This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic research and industrial applications. TNs, originally developed in quantum mechanics, have recently shown promise in solving partial differential equations (PDEs) due to their potential for exponential speedups over classical algorithms. Our study successfully employs TNs to solve linear elasticity equations with billions of degrees of freedom, achieving exponential reductions in both memory usage and computational time. These results demonstrate the practical viability of TNs as a powerful classical backend for executing quantum-inspired algorithms with significant efficiency gains. This work is based on our research conducted with IKERLAN.
Mixed-integer linear programming (MILP) plays a crucial role in artificial intelligence, biochemistry, finance, cryptography, etc. Notwithstanding popular for decades, the researches of MILP solvers are still limited by the resource consumption caused by complexity and failure of Moore's Law. Quantum-inspired Ising machines, as a new computing paradigm, can be used to solve integer programming problems by reducing them into Ising models. Therefore, it is necessary to understand the technical evolution of quantum inspired solvers to break the bottleneck. In this paper, the concept and tradition…
Recently, inspired by quantum annealing, many solvers specialized for unconstrained binary quadratic programming problems have been developed. For further improvement and application of these solvers, it is important to clarify the differences in their performance for various types of problems. In this study, the performance of four quadratic unconstrained binary optimization problem solvers, namely D-Wave Hybrid Solver Service (HSS), Toshiba Simulated Bifurcation Machine (SBM), Fujitsu DigitalAnnealer (DA), and simulated annealing on a personal computer, was benchmarked. The problems used for…
The increasing complexity of required computational tasks alongside the inherent limitations in conventional computing calls for disruptive innovation. LightSolver devised a new quantum-inspired computing paradigm, which utilizes an all-optical platform for solving hard optimization problems. In this work, LightSolver introduces its digital simulator and joins the 3-Regular 3-XORSAT (3R3X) challenge, which aims to map the best available state-of-the-art classical and quantum solvers. So far, the challenge has resulted in a clear exponential barrier in terms of time-to-solution (TTS), preventin…
In this paper we detail a classical algorithmic approach to the k-satisfiability (k-SAT) problem that is inspired by the quantum amplitude amplification algorithm. This work falls under the emerging field of quantum-inspired classical algorithms. To propose our modification, we adopt an existing problem model for k-SAT known as Universal SAT (UniSAT), which casts the Boolean satisfiability problem as a non-convex global optimization over a real-valued space. The quantum-inspired modification to UniSAT is to apply a conditioning operation to the objective function that has the effect of "amplif…
A Quantum Walk Inspired Qubit Lattice Algorithm for Simulating Electromagnetic Wave Propagation and Scattering in Conservative and Dissipative Magnetized Plasmas
Applied Research Laboratories, The University of Texas at Austin（德克萨斯大学奥斯汀分校应用研究实验室）
Two contrasting algorithmic paradigms for constraint satisfaction problems are successive local explorations of neighboring configurations versus producing new configurations using global information about the problem (e.g. approximating the marginals of the probability distribution which is uniform over satisfying configurations). This paper presents new algorithms for the latter framework, ultimately producing estimates for satisfying configurations using methods from Boolean Fourier analysis. The approach is broadly inspired by the quantum amplitude amplification algorithm in that it maxima…
We optimise a translationally invariant, sequential quantum circuit on a superconducting quantum device to simulate the groundstate of the quantum Ising model through its quantum critical point. We further demonstrate how the dynamical quantum critical point found in quenches of this model across its quantum critical point can be simulated. Our approach avoids finite-size scaling effects by using sequential quantum circuits inspired by infinite matrix product states. We provide efficient circuits and a variety of error mitigation strategies to implement, optimise and time-evolve these states.
Multi-Objective Optimization with Quantum-Annealing-Inspired Algorithms
Southern University of Science and Technology（南方科技大学）；International Quantum Academy（国际量子研究院）；University of Science and Technology of China（中国科学技术大学）；Hong Kong Polytechnic University（香港理工大学）
The excitation of vibrational modes in molecules affects the outcome of chemical reactions, for example by providing molecules with sufficient energy to overcome activation barriers. In this work, we introduce a quantum algorithm for simulating molecular vibrational excitations during vibronic transitions. We discuss how a special-purpose quantum computer can be programmed with molecular data to optimize a vibronic process such that desired modes get excited during the transition. We investigate the effect of such excitations on selective bond dissociation in pyrrole and butane during photoche…
We present a quantum algorithm for simulating the dynamics of Hamiltonians that are not necessarily sparse. Our algorithm is based on the input model where the entries of the Hamiltonian are stored in a data structure in a quantum random access memory (qRAM) which allows for the efficient preparation of states that encode the rows of the Hamiltonian. We use a linear combination of quantum walks to achieve poly-logarithmic dependence on precision. The time complexity of our algorithm, measured in terms of the circuit depth, is $O(t\sqrt{N}\|H\|\,\mathrm{polylog}(N, t\|H\|, 1/ε))$, where $t$ is …
SparQSim: Simulating Scalable Quantum Algorithms via Sparse Quantum State Representations
Key Laboratory of Quantum Information, Chinese Academy of Sciences, School of Physics, University of Science and Technology of China（中国科学院量子信息重点实验室，中国科学技术大学物理学院）；CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学中科院量子信息与量子Physics卓越创新中心）；Institute of Artificial Intelligence, Hefei Comprehensive National Science Center（合肥综合性国家科学中心人工智能研究院）；Institute of Advanced Technology, University of Science and Technology of China（中国科学技术大学先进技术研究院）；Origin Quantum Computing（本源量子）
Problems related to wavelength assignment (WA) in optical communications networks involve allocating transmission wavelengths for known transmission paths between nodes that minimize a certain objective function, for example, the total number of wavelengths. Playing a central role in modern telecommunications, this problem belongs to NP-complete class for a general case, so that obtaining optimal solutions for industry relevant cases is exponentially hard. In this work, we propose and develop a quantum-inspired algorithm for solving the wavelength assignment problem. We propose an advanced emb…
Satisfying Quantum Codes: Physics-Informed and Hardware-Aware Code Design with SAT Solvers
Michigan State University（密歇根州立大学）；Johns Hopkins Applied Physics Laboratory（约翰斯·霍普金斯大学应用物理实验室）；Johns Hopkins University（约翰斯·霍普金斯大学）；Unitary Foundation（Unitary基金会）；University of New Mexico（新墨西哥大学）
We develop a workflow to use current quantum computing hardware for solving quantum many-body problems, using the example of the fermionic Hubbard model. Concretely, we study a four-site Hubbard ring that exhibits a transition from a product state to an intrinsically interacting ground state as hopping amplitudes are changed. We locate this transition and solve for the ground state energy with high quantitative accuracy using a variational quantum algorithm executed on an IBM quantum computer. Our results are enabled by a variational ansatz that takes full advantage of the maximal set of commu…
Russian Quantum Center（俄罗斯量子中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；University of Oxford（牛津大学）；P. N. Lebedev Physics Institute（P. N. 列别杰夫物理研究所）
Quantum simulators and processors are rapidly improving nowadays, but they are still not able to solve complex and multidimensional tasks of practical value. However, certain numerical algorithms inspired by the physics of real quantum devices prove to be efficient in application to specific problems, related, for example, to combinatorial optimization. Here we implement a numerical annealer based on simulating the coherent Ising machine as a tool to sample from a high-dimensional Boltzmann probability distribution with the energy functional defined by the classical Ising Hamiltonian. Samples …
