Quantum linear system solver based on time-optimal adiabatic quantum computing and quantum approximate optimization algorithm

09/12/2019
by   Dong An, et al.
0

We demonstrate that with an optimally tuned scheduling function, adiabatic quantum computing (AQC) can solve a quantum linear system problem (QLSP) with O(κ/ϵ) runtime, where κ is the condition number, and ϵ is the target accuracy. This achieves the optimal time complexity with respect to κ. The success of the time-optimal AQC implies that the quantum approximate optimization algorithm (QAOA) can also achieve the O(κ) complexity with respect to κ. Our method is applicable to general non-Hermitian matrices (possibly dense), but the efficiency can be improved when restricted to Hermitian matrices, and further to Hermitian positive definite matrices. Numerical results indicate that QAOA can yield the lowest runtime compared to the time-optimal AQC, vanilla AQC, and the recently proposed randomization method. The runtime of QAOA is observed numerically to be only O(κpoly(log(1/ϵ))).

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/31/2019

Solving quantum linear system problem with near-optimal complexity

We present a simple algorithm to solve the quantum linear system problem...
research
01/27/2022

Quantum algorithm for dense kernel matrices using hierarchical splitting

Kernel matrices, which arise from discretizing a kernel function k(x,x')...
research
07/16/2019

Quantum Data Fitting Algorithm for Non-sparse Matrices

We propose a quantum data fitting algorithm for non-sparse matrices, whi...
research
03/04/2022

Quantum Approximate Optimization Algorithm for Bayesian network structure learning

Bayesian network structure learning is an NP-hard problem that has been ...
research
02/18/2019

A Quantum IP Predictor-Corrector Algorithm for Linear Programming

We introduce a new quantum optimization algorithm for Linear Programming...
research
09/16/2021

Quantum message-passing algorithm for optimal and efficient decoding

Recently, one of us proposed a quantum algorithm called belief propagati...
research
03/17/2023

One Weird Trick Tightens the Quantum Adversary Bound, Especially for Success Probability Close to 1/2

The textbook adversary bound for function evaluation states that to eval...

Please sign up or login with your details

Forgot password? Click here to reset