Compact quantum algorithms for time-dependent differential equations

• URL: http://arxiv.org/abs/2405.09767v2
• Date: Mon, 07 Oct 2024 16:01:16 GMT
• Title: Compact quantum algorithms for time-dependent differential equations
• Authors: Sachin S. Bharadwaj, Katepalli R. Sreenivasan,
• Abstract summary: We build on an idea based on linear combination of unitaries to simulate non-unitary, non-Hermitian quantum systems. We generate hybrid quantum-classical algorithms that efficiently perform iterative matrix-vector multiplication and matrix inversion operations.
• Score: 0.0
• License:
• Abstract: Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference to fluid equations. We build on an idea based on linear combination of unitaries to simulate non-unitary, non-Hermitian quantum systems, and generate hybrid quantum-classical algorithms that efficiently perform iterative matrix-vector multiplication and matrix inversion operations. Though these algorithms are end-to-end, they require relatively low-depth quantum circuits and protect quantum advantage, with the best-case asymptotic complexities, which we show} are near-optimal. We demonstrate the performance of the algorithms by conducting: (a) fully gate level, state-vector simulations using an in-house, high performance, quantum simulator called QFlowS; (b) experiments on a real quantum device; and (c) noisy simulations using Qiskit Aer. We also provide device specifications such as error-rates (noise) and state sampling (measurement) to accurately perform convergent flow simulations on noisy devices. The results offer evidence that the proposed algorithm is amenable for use on near-term quantum devices.

Related papers

• Performance Benchmarking of Quantum Algorithms for Hard Combinatorial Optimization Problems: A Comparative Study of non-FTQC Approaches [0.0]
  This study systematically benchmarks several non-fault-tolerant quantum computing algorithms across four distinct optimization problems. Our benchmark includes noisy intermediate-scale quantum (NISQ) algorithms, such as the variational quantum eigensolver. Our findings reveal that no single non-FTQC algorithm performs optimally across all problem types, underscoring the need for tailored algorithmic strategies.
  arXiv  Detail & Related papers  (2024-10-30T08:41:29Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
  Quantum computing sets the foundation for new ways of designing algorithms. New challenges arise concerning which field quantum speedup can be achieved. Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
  arXiv  Detail & Related papers  (2024-02-26T09:32:07Z)
• Two quantum algorithms for solving the one-dimensional advection-diffusion equation [0.0]
  Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection-diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared point-by-point with each other.
  arXiv  Detail & Related papers  (2023-12-30T21:23:15Z)
• Quantum Clustering with k-Means: a Hybrid Approach [117.4705494502186]
  We design, implement, and evaluate three hybrid quantum k-Means algorithms. We exploit quantum phenomena to speed up the computation of distances. We show that our hybrid quantum k-Means algorithms can be more efficient than the classical version.
  arXiv  Detail & Related papers  (2022-12-13T16:04:16Z)
• Decomposition of Matrix Product States into Shallow Quantum Circuits [62.5210028594015]
  tensor network (TN) algorithms can be mapped to parametrized quantum circuits (PQCs) We propose a new protocol for approximating TN states using realistic quantum circuits. Our results reveal one particular protocol, involving sequential growth and optimization of the quantum circuit, to outperform all other methods.
  arXiv  Detail & Related papers  (2022-09-01T17:08:41Z)
• An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation [55.41644538483948]
  Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in chip size and error rates. We derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions. The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond $mathcalO(103)$ spins.
  arXiv  Detail & Related papers  (2021-08-06T19:38:03Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Randomizing multi-product formulas for Hamiltonian simulation [2.2049183478692584]
  We introduce a scheme for quantum simulation that unites the advantages of randomized compiling on the one hand and higher-order multi-product formulas on the other. Our framework reduces the circuit depth by circumventing the need for oblivious amplitude amplification. Our algorithms achieve a simulation error that shrinks exponentially with the circuit depth.
  arXiv  Detail & Related papers  (2021-01-19T19:00:23Z)
• Efficient calculation of gradients in classical simulations of variational quantum algorithms [0.0]
  We present a novel derivation of an emulation strategy to precisely calculate the gradient in O(P) time. Our strategy is very simple, uses only 'apply gate', 'clone state' and 'inner product' primitives. It is compatible with gate parallelisation schemes, and hardware accelerated and distributed simulators.
  arXiv  Detail & Related papers  (2020-09-06T21:39:44Z)
• Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices [0.0]
  We introduce a quantum solver of contracted eigenvalue equations, the quantum analogue of classical methods for the energies. We demonstrate the algorithm though computations on both a quantum simulator and two IBM quantum processing units.
  arXiv  Detail & Related papers  (2020-04-23T18:35:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.