled measurements of the Hamiltonian according to one or more embodiments described herein is provided. For the sake of brevity, repeated descriptions of similar elements and / or processes employed in the corresponding embodiments are omitted.

[0185] At 502, the computer-implemented method 500 may include selecting, by a system operably coupled to a processor (e.g., processor 106, quantum processor, etc.) (e.g., via expected energy estimation system 102 and / or selection component 108), a quantum state measurement basis having probabilities defined based on ratios of Pauli operators in a Hamiltonian of a quantum system.

[0186] At 504 , computer-implemented method 500 may include acquiring, by the system (eg, via expected energy estimation system 102 and / or measurement component 110 ), quantum state measurements of qubits in the quantum system based on the quantum state measurement basis.

[0187] Figure 6 A flowchart illustrating an exemplary non-limiting computer-implemented method 600 that can facilitate estimating an expected energy value of a Hamiltonian based on data and / or entangled measurements of the Hamiltonian according to one or more embodiments described herein is provided. For the sake of brevity, repeated descriptions of similar elements and / or processes employed in the corresponding embodiments are omitted.

[0188] At 602, computer-implemented method 600 may include acquiring, by a system operably coupled to a processor (e.g., processor 106, quantum processor, etc.) (e.g., via expected energy estimation system 102 and / or measurement component 110), entangled quantum state measurements of qubits in a quantum system based on an entangled quantum state measurement basis.

[0189] At 604 , the computer-implemented method 600 can include calculating, by the system (eg, via the expected energy estimation system 102 and / or the computing component 302 ), an expected energy value of a Hamiltonian of the quantum system based on the entangled quantum state measurements.

[0190] Figure 7 A flowchart illustrating an exemplary non-limiting computer-implemented method 700 that can facilitate estimating an expected energy value of a Hamiltonian based on data and / or entangled measurements of the Hamiltonian according to one or more embodiments described herein is provided. For the sake of brevity, repeated descriptions of similar elements and / or processes employed in the corresponding embodiments are omitted.

[0191] At 702, computer-implemented method 700 may include obtaining a Hamiltonian for a quantum system. For example, 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, and / or other quantum systems. For example, 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 the Hamiltonian for the quantum system defined above may be received.

[0192] At 704a, 704b, and 704c, the computer-implemented method 700 may include determining whether data for a ratio of Pauli bases of a Hamiltonian operator is known to satisfy several properties. For example, the expected energy estimation system 102 (e.g., via read and / or write operations performed by the processor 106) may determine at 704a whether the Hamiltonian operator is an n-qubit system that is a sum of Pauli strings of at most weight -k (e.g., for some small k, are all terms of the Hamiltonian at most weight -k?). 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 704b whether the Hamiltonian operator is a sum of consecutive Pauli strings of weight -2k (e.g., is the Hamiltonian a Heisenberg model?). 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 704c whether the ratio of the Pauli basis for each term in the Hamiltonian is the same (e.g., is the ratio of the Pauli basis known to be the same for all terms in the Hamiltonian?).

[0193] If it is determined at 704a, 704b, and / or 704c that the data for the Hamiltonian satisfies some of the above-described properties, computer-implemented method 700 may include estimating (e.g., via expected energy estimation system 102, selection component 108, measurement component 110, state generation component 202, and / or computation component 302) the expected energy value of 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, at 706a, 706b, 706c, expected energy estimation system 102 (e.g., via selection component 108, measurement component 110, state generation component 202, computation component 302, etc.) may estimate the expected energy value of the Hamiltonian based on the data for the Hamiltonian by implementing the process described above with reference to Section 2.0 (e.g., by implementing one or more quantum states, equations, algorithms, and / or lemmas defined in Section 2.0 above).

[0194] If it is determined at 704a, 704b, and / or 704c that the data of the Hamiltonian does not follow the above-described characteristics, the computer-implemented method 700 may include estimating the expected energy value of the Hamiltonian using one or more of the methods described herein at 708a and / or 708b. For example, if it is determined at 704a that not all terms in the Hamiltonian have a weight of at most -k for some small k, then at 708a, the computer-implemented method 700 may include estimating the expected energy value of the Hamiltonian using conventional methods.

[0195] In another example, if it is determined at 704b that the data of the Hamiltonian does not follow the above characteristics, the computer-implemented method 700 may include determining whether the Hamiltonian is a Heisenberg model. For example, at 704b, the expected energy estimation system 102 (e.g., via read and / or write operations performed by the processor 106) may determine whether the Hamiltonian comprises a Hamiltonian for a 2n-qubit system that is a sum of consecutive weight-2k Pauli operators. If it is determined at 704b that the Hamiltonian is in the form of a Heisenberg model, at 708b, the computer-implemented method 700 may include estimating an expected energy value of the Hamiltonian based on the entangled measurement results (e.g., via the expected energy estimation system 102, the selection component 108, the measurement component 110, the state generation component 202, the calculation component 302, etc.). For example, if the Hamiltonian is in the form of a Heisenberg model, it is expected that energy estimation system 102 (e.g., via selection component 108, measurement component 110, state generation component 202, computation component 302, etc.) can implement one or more quantum states, equations, algorithms, and / or lemmas defined above in sections 1.0-1.6.

[0196] If it is determined at 704b that the Hamiltonian is not in the form of a Heisenberg model, the computer-implemented method 700 may include ending and / or proceeding with performing partial or full tomography on the qubit system.

[0197] For the simplicity of explanation, the computer-implemented method is depicted and described as a series of actions. It should be understood and recognized that this subject innovation is not limited by the order of the actions shown and / or the actions, and for example, actions can occur in different orders and / or occur simultaneously, and occur together with other actions that are not presented and described herein. In addition, not all actions shown are necessary for realizing the computer-implemented method according to the disclosed subject. In addition, it will be understood and appreciated by those skilled in the art that the computer-implemented method may alternatively be represented as a series of interrelated states via state diagrams or events. In addition, it should also be understood that the computer-implemented method disclosed hereinafter and throughout this specification can be stored on goods so that the computer-implemented method is transmitted and transferred to a computer. As used herein, the term goods is intended to encompass a computer program accessible from any computer-readable device or storage medium.

[0198] To provide context for various aspects of the disclosed subject matter, Figure 8 The following discussion is intended to provide a general description of a suitable environment in which aspects of the disclosed subject matter may be implemented. Figure 8 A block diagram illustrating an example non-limiting operating environment that can facilitate one or more embodiments described herein is shown. For the sake of brevity, repeated descriptions of similar elements employed in other embodiments described herein are omitted.

[0199] refer to Figure 8 A suitable operating environment 800 for implementing various aspects of the present disclosure may also include a computer 812. The computer 812 may also 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 available processors. 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 bus or external bus, and / or a local bus using any of a variety of available bus architectures, including but not limited to Industry Standard Architecture (ISA), Micro Channel Architecture (MSA), Extended ISA (EISA), Intelligent Drive Electronics (IDE), VESA Local Bus (VLB), Peripheral Component Interconnect (PCI), card bus, Universal Serial Bus (USB), Advanced Graphics Port (AGP), FireWire (IEEE 1394), and Small Computer System Interface (SCSI).

[0200] The system memory 816 may also include volatile memory 820 and non-volatile memory 822. A basic input / output system (BIOS), which includes the basic routines for transferring information between elements within the computer 812, such as during startup, is stored in the non-volatile memory 822. The computer 812 may also include removable / non-removable, volatile / non-volatile computer storage media. For example, Figure 8 Disk storage 824 is shown. Disk storage 824 may also include, but is not limited to, devices such as 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. Disk storage 824 may also include storage media, either alone or in combination with other storage media. To facilitate connection of disk storage 824 to system bus 818, a removable or non-removable interface, such as interface 826, is typically used. Figure 8 Also depicted is software that acts as an intermediary between a user and the basic computer resources described in the suitable operating environment 800. The software may also include, for example, an operating system 828. The operating system 828, which may be stored on disk storage 824, is used to control and allocate the resources of the computer 812.

[0201] System applications 830 utilize operating system 828 through, for example, program modules 832 and program data 834 stored in system memory 816 or on disk memory 824 to manage resources. It should be understood that the present disclosure can be implemented with different operating systems or combinations of operating systems. A user inputs commands or information into computer 812 via input device 836. Input device 836 includes, but is not limited to, pointing devices such as a mouse, trackball, stylus, touchpad, keyboard, microphone, joystick, game pad, satellite dish, scanner, TV tuner card, digital camera, digital video camera, webcam, etc. These and other input devices are connected to processing unit 814 via (one or more) interface ports 838 through system bus 818. Interface port 838 includes, for example, a serial port, parallel port, game port, and universal serial bus (USB). Output device 840 uses some of the same types of ports as input device 836. Thus, for example, a USB port can be used to provide input to computer 812 and output information from computer 812 to output device 840. Output adapters 842 are provided to illustrate the presence of some output devices 840, such as monitors, speakers, and printers, in addition to other output devices 840 that require special adapters. By way of illustration and not limitation, output adapters 842 include video and sound cards that provide connection devices between output devices 840 and system bus 818. It should be noted that other devices and / or systems of devices provide both input and output capabilities, such as remote computers 844.

[0202] Computer 812 can operate in a networked environment using logical connections to one or more remote computers, such as remote computer 844. Remote computer 844 can be a computer, server, router, network PC, workstation, microprocessor-based appliance, peer device, or other public network node, and can generally include many or all of the elements described with respect to computer 812. For the sake of simplicity, remote computer 844 is shown with only a memory storage device 846. Remote computer 844 is logically connected to computer 812 via a network interface 848, and then physically connected via a communication connection 850. Network interface 848 includes wired and / or wireless communication networks, such as a local area network (LAN), a wide area network (WAN), a cellular network, and the like. LAN technologies include fiber distributed data interface (FDDI), copper distributed data interface (CDDI), Ethernet, token ring, and the like. WAN technologies include, but are not limited to, point-to-point links, circuit-switched networks (such as integrated services digital networks (ISDN) and their variations), packet-switched networks, and digital subscriber lines (DSL). Communication connection 850 refers to the hardware / software used to connect network interface 848 to system bus 818. Although the communication connection 850 is shown internal to the computer 812 for clarity of illustration, it may also be external to the computer 812. For exemplary purposes only, the hardware / software used to connect to the network interface 848 may also include internal and external technologies, such as modems, including conventional telephone-grade modems, cable modems and DSL modems, ISDN adapters, and Ethernet cards.

[0203] Now see Figure 9 , depicts an illustrative cloud computing environment 950. As shown, cloud computing environment 950 includes one or more cloud computing nodes 910 with which local computing devices used by cloud consumers, such as, for example, personal digital assistants (PDAs) or cellular phones 954A, desktop computers 954B, laptop computers 954C, and / or automobile computer systems 954N, can communicate. Figure 9 Not shown, the cloud computing node 910 may further include a quantum platform (e.g., quantum computer, quantum hardware, quantum software, etc.), and the local computing device used by the cloud consumer can communicate with the quantum platform. The nodes 910 can communicate with each other. They can be physically or virtually grouped (not shown) in one or more networks, such as a private cloud, public cloud, open cloud or hybrid cloud, or a combination thereof, as described above. This allows the cloud computing environment 950 to provide infrastructure, platform and / or software as a service for which the cloud consumer does not need to maintain resources on a local computing device. It should be understood that Figure 9 The types of computing devices 954A-N shown in are intended to be illustrative only, and computing node 910 and cloud computing environment 950 may communicate with any type of computerized device over any type of network and / or network-addressable connection (e.g., using a web browser).

[0204] Now see Figure 10 , showing the cloud computing environment 950 ( Figure 9 ) provides a set of functional abstraction layers. It should be understood in advance that Figure 10 The components, layers, and functions shown in are intended to be illustrative only, and embodiments of the present invention are not limited thereto. As described, the following layers and corresponding functions are provided:

[0205] The hardware and software layer 1060 includes hardware and software components. Examples of hardware components include: mainframes 1061; servers based on RISC (Reduced Instruction Set Computer) architecture 1062; servers 1063; blade servers 1064; storage devices 1065; and network and networking components 1066. In some embodiments, software components include network application server software 1067, quantum platform routing software 1068, and / or quantum software ( Figure 10 not shown).

[0206] The virtualization layer 1070 provides an abstraction layer from which the following examples of virtual entities can be provided: virtual servers 1071 ; virtual storage 1072 ; virtual networks 1073 , including virtual private networks; virtual applications and operating systems 1074 ; and virtual clients 1075 .

[0207] In one example, the management layer 1080 may provide the functionality described below. Resource provisioning 1081 provides dynamic procurement of computing resources and other resources for performing tasks within a cloud computing environment. Metering and pricing 1082 provides cost tracking when utilizing resources within a cloud computing environment and bills or invoices the consumption of these resources. In one example, these resources may include application software licenses. Security provides authentication for cloud consumers and tasks, as well as protection for data and other resources. User portal 1083 provides access to the cloud computing environment for consumers and system administrators. Service level management 1084 provides cloud computing resource allocation and management so that required service levels are met. Service level agreement (SLA) planning and fulfillment 1085 provides pre-arrangement and procurement of cloud computing resources based on the expected future requirements of the cloud computing resources according to the SLA.

[0208] The workload layer 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 layer include: mapping and navigation 1091; software development and lifecycle management 1092; virtual classroom education delivery 1093; data analytics processing 1094; transaction processing 1095; and expected energy estimation software 1096.

[0209] The present invention can be the system, method, device and / or computer program product on any possible technical details integration degree.The computer program product can include thereon the computer-readable storage medium (or multiple media) with the computer-readable program instruction for making the processor perform various aspects of the present invention.The computer-readable storage medium can be the tangible device that can retain and store the instruction for the instruction execution device.The computer-readable storage medium can be, for example but not limited to, electronic storage device, magnetic storage device, optical storage device, electromagnetic storage device, semiconductor storage device or above-mentioned any suitable combination.The non-exhaustive list of the more specific example of computer-readable storage medium can also include the following: portable computer disk, hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital versatile disk (DVD), memory stick, floppy disk, mechanical encoding device such as punch card or the protruding structure in the groove with the instruction recorded thereon and any suitable combination of the above-mentioned. Computer-readable storage media as used herein should not be construed as transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses passing through fiber optic cables), or electrical signals transmitted through wires.

[0210] Computer-readable program instructions described herein can be downloaded to corresponding computing / processing equipment from a computer-readable storage medium via a network (for example, the Internet, local area network, wide area network and / or wireless network), or downloaded to an external computer or external storage device. The network can include copper transmission cables, optical transmission fibers, wireless transmissions, routers, firewalls, switches, gateway computers and / or edge servers. The network adapter card or the network interface in each computing / processing equipment receive the computer-readable program instructions from the network, and forward the computer-readable program instructions to be stored in the computer-readable storage medium in the corresponding computing / processing equipment. The computer-readable program instructions for performing operation of the present invention can be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-related instructions, microcode, firmware instructions, state setting data, configuration data of integrated circuits or source code or object code written in any combination of one or more programming languages, which include object-oriented programming languages (such as Smalltalk, C++ etc.) and process programming languages (such as "C" programming languages or similar programming languages). The computer-readable program instructions can be executed completely on the user's computer, partially on the user's computer, as a stand-alone software package, partially on the user's computer, partially on a remote computer, or completely on a remote computer or server. In the latter case, the remote computer can be connected to the user's computer via any type of network (including a local area network (LAN) or a wide area network (WAN)), or can be connected to an external computer (e.g., using an internet service provider via the internet). In certain embodiments, an electronic circuit comprising, for example, a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA) can perform computer-readable program instructions by utilizing the state information of the computer-readable program instructions to personalize the electronic circuit so as to perform various aspects of the present invention.

[0211] The present invention will be described below with reference to the flow chart and / or block diagram of the method, device (system) and computer program product according to an embodiment of the present invention.It should be understood that each square frame of the flow chart and / or block diagram and the combination of square frames in the flow chart and / or block diagram can be realized by computer-readable program instructions.These computer-readable program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device create a device for realizing the function / action specified in or in a plurality of frames of the flow chart and / or block diagram.These computer-readable program instructions can also be stored in a computer-readable storage medium, and these instructions make the computer, programmable data processing device, and / or other equipment work in a special way, so that the computer-readable storage medium wherein stored with instructions includes the manufacture of the instructions comprising the aspect of realizing the function / action specified in or in a plurality of frames in the flow chart and / or block diagram. Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device, so that a series of operational actions are performed on the computer, other programmable apparatus, or other device to produce computer-implemented processing, so that the instructions executed on the computer, other programmable apparatus, or other device implement the functions / actions specified in the flowchart and / or block diagram or multiple boxes.

[0212] The flow charts and block diagrams in the accompanying drawings illustrate the architecture, functions and operations of possible implementations of the systems, methods and computer program products according to different embodiments of the present invention. To this end, each box in the flow chart or block diagram may represent a module, segment or portion of an instruction, which includes one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions annotated in the box may not occur in the order annotated in the figure. For example, depending on the functions involved, the two blocks shown in succession may actually be executed substantially simultaneously, or the blocks may sometimes be executed in the opposite order. It should also be noted that each box in the block diagram and / or flow chart, and the combination of the boxes in the block diagram and / or flow chart, can be implemented using a dedicated hardware-based system that performs a specified function or action or performs a combination of dedicated hardware and computer instructions.

[0213] Although the subject matter has been described above in the general context of computer-executable instructions of a computer program product running on a computer and / or a computer, those skilled in the art will recognize that the present disclosure may also be implemented or combined with other program modules. Typically, a program module includes routines, programs, components, data structures, etc. that perform specific tasks and / or implement specific abstract data types. In addition, those skilled in the art will recognize that the computer-implemented method of the present invention can be practiced with other computer system configurations, including single-processor or multi-processor computer systems, small computing devices, mainframe computers, and computers, handheld computing devices (e.g., PDAs, phones), microprocessor-based or programmable consumer or industrial electronic products, etc. The illustrated aspects can also be implemented in a distributed computing environment, in which tasks are performed by remote processing devices linked through a communication network. However, some (if not all) aspects of the present invention can be practiced on stand-alone computers. In a distributed computing environment, program modules can be located in both local and remote memory storage devices. For example, in one or more embodiments, a computer-executable component can 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 can execute code of computer-executable components in a distributed manner, for example, multiple processors working in combination or in collaboration to execute code from one or more distributed memory units. As used herein, the term "memory" can encompass a single memory or memory unit at one location or a plurality of memories or memory units at one or more locations.

[0214] As used in this application, the terms "component", "system", "platform", "interface" and the like may refer to and / or may include computer-related entities or entities associated with an operating machine having one or more specific functions. The entities disclosed herein may be hardware, a combination of hardware and software, software, or software in execution. For example, a component may be, but is not limited to, a process, a processor, an object, an executable file, a thread of execution, a program, and / or a computer running on a processor. As an illustration, both an application running on a server and a server may be a component. One or more components may reside within a process and / or a thread of execution, and a component may be located on one computer and / or distributed between two or more computers. In another example, the corresponding component may be executed from different computer-readable media having different data structures stored thereon. Components may communicate via local and / or remote processes, such as according to a signal with one or more data packets (e.g., data from a component interacting with another component in a local system, a distributed system, and / or data from a component interacting with other systems across a network such as the Internet via the signal). As another example, a component may be a device having a specific functionality provided by a mechanical assembly 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 internal or external to the device and may execute at least a portion of the software or firmware application. As yet another example, a component may be a device that provides a specific functionality by an electronic assembly without a mechanical assembly, where the electronic assembly may include a processor or other device for executing the software or firmware that at least partially imparts the functionality to the electronic assembly. In one aspect, the component may emulate the electronic assembly via, for example, a virtual machine within a cloud computing system.

[0215] Furthermore, the term "or" is intended to mean an inclusive "or" rather than an exclusive "or". That is, unless specified otherwise, or clear from the context, "X employs A or B" is intended to mean any of the natural inclusive permutations. That is, if X employs A; X employs B; or X employs both A and B, then "X employs A or B" is satisfied in any of the foregoing cases. Furthermore, the articles "a" and "an" as used in the subject specification and drawings should generally be construed to mean "one or more" unless specified otherwise or clear from the context to direct to the singular form. As used herein, the terms "example" and / or "exemplary" are used to mean serving as an example, instance, or illustration. For the avoidance of doubt, the subject matter disclosed herein is not limited by such examples. Furthermore, 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, nor is it meant to exclude equivalent exemplary structures and techniques known to those of ordinary skill in the art.

[0216] As used in this specification, the term "processor" may refer to substantially any computational processing unit or device, including but not limited to a single-core processor, a single processor with software multi-threaded execution capability; a multi-core processor, a multi-core processor with software multi-threaded execution capability; a multi-core processor with hardware multi-threading technology; a parallel platform; and a parallel platform with distributed shared memory. In addition, a processor may refer to an integrated circuit, an application-specific integrated circuit (ASIC), a digital signal processor (DSP), a field-programmable gate array (FPGA), a programmable logic controller (PLC), a complex programmable logic device (CPLD), discrete gate or transistor logic, discrete hardware components, or any combination thereof, designed to perform the functions described herein. Further, the processor may utilize nanoscale architectures, such as but not limited to molecular and quantum dot-based transistors, switches, and gates, in order to optimize space usage or enhance the performance of a user device. The processor may also be implemented as a combination of computational processing units. In this disclosure, terms such as "storage," "storage," "data storage," "data store," "database," and substantially any other information storage component related to the operation and functionality of a component are used to refer to a "memory component," an entity embodied in "memory," or a component that includes memory. It should be understood that the memory and / or memory components described herein can be volatile memory or non-volatile memory, or can include both volatile and non-volatile memory. By way of example, and not limitation, non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable ROM (EEPROM), flash memory, or non-volatile random access memory (RAM) (e.g., ferroelectric RAM (FeRAM)). Volatile memory can include, for example, RAM that can act as external cache memory. By way of illustration, and not limitation, RAM can be available in many forms, such as synchronous RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), direct Rambus RAM (DRRAM), Direct Rambus Dynamic RAM (DRDRAM), and Rambus Dynamic RAM (RDRAM). Additionally, the memory components of the systems or computer-implemented methods disclosed herein are intended to comprise, without being limited to, these and any other suitable types of memory.

[0217] What has been described above includes only examples of systems and computer-implemented methods. Of course, for purposes of describing the present disclosure, it is not possible to describe every conceivable combination of components or computer-implemented method, but one of ordinary skill in the art will recognize that many further combinations and permutations of the present disclosure are possible. Furthermore, to the extent that the terms "including," "having," "having," and the like are used in the detailed description, claims, appendices, and drawings, these terms are intended to be inclusive in a manner similar to the term "comprising" in that "comprising" is to be interpreted as a transitional word when used in a claim.

[0218] The description of the various embodiments has been presented for illustrative purposes and is not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is selected to best explain the principles of the embodiments, practical applications, or technical improvements over technologies found in the marketplace, or to enable those of ordinary skill in the art to understand the embodiments disclosed herein.< / v>

Claims

1. A quantum system comprising: memory for storing computer-executable components; quantum devices that generate quantum states; as well as a processor that executes the computer-executable components stored in the memory, wherein the computer-executable components include: a selection component that selects a quantum state measurement basis having a probability defined by a ratio of Pauli operators in a Hamiltonian of the quantum system; as well as A measurement component acquires quantum state measurements of qubits in the quantum system based on the quantum state measurement basis.

2. The quantum system according to claim 1, wherein The quantum state measurement basis comprises a basis state of at least one of: a stabilizer state, a single-qubit stabilizer state, or a multi-qubit quantum state spanning a quantum state, the quantum state comprising a finite number of non-unit Pauli matrices, and wherein the Hamiltonian comprises a sum of weighted Pauli strings comprising the finite number of non-unit Pauli matrices.

3. The quantum system according to claim 1, wherein The measurement component acquires the quantum state measurements of the qubits based on the quantum state measurement basis to reduce at least one of: a number of quantum state measurements of the qubits used to calculate an expected energy value of the Hamiltonian operator; or an execution time of a variational quantum eigensolver algorithm executed by the quantum system.

4. The quantum system according to any one of claims 1 to 3, wherein: The computer executable components further include: A state generation component generates a product quantum state based on quantum state measurements of the qubit acquired according to a plurality of quantum state measurement bases.

5. The quantum system according to any one of claims 1 to 3, wherein: The computer executable components further include: A computation component computes an expected energy value of the Hamiltonian operator based on a product quantum state generated based on quantum state measurements of the qubits acquired according to a plurality of quantum state measurement bases.

6. A computer-implemented method comprising: selecting, by a system operatively coupled to the processor, a quantum state measurement basis having probabilities defined based on a ratio of Pauli operators in a Hamiltonian of the quantum system; as well as Quantum state measurements of qubits in the quantum system are acquired by the system based on the quantum state measurement basis.

7. The computer-implemented method of claim 6, wherein: The quantum state measurement basis comprises a basis state of at least one of: a stabilizer state, a single-qubit stabilizer state, or a multi-qubit quantum state spanning a quantum state comprising a defined number of non-unit Pauli matrices, and wherein the Hamiltonian comprises a sum of weighted Pauli strings comprising the defined number of non-unit Pauli matrices.

8. The computer-implemented method of claim 6, wherein: The collection includes: The quantum state measurements of the qubits in the quantum system are collected by the system based on the quantum state measurement basis to reduce at least one of: a number of quantum state measurements of the qubits used to calculate an expected energy value of the Hamiltonian operator; or an execution time of the quantum system to execute a variational quantum eigensolver algorithm.

9. The computer-implemented method of any one of claims 6 to 8, further comprising: A product quantum state is generated by the system based on quantum state measurements of the qubits acquired according to a plurality of quantum state measurement bases.

10. The computer-implemented method of any one of claims 6 to 8, further comprising: An expected energy value of the Hamiltonian operator is calculated by the system based on a product quantum state generated based on quantum state measurements of the qubits acquired according to a plurality of quantum state measurement bases.

11. A computer program product facilitating a process for estimating an expected energy value of a Hamiltonian operator, the computer program product comprising program instructions executable by a processor to cause the processor to: selecting, by the processor, a quantum state measurement basis having a probability defined by a ratio of Pauli operators in a Hamiltonian of a quantum system; and Quantum state measurements of qubits in the quantum system are acquired by the processor based on the quantum state measurement basis.

12. The computer program product of claim 11, wherein: The quantum state measurement basis comprises a basis state of at least one of: a stabilizer state, a single-qubit stabilizer state, or a multi-qubit quantum state spanning a quantum state comprising a finite number of non-unit Pauli matrices, and wherein the Hamiltonian comprises a sum of weighted Pauli strings comprising the finite number of non-unit Pauli matrices.

13. The computer program product of claim 11, wherein: The program instructions are further executable by the processor to cause the processor to: The processor acquires the quantum state measurements of the qubits in the quantum system based on the quantum state measurement basis to reduce at least one of: a number of quantum state measurements of the qubits used to calculate an expected energy value of the Hamiltonian operator; or an execution time of a variational quantum eigensolver algorithm executed by the quantum system.

14. The computer program product according to any one of claims 11 to 13, wherein: The program instructions are further executable by the processor to cause the processor to: A product quantum state is generated by the processor based on quantum state measurements of the qubits acquired according to a plurality of quantum state measurement bases.

15. The computer program product according to any one of claims 11 to 13, wherein: The program instructions are further executable by the processor to cause the processor to: An expected energy value of the Hamiltonian operator is calculated by the processor based on a product quantum state generated based on a plurality of quantum state measurements of the qubit acquired according to a plurality of quantum state measurement bases.

16. A quantum system comprising: memory for storing computer-executable components; quantum devices that generate quantum states; as well as a processor that executes the computer-executable components stored in the memory, wherein the computer-executable components include: a measurement component that acquires entangled quantum state measurements of qubits in the quantum system based on an entangled quantum state measurement basis, wherein the entangled quantum state measurement basis is selected based on a probability defined by a ratio of Pauli operators in a Hamiltonian operator of the quantum system; and A computing component calculates an expected energy value of a Hamiltonian operator of the quantum system based on the entangled quantum state measurement.

17. The quantum system according to claim 16, wherein The entangled quantum state measurement basis comprises a two-qubit quantum state, and wherein the Hamiltonian comprises a sum of consecutive weighted Pauli strings comprising a finite number of non-unit Pauli matrices.

18. The quantum system according to claim 16, wherein The measurement component acquires 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 an expected energy value of the Hamiltonian operator; or an execution time of a variational quantum eigensolver algorithm executed by the quantum system.

19. A quantum system according to any one of claims 16 to 18, wherein The computer executable components further include: A state generation component generates a quantum state based on a plurality of entangled quantum state measurements of the qubits acquired according to a plurality of entangled quantum state measurement bases.

20. A quantum system according to any one of claims 16 to 18, wherein The measurement component further collects a measurement of the entangled quantum state of the qubit based on an even or odd outcome of flipping the fair coin.

21. A computer-implemented method comprising: acquiring, by a system operatively coupled to the processor, entangled quantum state measurements of qubits in the quantum system based on an entangled quantum state measurement basis, wherein the entangled quantum state measurement basis is selected based on probabilities defined by ratios of Pauli operators in a Hamiltonian of the quantum system; and An expected energy value of a Hamiltonian of the quantum system is calculated by the system based on the entangled quantum state measurement.

22. The computer-implemented method of claim 21 , wherein: The entangled quantum state measurement basis comprises a two-qubit quantum state, and wherein the Hamiltonian comprises a sum of consecutive weighted Pauli strings comprising a finite number of non-unit Pauli matrices.

23. The computer-implemented method of claim 21 , wherein: The collection includes: The entangled quantum state measurements of the qubits in the quantum system are collected by the 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 an expected energy value of the Hamiltonian operator; or an execution time of a variational quantum eigensolver algorithm executed by the quantum system.

24. The computer-implemented method of any one of claims 21 to 23, further comprising: A quantum state is generated by the system based on a plurality of entangled quantum state measurements of the qubits acquired according to a plurality of entangled quantum state measurement bases.

25. The computer-implemented method of any one of claims 21 to 23, wherein: The collection further includes: The entangled quantum state measurement of the qubit is acquired by the system based on an even or odd outcome of a flipped fair coin.

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