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Several natural BQP-Complete problems

Pawel Wocjan·Shengyu Zhang
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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.

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Pawel Wocjan, Shengyu Zhang. 2006-06-21. Several natural BQP-Complete problems. https://arxiv.org/abs/quant-ph/0606179

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