REVIEW 3 cited by
Qubit-Efficient Quantum Algorithm for Linear Differential Equations
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Qubit-Efficient Quantum Algorithm for Linear Differential Equations
abstract
As quantum hardware rapidly advances toward the early fault-tolerant era, a key challenge is to develop quantum algorithms that are not only theoretically sound but also hardware-friendly on near-term devices. In this work, we propose a quantum algorithm for solving linear ordinary differential equations (ODEs) with a provable runtime guarantee. Our algorithm uses only a single ancilla qubit, and is locality preserving, i.e., when the coefficient matrix of the ODE is $k$-local, the algorithm only needs to implement the time evolution of $(k+1)$-local Hamiltonians. We also discuss the connection between our proposed algorithm and Lindbladian simulation as well as its application to the interacting Hatano-Nelson model, a widely studied non-Hermitian model with rich phenomenology.
Forward citations
Cited by 3 Pith papers
-
Circuit Depth Reduction of One-Ancilla Quantum Differential Equation Solver via Extrapolation
Classical step-size extrapolation reduces the maximum single-run circuit depth of a one-ancilla quantum ODE solver from O(1/ε) to O(polylog(1/ε)) without adding ancillae.
-
Quantum Differential Equation Solvers with Low State Preparation Cost: Eliminating the Time Dependence in Dissipative Equations
For strictly dissipative linear ODEs, quantum solvers based on time-marching or LCHS achieve query complexity O(polylog(1/ε)) that is independent of the evolution time T.
-
Circuit-Efficient Randomized Quantum Simulation of Non-Unitary Dynamics with Observable-Driven and Symmetry-Aware Designs
A randomized compilation of LCHS for non-unitary dynamics, with an observable-driven variant and a symmetry-aware sampler, claims reduced ancilla and circuit depth at the cost of more repetitions.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.