REVIEW 4 cited by
High-precision quantum algorithms for partial 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
abstract
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for linear ordinary differential equations are well established, the best previous quantum algorithms for linear partial differential equations (PDEs) have complexity $\mathrm{poly}(1/\epsilon)$, where $\epsilon$ is the error tolerance. By developing quantum algorithms based on adaptive-order finite difference methods and spectral methods, we improve the complexity of quantum algorithms for linear PDEs to be $\mathrm{poly}(d, \log(1/\epsilon))$, where $d$ is the spatial dimension. Our algorithms apply high-precision quantum linear system algorithms to systems whose condition numbers and approximation errors we bound. We develop a finite difference algorithm for the Poisson equation and a spectral algorithm for more general second-order elliptic equations.
Forward citations
Cited by 4 Pith papers
-
Structure-Preserving Quantum Simulation of Wave Equations on a Trapped-Ion Processor
On Quantinuum H2-2, Fourier-based structure-preserving circuits resolve subdomain kinetic-energy dynamics for structured 1D/2D acoustic and Dirac wave problems up to 4096 encoded degrees of freedom with MAE ~0.006–0.024.
-
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.
-
Variational Quantum Solutions to the Advection-Diffusion Equation for Applications in Fluid Dynamics
Hybrid variational quantum algorithm solves the advection-diffusion equation on small systems using current noisy IBM quantum hardware, with claimed logarithmic scaling in vector space dimension.
-
A Quantum Path to Partial Differential Equations
Lecture notes that organize quantum PDE algorithms around block encodings of finite-difference and finite-element operators, tracking discretization, preparation, normalization, postselection, and measurement costs.
Discussion (0). Sign in to comment.