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Methods and systems for quantum computing — 1Qb Information Technologies Inc. (US10826845B2)

1Qb Information Technologies Inc. · Google Patents

Google Patents · Patents · License: Open Access

patent, google patents, intellectual property, US10826845B2, 1Qb Information Technologies Inc., Majid Dadashikelayeh, en, 2020

ABSTRACT

Abstract

The present disclosure provides methods, systems, and media for quantum computing, including allowing access to quantum ready and/or quantum enabled computers in a distributed computing environment (e.g., the cloud). Such methods and systems may provide optimization and computational services. Methods and systems of the present disclosure may enable quantum computing to be relatively and readily scaled across various types of quantum computers and users at various locations, in some cases without the need for users to have a deep understanding of the resources, implementation or the knowledge that may be required for solving optimization problems using a quantum computer. Systems provided herein may include user interfaces that enable users to perform data analysis in a distributed computing environment while taking advantage of quantum technology in the backend.

Description

CROSS-REFERENCE

This application is a continuation of U.S. patent application Ser. No. 15/830,953, filed Dec. 4, 2017, which is a continuation-in-part of U.S. patent application Ser. No. 15/486,960, filed Apr. 13, 2017, now U.S. Pat. No. 9,870,273, which is a continuation-in-part of U.S. patent application Ser. No. 15/349,519, filed Nov. 11, 2016, now U.S. Pat. No. 9,660,859, which is a continuation of U.S. patent application Ser. No. 15/181,247, filed Jun. 13, 2016, now U.S. Pat. No. 9,537,953; U.S. patent application Ser. No. 15/486,960 also claims priority to U.S. Provisional Patent Application No. 62/436,093, filed Dec. 19, 2016; U.S. patent application Ser. No. 15/830,953 is also a continuation-in-part of U.S. patent application Ser. No. 15/165,655, filed May 26, 2016, each of which is entirely incorporated herein by reference.

BACKGROUND

Quantum computers typically make use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers may be different from digital electronic computers based on transistors. For instance, whereas digital computers require data to be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits (qubits), which can be in superpositions of states.

Systems of superconducting qubits are disclosed for instance in U.S. Patent Publication No. 2012/0326720 and U.S. Publication No. 2006/0225165 and manufactured by D-Wave Systems, IBM, and Google. Such analogue systems are used for implementing quantum computing algorithms, for example, the quantum adiabatic computation proposed by Farhi et. al., âQuantum computation by adiabatic evolutionâ (arXiv:quant-ph/0001106) and Grover's quantum search algorithm by L. Grover, âA fast quantum mechanical algorithm for database searchâ, Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, pp. 212-219 (1996) and also explained in Dam et. al., âHow Powerful is Adiabatic Quantum Computation?,â (arXiv:quant-ph/0206003), each of which is entirely incorporated herein by reference.

SUMMARY

Systems and methods disclosed herein relate to quantum information processing. The computational capability of a quantum computer is much more powerful than conventional digital computers. Quantum mechanics is now being used to construct a new generation of computers that can solve the most complex scientific problemsâand unlock every digital vault in the world. Such quantum computers can perform a computation in a time period (e.g., seconds) that may be significantly less than a time period of a conventional computer to perform the computation. However, the cost of quantum information processing is extremely high. To make quantum computing more accessible to general populations, a new computational infrastructure integrating quantum computers and digital computers is necessary.

Access to quantum computing resources is expensive. Therefore, a new system disclosed herein allows shared access to quantum computing resources. A purpose of the system disclosed herein is to provide quantum computing services (e.g., optimization) on a cloud computing platform. The quantum computing services based on today's technologies have a potential to add additional functionalities as they are developed. Using a software development kit, users are not required to have a deep understanding of the internal architectures and mechanisms of quantum computing resources, implementation, or knowledge required for solving optimization problems using a quantum computer. The system disclosed herein may provide user interfaces for data analysis services on the cloud while taking advantage of quantum technology in a backend.

Systems and methods disclosed herein may be able to improve the quality of computing services with much greater capability, flexibility, and affordable costs. Scalable quantum computers disclosed herein may be complementary to digital computers wherein special-purpose computing resources are programmed or configured for certain classes of problems. Users in need of quantum computing services for their specific computing problems can access quantum-computing resources remotely, such as on the cloud. Users can run algorithms and experiments on quantum computers and processors working with individual quantum bits (qubits). Users may not be required to understand the internal architecture and mechanisms of quantum computing resources. Users' different familiarities with the issues and relevant solutions in their respective practices, such as, for example, weather forecasting, financial analysis, cryptography, logistical planning, search for Earth-like planets, and drug discovery, etc. may provide them a flexibility of accessing different quantum computing resources using methods and systems disclosed herein. Quantum computing services provided through the cloud can provide significantly faster service than digital computers.

Systems and methods provided herein may improve functionality of a quantum computer, such as, for example, by providing remote access to the quantum computer and facilitating the manner in which requests are processed. This can enable quantum computing to be scaled across multiple users at various locations.

The present disclosure provides methods and systems that enable ready access to a quantum computer. Such access may be remote access or local access. The quantum computer may be accessed over a network, such as through a cloud-based interface.

The present disclosure provides systems and methods for quantum information processing. Many methods exist for solving a binary polynomially constrained polynomial programming problem using a system of superconducting qubits. The method disclosed herein can be used in conjunction with any method on any solver for solving a binary polynomially constrained polynomial programming problem to solve a mixed-integer polynomially constrained polynomial programming problem.

Current implementations of quantum devices have limited numbers of superconducting qubits and are furthermore prone to various sources of noise. In practice, this restricts the usage of the quantum device to a limited number of qubits and a limited range of applicable local field biases and couplings strengths. Therefore there is need for methods of efficient encoding of data on the qubits of a quantum device.

Disclosed invention herein relates to quantum information processing. This application pertains to a method for storing integers on superconducting qubits and setting a system of such superconducting qubits having a Hamiltonian representative of a polynomial on a bounded integer domain.

The method disclosed herein can be used as a preprocessing step for solving a mixed integer polynomially constrained polynomial programming problem with a solver for binary polynomially constrained polynomial programming problems. One way to achieve the mentioned conversion is to cast each integer variable x as a linear function of binary variables, y i for i=1, . . . , d:

x=Î£ i=1 d c i y i ,

The tuple (c 1 , c d ) is what's referred to as an integer encoding. A few well-known integer encodings are:

Binary Encoding, in which c i =2 i-1

Unary Encoding, in which c 1 =1. Sequential Encoding, in which c 1 =i.

Current implementations of quantum devices have limited numbers of superconducting qubits and are furthermore prone to various sources of noise, including thermal and decoherence effects of the environment and the system as disclosed by Katzgraber et. al., âSeeking quantum speedup through spin glasses: the good, the bad, and the uglyâ (arXiv:1505.01545v2). In practice, this restricts the usage of the quantum device to a limited number of qubits and a limited range of applicable ferromagnetic biases and couplings.

Consequently the integer encodings formulated above, become incompetent for representing polynomial in several integer variables as the Hamiltonian of the systems mentioned above. The unary encoding suffers from exploiting a large number of qubits and on the other hand, in the binary and sequential encoding the coefficients c i can be too large and therefore the behavior of the system is affected considerably by the noise.

In an aspect, disclosed herein is a method for setting a system of superconducting qubits having a Hamiltonian representative of a polynomial on a bounded integer domain via bounded-coefficient encoding, the method comprising: using one or more computer processors to obtain (i) the polynomial on the bounded integer domain and (ii) integer encoding parameters; computing a bounded-coefficient encoding using the integer encoding parameters; recasting each integer variable as a linear function of binary variables using the bounded-coefficient encoding, and providing additional constraints on the attained binary variables to avoid degeneracy in the encoding, if required by a user; substituting each integer variable with an equivalent binary representation, and computing the coefficients of the equivalent binary representation of the polynomial on the bounded integer domain; performing a degree reduction on the obtained equivalent binary representation of the polynomial on the bounded integer domain to provide an equivalent polynomial of degree at most two in binary variables; and setting local field biases and coupling strengths on the system of superconducting qubits using the coefficients of the derived polynomial of degree at most two in several binary variables. In some embodiments, the polynomial on a bounded integer domain is a single bounded integer variable. In further embodiments, setting local field biases and coupling strengths comprises assigning a plurality of qubits to have a plurality of corresponding local field biases; each local field bias corresponding to each of the qubits in the plurality of qubits is provided using the parameters of the integer encoding. In some embodiments, the polynomial on a bounded integer domain is a linear function of several bounded integer variables. In further embodiments, setting local field biases and coupling strengths comprises assigning a plurality of qubits to have a plurality of corresponding local field biases; each local field bias corresponding to each of the qubits in the plurality of qubits is provided using the linear function and parameters of the integer encoding. In some embodiments, the polynomial on a bounded integer domain is a quadratic polynomial of several bounded integer variables. In further embodiments, setting local field biases and coupling strengths comprises embedding the equivalent binary representation of the polynomial of degree at most two on a bounded integer domain to the layout of a system of superconducting qubits comprising local fields on each of the plurality of the superconducting qubits and couplings in a plurality of pairs of the plurality of the superconducting qubits. In some embodiments, the system of superconducting qubits is a quantum annealer. In further embodiments, the method comprises performing an optimization of the polynomial on a bounded integer domain via bounded-coefficient encoding. In further embodiments, the optimization of the polynomial on a bounded integer domain via bounded-coefficient encoding is obtained by quantum adiabatic evolution of an initial transverse field on the superconducting qubits to the final Hamiltonian on a measurable axis. In further embodiments, the optimization of the polynomial on a bounded integer domain via bounded-coefficient encoding comprises: providing the equivalent polynomial of degree at most two in binary variables; providing a system of non-degeneracy constraints; and solving the problem of optimization of the equivalent polynomial of degree at most two in binary variables subject to the system of non-degeneracy constraints as a binary polynomially constrained polynomial programming problem. In some embodiments, the method comprises solving a polynomially constrained polynomial programming problem on a bounded integer domain via bounded-coefficient encoding. In some embodiments, solving the polynomially constrained polynomial programming problem on a bounded integer domain via bounded-coefficient encoding is obtained by quantum adiabatic evolution of an initial transverse field on the superconducting qubits to the final Hamiltonian on a measurable axis. In further embodiments, solving the polynomially constrained polynomial programming problem on a bounded integer domain via bounded-coefficient encoding comprises: computing the bounded-coefficient encoding of the objective function and constraints of the polynomially constrained polynomial programming problem using the integer encoding parameters to obtain an equivalent polynomially constrained polynomial programming problem in several binary variables; providing a system of non-degeneracy constraints; adding the system of non-degeneracy constraints to the constraints of the obtained polynomially constrained polynomial programming problem in several binary variables; and solving the problem of optimization of the obtained polynomially constrained polynomial programming problem in several binary variables. In some embodiments, the obtaining of integer encoding parameters comprises obtaining an upper bound on the coefficients of the bounded-coefficient encoding directly. In some embodiments, the obtaining of integer encoding parameters comprises obtaining an upper bound on the coefficients of the bounded-coefficient encoding based on error tolerances â l and â c of local field biases and couplings strengths of the system of superconducting qubits. In some embodiments, obtaining an upper bound on the coefficient of the bounded-coefficient encoding comprises finding a feasible solution to a system of inequality constraints.

CROSS-REFERENCE

BACKGROUND

SUMMARY

x=Î£ i=1 d c i y i ,

The tuple (c 1 , c d ) is what's referred to as an integer encoding. A few well-known integer encodings are:

Binary Encoding, in which c i =2 i-1

Unary Encoding, in which c 1 =1. Sequential Encoding, in which c 1 =i.

In another aspect, disclosed herein is a system comprising: a sub-system of superconducting qubits; a computer operatively coupled to the sub-system of superconducting qubits, wherein the computer comprises at least one computer processor, an operating system configured to perform executable instructions, and a memory; and a computer program including instructions executable by the at least one computer processor to generate an application for setting the sub-system of superconducting qubits having a Hamiltonian representative of a polynomial on a bounded integer domain via bounded-coefficient encoding, the application comprising: a software module programmed or otherwise configured to obtain the polynomial on the bounded integer domain; a software module programmed or otherwise configured to obtain integer encoding parameters; a software module programmed or otherwise configured to compute a bounded-coefficient encoding using the integer encoding parameters; a software module programmed or otherwise configured to recast each integer variable as a linear function of binary variables using the bounded-coefficient encoding, and providing additional constraints on the attained binary variables to avoid degeneracy in the encoding, if required by a user; a software module programmed or otherwise configured to substitute each integer variable with an equivalent binary representation, and compute the coefficients of the equivalent binary representation of the polynomial on the bounded integer domain; a software module programmed or otherwise configured to perform a degree reduction on the obtained equivalent binary representation of the polynomial on the bounded integer domain to provide an equivalent polynomial of degree at most two in binary variables; and a software module programmed or otherwise configured to set local field biases and coupling strengths on the system of superconducting qubits using the coefficients of the derived polynomial of degree at most two in several binary variables. In some embodiments, the polynomial on a bounded integer domain is a single bounded integer variable. In further embodiments, setting local field biases and coupling strengths comprises assigning a plurality of qubits to have a plurality of corresponding local field biases; each local field bias corresponding to each of the qubits in the plurality of qubits is provided using the parameters of the integer encoding. In some embodiments, the polynomial on a bounded integer domain is a linear function of several bounded integer variables. In further embodiments, setting local field biases and coupling strengths comprises assigning a plurality of qubits to have a plurality of corresponding local field biases; each local field bias corresponding to each of the qubits in the plurality of qubits is provided using the linear function and parameters of the integer encoding. In some embodiments, the polynomial on a bounded integer domain is a quadratic polynomial of several bounded integer variables. In further embodiments, setting local field biases and coupling strengths comprises embedding the equivalent binary representation of the polynomial of degree at most two on a bounded integer domain to the layout of a system of superconducting qubits comprising local fields on each of the plurality of the superconducting qubits and couplings in a plurality of pairs of the plurality of the superconducting qubits. In some embodiments, the system of superconducting qubits is a quantum annealer. In further embodiments, the system comprises performing an optimization of the polynomial on a bounded integer domain via bounded-coefficient encoding. In further embodiments, the optimization of the polynomial on a bounded integer domain via bounded-coefficient encoding is obtained by quantum adiabatic evolution of an initial transverse field on the superconducting qubits to the final Hamiltonian on a measurable axis. In further embodiments, the optimization of the polynomial on a bounded integer domain via bounded-coefficient encoding comprises: providing the equivalent polynomial of degree at most two in binary variables; providing a system of non-degeneracy constraints; and solving the problem of optimization of the equivalent polynomial of degree at most two in binary variables subject to the system of non-degeneracy constraints as a binary polynomially constrained polynomial programming problem. In some embodiments, the system comprises solving a polynomially constrained polynomial programming problem on a bounded integer domain via bounded-coefficient encoding. In some embodiments, solving the polynomially constrained polynomial programming problem on a bounded integer domain via bounded-coefficient encoding is obtained by quantum adiabatic evolution of an initial transverse field on the superconducting qubits to the final Hamiltonian on a measurable axis. In further embodiments, solving the polynomially constrained polynomial programming problem on a bounded integer domain via bounded-coefficient encoding comprises: computing the bounded-coefficient encoding of the objective function and constraints of the polynomially constrained polynomial programming problem using the integer encoding parameters to obtain an equivalent polynomially constrained polynomial programming problem in several binary variables; providing a system of non-degeneracy constraints; adding the system of non-degeneracy constraints to the constraints of the obtained polynomially constrained polynomial programming problem in several binary variables; and solving the problem of optimization of the obtained polynomially constrained polynomial programming problem in several binary variables. In some embodiments, the obtaining of integer encoding parameters comprises obtaining an upper bound on the coefficients of the bounded-coefficient encoding directly. In some embodiments, the obtaining of integer encoding parameters comprises obtaining an upper bound on the coefficients of the bounded-coefficient encoding based on error tolerances â l and â c of local field biases and couplings strengths of the system of superconducting qubits. In some embodiments, obtaining an upper bound on the coefficient of the bounded-coefficient encoding comprises finding a feasible solution to a system of inequality constraints.

In another aspect, disclosed herein is a non-transitory computer-readable medium comprising machine-executable code that, upon execution by one or more computer processors, implements a method for setting a system of superconducting qubits having a Hamiltonian representative of a polynomial on a bounded integer domain via bounded-coefficient encoding, the method comprising: using one or more computer processors to obtain (i) the polynomial on the bounded integer domain and (ii) integer encoding parameters; computing the bounded-coefficient encoding using the integer encoding parameters; recasting each integer variable as a linear function of binary variables using the bounded-coefficient encoding, and providing additional constraints on the attained binary variables to avoid degeneracy in the encoding, if required by a user; substituting each integer variable with an equivalent binary representation, and computing the coefficients of the equivalent binary representation of the polynomial on the bounded integer domain; performing a degree reduction on the obtained equivalent binary representation of the polynomial on the bounded integer domain to provide an equivalent polynomial of degree at most two in binary variables; and setting local field biases and coupling strengths on the system of superconducting qubits using the coefficients of the derived polynomial of degree at most two in several binary variables.

Disclosed is a method for setting a system of superconducting qubits having a Hamiltonian representative of a polynomial on a bounded integer domain via bounded-coefficient encoding, the method comprising obtaining (i) the polynomial on the bounded integer domain and (ii) integer encoding parameters; computing the bounded-coefficient encoding using the integer encoding parameters; recasting each integer variable as a linear function of binary variables using the bounded-coefficient encoding, and providing additional constraints on the attained binary variables to avoid degeneracy in the encoding, if required by a user; substituting each integer variable with an equivalent binary representation, and computing the coefficients of the equivalent binary representation of the polynomial on the bounded integer domain; performing a degree reduction on the obtained equivalent binary representation of the polynomial on the bounded integer domain to provide an equivalent polynomial of degree at most two in binary variables; and setting local field biases and coupling strengths on the system of superconducting qubits using the coefficients of the derived polynomial of degree at most two in several binary variables.

In some embodiments, the obtaining of a polynomial in n variables on a bounded integer domain comprises of providing the plurality of terms in the polynomial; each term of the polynomial further comprises of the coefficient of the term and a list of size n representative of the power of each variables in the term in the matching index. The obtaining of a polynomial on a bounded integer domain further comprises of obtaining a list of upper bounds on each integer variable.

In a particular case where the provided polynomial is of degree at most two, the obtaining of a polynomial on bounded domain comprises of providing coefficients q i of each linear term x i for i=1, . . . , n, and coefficients Q ij +Q ji of each quadratic term x i x j for all choices of distinct elements {i, j}â{1, . . . , n} and an upper bound on each integer variable.

In some embodiments, the obtaining of integer encoding parameters comprises of either obtaining an upper bound on the value of the coefficients of the encoding directly; or obtaining the error tolerance â l and â c of the local field biases and couplings, respectively, and computing the upper bound of the coefficients of the encoding from these error tolerances. This application proposes a technique for computing upper bound of the coefficients of the encoding from â l and â c for the special case that the provided polynomial is of degree at most two.

In some embodiments, the integer encoding parameters are obtained from at least one of a user, a computer, a software package and an intelligent agent.

In some embodiments, the bounded-coefficient encoding is derived and the integer variables are represented as a linear function of a set of binary variables using the bounded-coefficient encoding, and a system of non-degeneracy constraints is returned.

In another aspect, disclosed is a digital computer comprising: a central processing unit; a display device; a memory unit comprising an application for storing data and computing arithmetic operations; and a data bus for interconnecting the central processing unit, the display device, and the memory unit.

In another aspect, there is disclosed a non-transitory computer-readable storage medium for storing computer-executable instructions which, when executed, cause a digital computer to perform arithmetic and logical operations.

In another aspect, there is disclosed a system of superconducting qubits comprising; a plurality of superconducting qubits; a plurality of couplings between a plurality of pairs of superconducting qubits; a quantum device control system capable of setting local field biases on each of the superconducting qubits and couplings strengths on each of the couplings.

The method disclosed herein makes it possible to represent a polynomial on a bounded integer domain on a system of superconducting qubits. The method comprises of obtaining (i) the polynomial on the bounded integer domain and (ii) integer encoding parameters; computing the bounded-coefficient encoding using the integer encoding parameters; recasting each integer variable as a linear function of binary variables using the bounded-coefficient encoding, and providing additional constraints on the attained binary variables to avoid degeneracy in the encoding, if required by a user; substituting each integer variable with an equivalent binary representation, and computing the coefficients of the equivalent binary representation of the polynomial on the bounded integer domain; performing a degree reduction on the obtained equivalent binary representation of the polynomial on the bounded integer domain to provide an equivalent polynomial of degree at most two in binary variables; and setting local field biases and coupling strengths on the system of superconducting qubits using the coefficients of the derived polynomial of degree at most two in several binary variables.

In some embodiments of this application, the method disclosed herein makes it possible to find the optimal solution of a mixed integer polynomially constrained polynomial programming problem through solving its equivalent binary polynomially constrained polynomial programming problem. In one embodiment, solving a mixed integer polynomially constrained polynomial programming problem comprises finding a binary representation of all polynomials appearing the objective function and the constraints of the problem using the bounded-coefficient encoding and applying the methods disclosed in U.S. patent application Ser. No. 15/051,271, U.S. patent application Ser. No. 15/014,576, CA Patent Application No. 2921711 and CA Patent Application No. 2881033, each of which is entirely incorporated herein by reference, to the obtained equivalent binary polynomially constrained polynomial programming problem.

In yet another aspect, the present disclosure provides a method for using a digital computer to generate and direct a computational task to a quantum computing resource comprising at least one quantum computer over a network, wherein the digital computer comprises at least one computer processor and at least one computer memory, the method comprising: retrieving a programming problem from the computer memory of the digital computer; using the at least one computer processor of the digital computer to generate an equivalent of the programming problem; generating a request comprising the equivalent of the programming problem generated by the at least one computer processor of the digital computer; and directing the request from the digital computer to the quantum computing resource over the network, wherein the equivalent of the programming problem is usable by the at least one quantum computer of the quantum computing resource to solve the programming problem.

In some embodiments, the request is directed from the digital computer to the quantum computing resource through a cloud-based interface. In some embodiments, the network is a local network. In some embodiments, the at least one quantum computer performs one or more quantum algorithms to the programming problem.

In some embodiments, the request is generated using an application programming interface (API).

In some embodiments, wherein the method further comprises obtaining (i) a polynomial on a bounded integer domain and (ii) integer encoding parameters, and computing a bounded-coefficient encoding using the integer encoding parameters. In some embodiments, the method further comprises using the one or more computer processors to transform each integer variable of the polynomial to a linear function of binary variables using the bounded-coefficient encoding. In some embodiments, the method further comprises providing constraints on the binary variables to avoid degeneracy in the bounded-coefficient encoding, if required by a user. In some embodiments, the method further comprises substituting each integer variable of the polynomial with an equivalent binary representation, and using the at least one computer processor to compute coefficients of an equivalent binary representation of the polynomial on the bounded integer domain. In some embodiments, the method further comprises performing a degree reduction on the equivalent binary representation of the polynomial on the bounded integer domain to generate an equivalent polynomial. In some embodiments, the equivalent polynomial is of a degree of at most two in binary variables. In some embodiments, the method further comprises setting local field biases and coupling strengths on the at least one quantum computer using the coefficients of the equivalent polynomial of the degree of at most two in binary variables to generate the equivalent of the programming problem. In some embodiments, the equivalent of the programming problem comprises a Hamiltonian representative of the polynomial on the bounded integer domain. In some embodiments, the Hamiltonian is usable by the at least one quantum computer to solve the programming problem.

In yet another aspect, the present disclosure provides a system comprising a digital computer for generating and directing a computational task to a quantum computing resource comprising at least one quantum computer over a network, wherein the digital computer comprises at least one computer processor and at least one computer memory, wherein the at least one computer processor is programmed to: retrieve a programming problem from the computer memory of the digital computer; use the at least one computer processor of the digital computer to generate an equivalent of the programming problem; generate a request comprising the equivalent of the programming problem generated by the at least one computer processor of the digital computer; and direct the request from the digital computer to the quantum computing resource over the network, wherein the equivalent of the programming problem is usable by the at least one quantum computer of the quantum computing resource to solve the programming problem.

In some embodiments, the at least one computer processor is programmed to direct the request from the digital computer to the quantum computing resource through a cloud-based interface. In some embodiments, the network is a local network.

In some embodiments, the at least one computer processor is programmed to obtain (i) a polynomial on a bounded integer domain and (ii) integer encoding parameters, and compute a bounded-coefficient encoding using the integer encoding parameters. In some embodiments, the at least one computer processor is programmed to (i) transform each integer variable of the polynomial to a linear function of binary variables using the bounded-coefficient encoding, and (ii) substitute each integer variable of the polynomial with an equivalent binary representation, and using the at least one computer processor to compute coefficients of an equivalent binary representation of the polynomial on the bounded integer domain. In some embodiments, the at least one computer processor is programmed to perform a degree reduction on the equivalent binary representation of the polynomial on the bounded integer domain to generate an equivalent polynomial, wherein the equivalent polynomial is of a degree of at most two in binary variables. In some embodiments, the at least one computer processor is programmed to set local field biases and coupling strengths on the at least one quantum computer using the coefficients of the equivalent polynomial of the degree of at most two in binary variables to generate the equivalent of the programming problem. In some embodiments, the equivalent of the programming problem comprises a Hamiltonian representative of the polynomial on the bounded integer domain. In some embodiments, the Hamiltonian is usable by the at least one quantum computer to solve the programming problem.

Additional aspects and advantages of the present disclosure will become readily apparent to those skilled in this art from the following detailed description, wherein only illustrative embodiments of the present disclosure are shown and described. As will be realized, the present disclosure is capable of other and different embodiments, and its several details are capable of modifications in various obvious respects, all without departing from the disclosure. Accordingly, the drawings and description are to be regarded as illustrative in nature, and not as restrictive.

INCORPORATION BY REFERENCE

All publications, patents, and patent applications mentioned in this specification are herein incorporated by reference to the same extent as if each individual publication, patent, or patent application was specifically and individually indicated to be incorporated by reference.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features of the invention are set forth with particularity in the appended claims. A better understanding of the features and advantages of the present invention will be obtained by reference to the following detailed description that sets forth illustrative embodiments, in which the principles of the invention are utilized, and the accompanying drawings (also âfigureâ and âFIG.â herein), of which:

FIG. 1 shows a non-limiting example of an Application Program Interface (API) gateway and a queuing unit.

FIG. 2 shows a non-limiting example of an API gateway, a queuing unit, and a database service.

FIG. 3 shows a non-limiting example of a queuing unit, database service, and a cluster manager.

FIG. 4 shows a non-limiting example of a cluster manager and a logging unit.

FIG. 5 shows a non-limiting example of a computing architecture of a cloud platform for accessing shared quantum computing resources.

FIG. 6 shows a non-limiting example of a quantum-enabled computing platform.

FIG. 7 shows a non-limiting example of an analysis tree for decomposing a given problem into sub-problems in quantum and classical computing resources.

FIG. 8 shows a non-limiting example of a method for setting a system of superconducting qubits having a Hamiltonian representative of a polynomial on a bounded integer domain; in this case, a flowchart of all steps used for setting a system of superconducting qubits in such a way.

FIG. 9 shows a non-limiting example of a method for setting a system of superconducting qubits having a Hamiltonian representative of a polynomial on a bounded integer domain; in this case, a diagram of a system comprising of a digital computer interacting with a system of superconducting qubits.

FIG. 10 shows a non-limiting example of a method for setting a system of superconducting qubits having a Hamiltonian representative of a polynomial on a bounded integer domain; in this case, a detailed diagram of a system comprising of a digital computer interacting with a system of superconducting qubits used for computing the local fields and couplers.

FIG. 11 shows a non-limiting example of a method for setting a system of superconducting qubits having a Hamiltonian representative of a polynomial on a bounded integer domain; in this case, a flowchart of a step for providing a polynomial on a bounded integer domain.

FIG. 12 shows a non-limiting example of a method for setting a system of superconducting qubits having a Hamiltonian representative of a polynomial on a bounded integer domain; in this case, a flowchart of a step for providing encoding parameters.

FIG. 13 shows a non-limiting example of a method for setting a system of superconducting qubits having a Hamiltonian representative of a polynomial on a bounded integer domain; in this case, a flowchart of a step for computing the bounded-coefficient encoding.

FIG. 14 shows a non-limiting example of a method for setting a system of superconducting qubits having a Hamiltonian representative of a polynomial on a bounded integer domain; in this case, a flowchart of a step for converting a polynomial on a bounded integer domain to an equivalent polynomial in several binary variables.

DETAILED DESCRIPTION

While various embodiments of the invention have been shown and described herein, it will be obvious to those skilled in the art that such embodiments are provided by way of example only. Numerous variations, changes, and substitutions may occur to those skilled in the art without departing from the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed.

Methods and Systems for Non-Classical Computing on the Cloud

Quantum computing resources may be rare. Access to quantum computing resources may be expensive or such quantum computing resources may be inaccessible given geographic limitations. Even though a user may have direct access to a quantum computer, the user may be required to possess sophisticated expertise to configure the quantum computer and/or choose an adequate quantum algorithm for solving a computational task; otherwise, the user does not gain the benefit from the speedy computations offered by the quantum computer. Even a superior quantum computer may not exhibit any advantage over classical computing resources in solving a problem if the right algorithm, the right problem, and the right parameters are not chosen. On the other hand, from a user's perspective, a computational problem may be a very large computational task involving many smaller sub-tasks. Each of these sub-tasks may possess a different complexity characteristic. Therefore, using the right computing resource, the right algorithm, and the right parameter may be essential to solve the original problem efficiently and/or benefit from the potential quantum speedup.

The present disclosure provides systems and methods that offer quantum-ready services and/or quantum-enabled services. Quantum-ready services may advantageously make it easier for a user to manage quantum resources and switch between a classical or quantum computation resource. Additionally, a quantum-enabled framework may allow users to use both classical and quantum resources in a hybrid manner such that the framework intelligently chooses the right solver and the right parameters for each particular sub-problem or subtask.

The present disclosure provides systems and methods that may allow shared or distributed access to quantum computing resources (e.g., a quantum-ready or quantum-enabled services). The disclosed system may provide quantum computing services (e.g., optimization based on quantum algorithms) on a cloud computing platform. Using a software development kit (SDK), users may not be required to have a deep understanding of the quantum computing resources, implementation, or the knowledge required for solving optimization problems using a quantum computer. For example, use of an SDK to provide a user with shared or distributed access to quantum computing resources is disclosed in PCT International Application PCT/CA2017/050320, âMethods and Systems for Quantum Computing,â which is entirely incorporated herein by reference.

The present disclosure provides systems and methods for facilitating quantum computing in a distributed environment, such as over a network (e.g., in the cloud). For example, a user at a first location may submit a request for a calculation or task to be performed by a quantum computer (e.g., an adiabatic quantum computer) at a second location that is remotely located with respect to the first location. The request may be directed over a network to one or more computer servers, which subsequently direct a request to the quantum computer to perform the calculation or task.

Provided herein are systems and methods that provide optimization services in a distributed computing environment (e.g., the cloud), which may utilize quantum computing technology, such as an adiabatic quantum computer. Methods and systems of the present disclosure enable quantum computing to be relatively and readily scaled across various types of quantum computers and users in various locations, in some cases without a need for users to have a deep understanding of the resources, implementation, or the knowledge required for solving optimization problems using a quantum computer. Systems provided herein may include user interfaces that enable users to perform data analysis in a distributed computing environment (e.g., in the cloud) while taking advantage of quantum technology in the backend.

In some embodiments, systems, media, networks, and methods include a quantum computer, or use of the same. Quantum computation uses quantum bits (qubits), which can be in superpositions of states. A quantum Turing machine is a theoretical model of such a computer, and is also known as a universal quantum computer. Quantum computers share theoretical similarities with non-deterministic and probabilistic computers.

In some embodiments, a quantum computer comprises one or more quantum processors. A quantum computer may be configured to perform one or more quantum algorithms. A quantum computer may store or process data represented by quantum bits (qubits). A quantum computer may be able to solve certain problems much more quickly than any classical computers that use even the best currently available algorithms, like integer factorization using Shor's algorithm or the simulation of quantum many-body systems. There exist quantum algorithms, such as Simon's algorithm, that run faster than any possible probabilistic classical algorithm. Examples of quantum algorithms include, but are not limited to, quantum optimization algorithms, quantum Fourier transforms, amplitude amplifications, quantum walk algorithms, and quantum evolution algorithms. Quantum computers may be able to efficiently solve problems that no classical computer may be able to solve within a reasonable amount of time. Thus, a system disclosed herein utilizes the merits of quantum computing resources to solve complex problems.

Any type of quantum computers may be suitable for the technologies disclosed herein. Examples of quantum computers include, but are not limited to, adiabatic quantum computers, quantum gate arrays, one-way quantum computer, topological quantum computers, quantum Turing machines, superconductor-based quantum computers, trapped ion quantum computers, optical lattices, quantum dot computers, spin-based quantum computers, spatial-based quantum computers, Loss-DiVincenzo quantum computers, nuclear magnetic resonance (NMR) based quantum computers, liquid-NMR quantum computers, solid state NMR Kane quantum computers, electrons-on-helium quantum computers, cavity-quantum-electrodynamics based quantum computers, molecular magnet quantum computers, fullerene-based quantum computers, linear optical quantum computers, diamond-based quantum computers, Bose-Einstein condensate-based quantum computers, transistor-based quantum computers, and rare-earth-metal-ion-doped inorganic crystal based quantum computers. A quantum computer may comprise one or more of: a quantum annealer, an Ising solver, an optical parametric oscillator (OPO), or a gate model of quantum computing.

A system of the present disclosure may include or employ quantum-ready or quantum-enabled computing systems. A quantum-ready computing system may comprise a digital computer operatively coupled to a quantum computer. The quantum computer may be configured to perform one or more quantum algorithms. A quantum-enabled computing system may comprise a quantum computer and a classical computer, the quantum computer and the classical computer operatively coupled to a digital computer. The quantum computer may be configured to perform one or more quantum algorithms for solving a computational problem. The classical computer may comprise at least one classical processor and computer memory, and may be configured to perform one or more classical algorithms for solving a computational problem.

The term âquantum annealerâ and like terms generally refer to a system of superconducting qubits that carries optimization of a configuration of spins in an Ising spin model using quantum annealing, as described, for example, in Farhi, E. et al., âQuantum Adiabatic Evolution Algorithms versus Simulated Annealingâ arXiv.org: quant ph/0201031 (2002), pp. 1-16. An embodiment of such an analog processor is disclosed by McGeoch, Catherine C. and Cong Wang, (2013), âExperimental Evaluation of an Adiabatic Quantum System for Combinatorial Optimizationâ Computing Frontiers,â May 14-16, 2013 (http://www.cs.amherst.edu/ccm/cf14-mcgeoch.pdf) and also disclosed in U.S. Patent Application Publication Number US 2006/0225165.

In some embodiments, a classical computer may be configured to perform one or more classical algorithms. A classical algorithm (or classical computational task) may be an algorithm (or computational task) that is able to be executed by one or more classical computers without the use of a quantum computer, a quantum-ready computing service, or a quantum-enabled computing service. A classical algorithm may be a non-quantum algorithm. A classical computer may be a computer which does not comprise a quantum computer, a quantum-ready computing service, or a quantum-enabled computer. A classical computer may process or store data represented by digital bits (e.g., zeroes (â0â) and ones (â1â)) rather than quantum bits (qubits). Examples of classical computers include, but are not limited to, server computers, desktop computers, laptop computers, notebook computers, sub-notebook computers, netbook computers, netpad computers, set-top computers, media streaming devices, handheld computers, Internet appliances, mobile smartphones, tablet computers, personal digital assistants, video game consoles, and vehicles.

In an aspect, the present disclosure provides a system for quantum-ready optimization. The computing system may comprise a digital computer operatively coupled to a remote quantum computer over a network. The quantum computer may be configured to perform one or more quantum algorithms. The digital computer may comprise at least one computer processor and computer memory. The computer memory may include a computer program with instructions executable by the at least one computer processor to render an application. The application may facilitate use of the quantum computer by a user.

In another aspect, the present disclosure provides a system for quantum-enabled optimization. The computing system may comprise a quantum computer and a classical computer, the quantum computer and the classical computer operatively coupled to a digital computer over a network. The quantum computer may be configured to perform one or more quantum algorithms for solving a computational problem. The classical computer may comprise at least one classical processor and computer memory, and may be configured to perform one or more classical algorithms for solving a computational problem. The digital computer may comprise at least one computer processor and computer memory, wherein the digital computer may include a computer program with instructions executable by the at least one computer processor to render an application. The application may facilitate use of the quantum computer and/or the classical computer by a user.

Some implementations may use quantum computers along with classical computers operating on bits, such as personal desktops, laptops, supercomputers, distributed computing, clusters, cloud-based computing resources, smartphones, or tablets.

The system may include a gateway programmed or configured to receive a request over the network. The request may comprise a computational task. Examples of a computational task include, but are not limited to, search, optimization, statistical analysis, modeling, data processing, etc. In some embodiments, a request may comprise a dataset; for example, a data matrix including variables and observations for creating a modeling or analyzing statistics of the data set. Further, a solution may be derived; for example, an optimal model underlying a given dataset is derived from a quantum computer; a statistical analysis is performed by a quantum computer.

The system may comprise a queuing unit programmed or configured to store and order the request in one or more queues. The system may comprise a cluster manager programmed or configured to create an instance/container (also âworkerâ herein) to (1) translate the request in the queue into one or more quantum machine instructions, (2) deliver the one or more quantum machine instructions to the quantum computer over the network to perform the computational task, and (3) receive one or more solutions from the quantum computer. The one or more solutions may be stored in a database of the system. The system may comprise a logging unit programmed or configured to log an event of the worker.

The system may comprise an interface for a user. In some embodiments, the interface may comprise an application programming interface (API). The interface may provide a programmatic model that abstracts away (e.g., by hiding from the user) the internal details (e.g., architecture and operations) of the quantum computer. In some embodiments, the interface may minimize a need to update the application programs in response to changing quantum hardware. In some embodiments, the interface may remain unchanged when the quantum computer has a change in internal structure.

Gateway

Systems, media, networks, and methods of the present disclosure may comprise a gateway that may be programmed or configured to receive a request from a user. The request may comprise a computational task. In some embodiments, the gateway is programmed or configured to authenticate a user of the system. In some embodiments, the gateway is programmed or configured to monitor system and data security. As an example, a gateway may use secure sockets layer (SSL) for encrypting requests and responses. In some embodiments, a gateway is programmed or configured to route the request to one of the at least one digital processor. In some embodiments, a gateway is programmed or configured to monitor data traffic.

In some embodiments, the systems, media, networks, and methods comprise a queuing unit. In some embodiments, a queuing unit is programmed or configured to place the request in the queue. When a queue comprises more than one request, the more than one requests may be placed in order. The order may be based on first-in-first-out, or based on timing, or based on available quantum computing resources. In some embodiments, a queuing unit is further programmed or configured to reorder the request in the queue. In some embodiments, a queuing unit is responsible for preventing message loss. The tasks submitted may be stored in the queue and may be accessed in order by the microservices that need to work with them.

A gateway may be a microservice used for authentication, routing, security, and monitoring purposes. Referring to FIG. 1 , a request 101 is received by an application programming interface (API) gateway 111 and then forwarded through to one or more target microservices. In some embodiments, when the target microservices are not a

CLAIMS

Claims ( 18 )

What is claimed is:

1. A method for using a computer to generate a request comprising a computational task usable by at least one non-classical computer in communication with said computer over a distributed computing environment, wherein said computer comprises at least one computer processor, said method comprising:

(a) using said at least one computer processor to (i) retrieve a first programming problem from computer memory, and (ii) using a bounded-coefficient encoding to transform said first programming problem from an integer representation to a binary representation to generate a second programming problem from said first programming problem;

(b) generating said request comprising said computational task corresponding to said second programming problem in said computer memory, wherein said computational task is usable by said at least one non-classical computer to solve said second programming problem; and

(c) directing said request from said computer to said non-classical computer over said distributed computing environment.

2. The method of claim 1 , wherein said at least one non-classical computer is configured to perform one or more non-classical algorithms on said second programming problem.

3. The method of claim 1 , wherein said request is generated using an application programming interface (API).

4. The method of claim 1 , wherein said first programming problem comprises a polynomial on a bounded integer domain and integer encoding parameters, and wherein (a) further comprises computing said bounded-coefficient encoding using said integer encoding parameters to generate said second programming problem.

5. The method of claim 4 , wherein (a) further comprises recasting each integer variable of said polynomial to a linear function of binary variables using said bounded-coefficient encoding to yield said second programming problem.

6. The method of claim 5 , further comprising providing constraints on said binary variables for no degeneracy in said bounded-coefficient encoding.

7. The method of claim 4 , wherein said second programming problem comprises a Hamiltonian representative of said polynomial on said bounded integer domain.

8. The method of claim 7 , wherein said Hamiltonian is usable by said at least one non-classical computer to solve said second programming problem.

9. The method of claim 1 , further comprising directing said request from said computer to said at least one non-classical computer over said distributed computing environment.

10. The method of claim 1 , wherein said first programming problem comprises a mixed-integer polynomially constrained polynomial programming problem, and wherein said second programming problem comprises a binary polynomially constrained polynomial programming problem.

11. A system comprising a computer for generating a request comprising a computational task usable by at least one non-classical computer in communication with said computer over a distributed computing environment, wherein said computer comprises at least one computer processor, wherein said computer is configured to:

(a) use said at least one computer processor to (i) retrieve a first programming problem from computer memory, and (ii) use a bounded-coefficient encoding to transform said first programming problem from an integer representation to a binary representation to generate a second programming problem from said first programming problem;

(b) generate said request comprising said computational task corresponding to said second programming problem in said computer memory, wherein said computational task is usable by said at least one non-classical computer to solve said second programming problem; and

(c) directing said request from said computer to said non-classical computer over said distributed computing environment.

12. The system of claim 11 , wherein said computer is configured to generate said request using an application programming interface (API).

13. The system of claim 11 , wherein said first programming problem in comprises a polynomial on a bounded integer domain and integer encoding parameters, and wherein in (b) said computer is configured to compute said bounded-coefficient encoding using said integer encoding parameters to generate said second programming problem.

14. The system of claim 13 , wherein in (b) said computer is configured to recast each integer variable of said polynomial to a linear function of binary variables using said bounded-coefficient encoding to yield said second programming problem.

15. The system of claim 14 , wherein said computer is configured to provide constraints on said binary variables for no degeneracy in said bounded-coefficient encoding.

16. The system of claim 13 , wherein said second programming problem comprises a Hamiltonian representative of said polynomial on said bounded integer domain.

17. The system of claim 11 , wherein said computer is configured to direct said request to said at least one non-classical computer over said distributed computing environment.

18. The system of claim 11 , wherein said first programming problem comprises a mixed-integer polynomially constrained polynomial programming problem, and wherein said second programming problem comprises a binary polynomially constrained polynomial programming problem.

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