Exponential quantum advantages for practical non-Hermitian eigenproblems
arXiv:2401.12091 · doi:10.1103/3n8f-k8pl
Abstract
Non-Hermitian physics has emerged as a rich field of study, with applications ranging from -symmetry breaking and skin effects to non-Hermitian topological phase transitions. Yet most studies remain restricted to small-scale or classically tractable systems. While quantum computing has shown strong performance in Hermitian eigenproblems, its extension to the non-Hermitian regime remains largely unexplored. Here, we develop a quantum algorithm to address general non-Hermitian eigenvalue problems, specifically targeting eigenvalues near a given line in the complex plane -- thereby generalizing previous results on ground state energy and spectral gap estimation for Hermitian matrices. Our method combines a fuzzy quantum eigenvalue detector with a divide-and-conquer strategy to efficiently isolate relevant eigenvalues. This yields a provable exponential quantum speedup for non-Hermitian eigenproblems. Furthermore, we discuss the broad applications in detecting spontaneous -symmetry breaking, estimating Liouvillian gaps, and analyzing classical Markov processes. These results highlight the potential of quantum algorithms in tackling challenging problems across quantum physics and beyond.
8+15 pages, 3+5 figures
References in corpus (31)
- A variational eigenvalue solver on a quantum processor
- Exceptional Topology of Non-Hermitian Systems
- Non-Hermitian Physics
- Adiabatic Quantum Computing
- Symmetry and Topology in Non-Hermitian Physics
- Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
- Floquet Engineering of Quantum Materials
- Non-Hermitian Boundary Modes
- Hamiltonian Simulation by Qubitization
- Colloquium: Understanding Quantum Weak Values: Basics and Applications
- Non-Hermitian skin effect and chiral damping in open quantum systems
- Topological phase transition in non-Hermitian quasicrystals
- Observation of parity-time symmetry breaking in a single spin system
- Non-Hermitian topological phenomena: A review
- Variational quantum simulation of general processes
- Non-Hermitian Kondo effect in ultracold alkaline-earth atoms
- Near-optimal ground state preparation
- Exact Bethe ansatz spectrum of a tight-binding chain with dephasing noise
- Ground state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices
- Topological Phase Transition driven by Infinitesimal Instability: Majorana Fermions in Non-Hermitian Spintronics
- Preparing ground states of quantum many-body systems on a quantum computer
- Resolving Discrepancy between Liouvillian Gap and Relaxation Time in Boundary-Dissipated Quantum Many-Body Systems
- Driven quantum dynamics: will it blend?
- Single-ancilla ground state preparation via Lindbladians
- Noisy Spins and the Richardson-Gaudin Model
- Variational Quantum Algorithm for Non-equilibrium Steady States
- Solving the Liouvillian Gap with Artificial Neural Networks
- Degeneracies and symmetry breaking in pseudo-Hermitian matrices
- Exponential size scaling of the Liouvillian gap in boundary-dissipated systems with Anderson localization
- Circuit complexity of quantum access models for encoding classical data
- Variational quantum algorithms for scanning the complex spectrum of non-Hermitian systems