Several natural BQP-Complete problems

TL;DR

This paper introduces several new BQP-complete problems related to linear algebra, enhancing understanding of quantum computational power and its limitations by expanding the set of known hardest problems.

Contribution

It presents new BQP-complete problems based on linear algebra, differing from previous problems and closely related to quantum algorithms and complexity theory.

Findings

New BQP-complete problems introduced

Problems are of linear algebra nature

Enhances understanding of quantum computational complexity

Abstract

A central problem in quantum computing is to identify computational tasks which can be solved substantially faster on a quantum computer than on any classical computer. By studying the hardest such tasks, known as BQP-complete problems, we deepen our understanding of the power and limitations of quantum computers. We present several BQP-complete problems, including Local Hamiltonian Eigenvalue Sampling and Phase Estimation Sampling. Different than the previous known BQP-complete problems (the Quadratically Signed Weight Enumerator problem [KL01] and the Approximation of Jones Polynomials [FKW02, FLW02, AJL06]), our problems are of a basic linear algebra nature and are closely related to the well-known quantum algorithm and quantum complexity theories.