Quantum computation and quantum information
Quantum computation and quantum information
Quantum Circuits That Can Be Simulated Classically in Polynomial Time
SIAM Journal on Computing
Both Toffoli and controlled-NOT need little help to do universal quantum computing
Quantum Information & Computation
Classical simulation and complexity of quantum computations
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
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We describe a simple formalism for generating classes of quantum circuits that are classically efficiently simulatable and show that the efficient simulation of Clifford circuits (Gottesman-Knill theorem) and of matchgate circuits (Valiant's theorem) appear as two special cases. Viewing these simulatable classes as subsets of the space of all quantum computations, we may consider minimal extensions that suffice to regain full quantum computational power, which provides an approach to exploring the efficacy of quantum over classical computation.