Yaoyun Shi

Classical simulation of quantum many-body systems with a tree tensor network

We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement (Schmidt number) is small for any bipartite split along an edge of the tree. As an application, we show that any one-way quantum computation on a tree graph can be efficiently simulated with a classical computer.

Simulating Quantum Computation by Contracting Tensor Networks

The treewidth of a graph is a useful combinatorial measure of how close the graph is to a tree. We prove that a quantum circuit with

Quantum lower bounds for the collision and the element distinctness problems

T

Quantum Complexities of Ordered Searching, Sorting, and Element Distinctness

gates whose underlying graph has a treewidth

Robust protocols for securely expanding randomness and distributing keys using untrusted quantum devices

d

The communication complexity of the Hamming distance problem

can be simulated deterministically in

Lower bounds of quantum black-box complexity and degree of approximating polynomials by influence of Boolean variables

T^{O(1)}\exp[O(d)]

Using spam farm to boost PageRank

time, which, in particular, is polynomial in

On the parity complexity measures of Boolean functions

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Efficient Protocols for Generating Bipartite Classical Distributions and Quantum States

if