A user interface (UI), data structures and algorithms facilitate programming, analyzing, debugging, embedding, and/or modifying problems that are embedded or to be embedded on an analog processor (e.g., quantum processor), increasing computational efficiency and/or accuracy of problem solutions. The UI provides graph representations (e.g., source graph, target graph and correspondence therebetween) with nodes and edges which may map to hardware components (e.g., qubits, couplers) of the analog processor. Characteristics of solutions are advantageously represented spatially associated (e.g., overlaid or nested) with characteristics of a problem. Characteristics (e.g., bias state) may be represented by color, pattern, values, icons. Issues (e.g., broken chains) may be detected and alerts provided. Problem representations may be modified via the UI, and a computer system may autonomously generate new instances of the problem representation, update data structures, embed the new instance and cause the new instance to be executed by the analog processor.

A method for solving a problem using a quantum oracle may include a classical computer program: selecting an implementation for a problem from one or more different implementations in a dictionary of implementations; preparing the implementation using bounds on a quantum circuit to solve the problem and encoding input data for the problem into a quantum state; selecting an oracle to monitor and measure the quantum state based on the implementation, wherein the oracle identifies a pattern of interest in the quantum state; transpiling the prepared implementation and the oracle into a set of machine-readable instructions; sending the set of machine-readable instructions to a quantum computer, wherein the quantum computer executes the set of machine-readable instructions and returns an array of results, the array of results representing measurements of the quantum state using the oracle; and analyzing the array of results and outputting the analysis.

Systems and methods are configured to provide a first problem to be solved to a network of memristors. A second problem to be solved can be gradually provided to the network of memristors. Controlled noise can be applied to the network of memristors for at least a portion of time during which the second problem is “gradually” provided to the network of memristors. A solution to the second problem can be determined.

A public-key scheme of Homomorphic Encryption (HE) in the framework Quotient Algebra Partition (QAP) comprises: encryption, computation and decryption. With the data receiver choosing a partition or a QAP, [n, k, C], a public key Key.sub.pub=(VQ.sub.en, Gen.sub.ε) and a private key Key.sub.priv=.sup.†P.sup.† are produced, where VQ.sub.en is the product of an n-qubit permutation V and an n-qubit encoding operator Q.sub.en, Gen.sub.ε an error generator randomly provides a dressed operator Ē=V.sup.†EV spinor error E of [n, k, C]. Then, by Key.sub.pub, the sender can encode his k-qubit plaintext Ix) into an n-qubit ciphertext |ψ.sub.en, which is transmitted to the cloud. The receiver prepares the instruction of encoded computation U.sub.en=PV.sup.†Q.sub.en.sup.† for a given k-qubit action M and sends to cloud, where is the error-correction operator of [n, k, C], =I.sub.2.sub.n−k.Math.M the tensor product of the (n−k)-qubit identity I.sub.2.sub.n−k and M , and V.sup.†Q.sup.†.sub.en and P the complex-transposes of VQ.sub.en and

Monte Carlo methods are described for efficiently simulating a separately frustration-free Hamiltonian of a many-body quantum system on a classical computer. Also disclosed are methods for designing a separately frustration-free Hamiltonian to simulate a prescribed quantum system. Further described are methods for solving a prescribed computational problem by designing a quantum system having a separately frustration-free Hamiltonian and simulating the designed quantum system via Monte Carlo on a classical computer.

Monte Carlo methods are described for efficiently simulating a separately frustration-free Hamiltonian of a many-body quantum system on a classical computer. Also disclosed are methods for designing a separately frustration-free Hamiltonian to simulate a prescribed quantum system. Further described are methods for solving a prescribed computational problem by designing a quantum system having a separately frustration-free Hamiltonian and simulating the designed quantum system via Monte Carlo on a classical computer.

Systems, computer-implemented methods and/or computer program products that can facilitate providing a defined parameter, determining whether to employ the defined parameter for a variational quantum algorithm, and running the variational quantum algorithm on a quantum system, are provided. According to an embodiment, a system can comprise a memory that stores computer executable components and a processor that executes the computer executable components stored in the memory. The computer executable components can comprise a decision component that determines, based upon an uncertainty prediction regarding the usability of the defined parameter that has been output from a machine learning model, whether to employ the defined parameter in a variational quantum algorithm, such as run on a quantum system.

Various embodiments of the present disclosure provide systems and methods for generally generating and transforming physical quantum representations of multi-dimensional tensor data objects. Specifically, various embodiments enable the rapid and efficient generation of a physical quantum representation representing the Fourier transform of a multi-dimensional tensor data object based at least in part on manipulating another physical quantum representation of the multi-dimensional tensor data object itself via quantum manipulation operations. Information may be extracted from the generated physical quantum representation to determine the Fourier transform of the multi-dimensional tensor data object. Accordingly, various embodiments may comprise quantum manipulation operations for a tensor-form quantum Fourier transform (TQFT) for a multi-dimensional tensor data object. Various embodiments for the TQFT are advantageously comprehensive, versatile, and applicable to any quantum representation form for a multi-dimensional tensor data object. The TQFT may be performed in any quantum computing system and/or simulated quantum computing system.

A method for compiling executable code for execution on a computer includes: (a) receiving source code instructing the computer to execute an interval test to determine whether an interval defined by integers a and b encloses an integer x; (b) decomposing the interval test into a first comparison between the integer a and the integer x and a second comparison between the integer b and the integer x; and (c) returning instruction code directing the computer to evaluate the first and second comparisons cooperatively, at lower complexity than the combined complexities of the first and second comparisons enacted separately.

A method for compiling executable code for execution on a computer includes: (a) receiving source code instructing the computer to execute an interval test to determine whether an interval defined by integers a and b encloses an integer x; (b) decomposing the interval test into a first comparison between the integer a and the integer x and a second comparison between the integer b and the integer x; and (c) returning instruction code directing the computer to evaluate the first and second comparisons cooperatively, at lower complexity than the combined complexities of the first and second comparisons enacted separately.