Quantum computation and quantum information
Quantum computation and quantum information
Quantum Circuits That Can Be Simulated Classically in Polynomial Time
SIAM Journal on Computing
The computational complexity of linear optics
Proceedings of the forty-third annual ACM symposium on Theory of computing
Permutational quantum computing
Quantum Information & Computation
Adptive quantum computation, constant depth quantum circuits and arthur-merlin games
Quantum Information & Computation
Commutative version of the local Hamiltonian problem and common eigenspace problem
Quantum Information & Computation
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Bounds on the power of constant-depth quantum circuits
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Simulating quantum computers with probabilistic methods
Quantum Information & Computation
Complexity of commuting Hamiltonians on a square lattice of qubits
Quantum Information & Computation
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The study of quantum circuits composed of commuting gates is particularly useful to understand the delicate boundary between quantum and classical computation. Indeed, while being a restricted class, commuting circuits exhibit genuine quantum effects such as entanglement. In this paper we show that the computational power of commuting circuits exhibits a surprisingly rich structure. First we show that every 2-local commuting circuit acting on d-level systems and followed by single-qudit measurements can be efficiently simulated classically with high accuracy. In contrast, we prove that such strong simulations are hard for 3-local circuits. Using sampling methods we further show that all commuting circuits composed of exponentiated Pauli operators eiθP can be simulated efficiently classically when followed by single-qubit measurements. Finally, we show that commuting circuits can efficiently simulate certain non-commutative processes, related in particular to constant-depth quantum circuits. This gives evidence that the power of commuting circuits goes beyond classical computation.