Threshold Computation and Cryptographic Security
SIAM Journal on Computing
Quantum computation and quantum information
Quantum computation and quantum information
Quantum Circuits That Can Be Simulated Classically in Polynomial Time
SIAM Journal on Computing
SIAM Journal on Computing
Invited Talk: Embedding Classical into Quantum Computation
Mathematical Methods in Computer Science
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Quantum computing is widely regarded as being able to offer computational complexity benefits beyond the possibilities of classical computing. Yet the relationship of quantum to classical computational complexity is little understood. A fundamental approach to exploring this issue is to study the extent to which quantum computations (especially with restricted sub-universal ingredients) can be classically efficiently simulated. We will discuss a series of results relating to the classical simulation of some interesting classes of quantum computations, particularly Clifford circuits, matchgate circuits and a simple class of quantum circuits (so-called IQP circuits) comprising commuting gates. We will outline an argument that a suitably efficient classical simulation of the latter class would imply a collapse of the polynomial hierarchy.