Browse
Submit Data
Databases
API
Help

Dataset Information

25 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Quantum Annealing for Prime Factorization.

ABSTRACT: We have developed a framework to convert an arbitrary integer factorization problem to an executable Ising model by first writing it as an optimization function then transforming the k-bit coupling (k ? 3) terms to quadratic terms using ancillary variables. Our resource-efficient method uses [Formula: see text] binary variables (qubits) for finding the factors of an integer N. We present how to factorize 15, 143, 59989, and 376289 using 4, 12, 59, and 94 logical qubits, respectively. This method was tested using the D-Wave 2000Q for finding an embedding and determining the prime factors for a given composite number. The method is general and could be used to factor larger integers as the number of available qubits increases, or combined with other ad hoc methods to achieve better performances for specific numbers.

SUBMITTER: Jiang S

PROVIDER: S-EPMC6281593 | biostudies-literature | 2018 Dec

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Quantum Annealing for Prime Factorization.

Jiang Shuxian S Britt Keith A KA McCaskey Alexander J AJ Humble Travis S TS Kais Sabre S

Scientific reports 20181205 1

We have developed a framework to convert an arbitrary integer factorization problem to an executable Ising model by first writing it as an optimization function then transforming the k-bit coupling (k ≥ 3) terms to quadratic terms using ancillary variables. Our resource-efficient method uses [Formula: see text] binary variables (qubits) for finding the factors of an integer N. We present how to factorize 15, 143, 59989, and 376289 using 4, 12, 59, and 94 logical qubits, respectively. This method ...[more]

PMID: 30518780

Similar Datasets

Prime factorization using quantum annealing and computational algebraic geometry.

Project description:We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gröbner bases. We present a novel autonomous algorithm which combines the two approaches and leads to the factorization of all bi-primes up to just over 200000, the largest number factored to date using a quantum processor. We also explain how Gröbner bases can be used to reduce the degree of Hamiltonians.

| S-EPMC5318873 | biostudies-literature

Reinforcement Quantum Annealing: A Hybrid Quantum Learning Automata.

Project description:We introduce the notion of reinforcement quantum annealing (RQA) scheme in which an intelligent agent searches in the space of Hamiltonians and interacts with a quantum annealer that plays the stochastic environment role of learning automata. At each iteration of RQA, after analyzing results (samples) from the previous iteration, the agent adjusts the penalty of unsatisfied constraints and re-casts the given problem to a new Ising Hamiltonian. As a proof-of-concept, we propose a novel approach for casting the problem of Boolean satisfiability (SAT) to Ising Hamiltonians and show how to apply the RQA for increasing the probability of finding the global optimum. Our experimental results on two different benchmark SAT problems (namely factoring pseudo-prime numbers and random SAT with phase transitions), using a D-Wave 2000Q quantum processor, demonstrated that RQA finds notably better solutions with fewer samples, compared to the best-known techniques in the realm of quantum annealing.

| S-EPMC7224393 | biostudies-literature

Prime factorization algorithm based on parameter optimization of Ising model.

Project description:This paper provides a new (second) way, which is completely different from Shor's algorithm, to show the optimistic potential of a D-Wave quantum computer for deciphering RSA and successfully factoring all integers within 10000. Our method significantly reduced the local field coefficient [Formula: see text] and coupling term coefficient [Formula: see text] by more than 33% and 26%, respectively, of those of Ising model, which can further improve the stability of qubit chains and improve the upper bound of integer factorization. In addition, our results obtained the best index (20-bit integer (1028171)) of quantum computing for deciphering RSA via the quantum computing software environment provided by D-Wave. Furthermore, Shor's algorithm requires approximately 40 qubits to factor the integer 1028171, which is far beyond the capacity of universal quantum computers. Thus, post quantum cryptography should further consider the potential of the D-Wave quantum computer for deciphering the RSA cryptosystem in future.

| S-EPMC7188840 | biostudies-literature

Hybrid quantum annealing via molecular dynamics.

Project description:A novel quantum-classical hybrid scheme is proposed to efficiently solve large-scale combinatorial optimization problems. The key concept is to introduce a Hamiltonian dynamics of the classical flux variables associated with the quantum spins of the transverse-field Ising model. Molecular dynamics of the classical fluxes can be used as a powerful preconditioner to sort out the frozen and ambivalent spins for quantum annealers. The performance and accuracy of our smooth hybridization in comparison to the standard classical algorithms (the tabu search and the simulated annealing) are demonstrated by employing the MAX-CUT and Ising spin-glass problems.

| S-EPMC8056001 | biostudies-literature

Finding Hadamard Matrices by a Quantum Annealing Machine.

Project description:Finding a Hadamard matrix (H-matrix) among the set of all binary matrices of corresponding order is a hard problem, which potentially can be solved by quantum computing. We propose a method to formulate the Hamiltonian of finding H-matrix problem and address its implementation limitation on existing quantum annealing machine (QAM) that allows up to quadratic terms, whereas the problem naturally introduces higher order ones. For an M-order H-matrix, such a limitation increases the number of variables from M2 to (M3 + M2 - M)/2, which makes the formulation of the Hamiltonian too exhaustive to do by hand. We use symbolic computing techniques to manage this problem. Three related cases are discussed: (1) finding N < M orthogonal binary vectors, (2) finding M-orthogonal binary vectors, which is equivalent to finding a H-matrix, and (3) finding N-deleted vectors of an M-order H-matrix. Solutions of the problems by a 2-body simulated annealing software and by an actual quantum annealing hardware are also discussed.

| S-EPMC6779766 | biostudies-literature

Nonnegative/Binary matrix factorization with a D-Wave quantum annealer.

Project description:D-Wave quantum annealers represent a novel computational architecture and have attracted significant interest. Much of this interest has focused on the quantum behavior of D-Wave machines, and there have been few practical algorithms that use the D-Wave. Machine learning has been identified as an area where quantum annealing may be useful. Here, we show that the D-Wave 2X can be effectively used as part of an unsupervised machine learning method. This method takes a matrix as input and produces two low-rank matrices as output-one containing latent features in the data and another matrix describing how the features can be combined to approximately reproduce the input matrix. Despite the limited number of bits in the D-Wave hardware, this method is capable of handling a large input matrix. The D-Wave only limits the rank of the two output matrices. We apply this method to learn the features from a set of facial images and compare the performance of the D-Wave to two classical tools. This method is able to learn facial features and accurately reproduce the set of facial images. The performance of the D-Wave shows some promise, but has some limitations. It outperforms the two classical codes in a benchmark when only a short amount of computational time is allowed (200-20,000 microseconds), but these results suggest heuristics that would likely outperform the D-Wave in this benchmark.

| S-EPMC6287781 | biostudies-literature

Solving Set Cover with Pairs Problem using Quantum Annealing.

Project description:Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that plays an important role in networking, computational biology, and biochemistry. We show an explicit construction of Ising Hamiltonians whose ground states encode the solution of SCP instances. We numerically simulate the time-dependent Schrödinger equation in order to test the performance of quantum annealing for random instances and compare with that of simulated annealing. We also discuss explicit embedding strategies for realizing our Hamiltonian construction on the D-wave type restricted Ising Hamiltonian based on Chimera graphs. Our embedding on the Chimera graph preserves the structure of the original SCP instance and in particular, the embedding for general complete bipartite graphs and logical disjunctions may be of broader use than that the specific problem we deal with.

| S-EPMC5037405 | biostudies-literature

Quantum versus simulated annealing in wireless interference network optimization.

Project description:Quantum annealing (QA) serves as a specialized optimizer that is able to solve many NP-hard problems and that is believed to have a theoretical advantage over simulated annealing (SA) via quantum tunneling. With the introduction of the D-Wave programmable quantum annealer, a considerable amount of effort has been devoted to detect and quantify quantum speedup. While the debate over speedup remains inconclusive as of now, instead of attempting to show general quantum advantage, here, we focus on a novel real-world application of D-Wave in wireless networking-more specifically, the scheduling of the activation of the air-links for maximum throughput subject to interference avoidance near network nodes. In addition, D-Wave implementation is made error insensitive by a novel Hamiltonian extra penalty weight adjustment that enlarges the gap and substantially reduces the occurrence of interference violations resulting from inevitable spin bias and coupling errors. The major result of this paper is that quantum annealing benefits more than simulated annealing from this gap expansion process, both in terms of ST99 speedup and network queue occupancy. It is the hope that this could become a real-word application niche where potential benefits of quantum annealing could be objectively assessed.

| S-EPMC4867427 | biostudies-literature

Quantum annealing with all-to-all connected nonlinear oscillators.

Project description:Quantum annealing aims at solving combinatorial optimization problems mapped to Ising interactions between quantum spins. Here, with the objective of developing a noise-resilient annealer, we propose a paradigm for quantum annealing with a scalable network of two-photon-driven Kerr-nonlinear resonators. Each resonator encodes an Ising spin in a robust degenerate subspace formed by two coherent states of opposite phases. A fully connected optimization problem is mapped to local fields driving the resonators, which are connected with only local four-body interactions. We describe an adiabatic annealing protocol in this system and analyse its performance in the presence of photon loss. Numerical simulations indicate substantial resilience to this noise channel, leading to a high success probability for quantum annealing. Finally, we propose a realistic circuit QED implementation of this promising platform for implementing a large-scale quantum Ising machine.

| S-EPMC5472748 | biostudies-literature

Efficiency of quantum vs. classical annealing in nonconvex learning problems.

Project description:Quantum annealers aim at solving nonconvex optimization problems by exploiting cooperative tunneling effects to escape local minima. The underlying idea consists of designing a classical energy function whose ground states are the sought optimal solutions of the original optimization problem and add a controllable quantum transverse field to generate tunneling processes. A key challenge is to identify classes of nonconvex optimization problems for which quantum annealing remains efficient while thermal annealing fails. We show that this happens for a wide class of problems which are central to machine learning. Their energy landscapes are dominated by local minima that cause exponential slowdown of classical thermal annealers while simulated quantum annealing converges efficiently to rare dense regions of optimal solutions.

| S-EPMC5816144 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data