Solution of the matrix equation AX + XB = C [F4]
Communications of the ACM
Quantum computers that can be simulated classically in polynomial time
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Permutational quantum computing
Quantum Information & Computation
Lagrangian representation for fermionic linear optics
Quantum Information & Computation
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Fermionic linear optics is a limited form of quantum computation which is known to be efficiently simulable on a classical computer. We revisit and extend this result by enlarging the set of available computational gates: in addition to unitaries and measurements, we allow dissipative evolution governed by a Markovian master equation with linear Lindblad operators. We show that this more general form of fermionic computation is also simulable efficiently by classical means. Given a system of N fermionic modes, our algorithm simulates any such gate in time O(N3) while a single-mode measurement is simulated in time O(N2). The steady state of the Lindblad equation can be computed in time O(N3).