High-order quantum algorithm for solving linear differential equations

2010/10/31 by Dominic W. Berry, Dominic W Berry · 6 citations
Computer Science · Mathematics · Physics and Astronomy · #Differential equation #Linear differential equation #Linear scale #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum algorithm for linear systems of equations #Quantum computer #Quantum many-body systems #Quantum phase estimation algorithm #cs.NA #math.NA #quant-ph

paper · pdf · doi:10.1088/1751-8113/47/10/105301

published as J. Phys. A: Math. Theor. 47, 105301 (2014) · 14 pages, improved efficiency

arxiv created 2014/01/28 · openalex publication_date 2014/02/19 · arxiv updated 2014/02/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms to general inhomogeneous sparse linear differential equations, which describe many classical physical systems. We examine the use of high-order methods to improve the efficiency. These provide scaling close to Δ t² in the evolution time Δ t. As with other algorithms of this type, the solution is encoded in amplitudes of the quantum state, and it is possible to extract global features of the solution.

Citations

• A special stability problem for linear multistep methods
• Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
• On the Relationship Between Continuous- and Discrete-Time Quantum Walk
• Simulating physics with computers

Cited by

• PolyQROM: Orthogonal-Polynomial-Based Quantum Reduced-Order Model for Flow Field Analysis
• Hybrid Quantum-Classical Algorithm for Hamiltonian Simulation
• Physics-Informed Quantum Machine Learning with Hard Constraint Embedding for Nonlinear Differential Equations of the First Order
• A variational eigenvalue solver on a photonic quantum processor
• Quantum Simulation-Based Optimization for Cooling System Design
• Linear and Logarithmic Time Compositions of Quantum Many-Body Operators

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