Information Processing Letters
The Invariants of the Clifford Groups
Designs, Codes and Cryptography
Quantum computation and quantum information
Quantum computation and quantum information
Quantum Circuits That Can Be Simulated Classically in Polynomial Time
SIAM Journal on Computing
Simulating Quantum Computation by Contracting Tensor Networks
SIAM Journal on Computing
A linearized stabilizer formalism for systems of finite dimension
Quantum Information & Computation
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We study classical simulation of quantum computation, taking the Gottesman-Knilltheorem as a starting point. We show how each Clifford circuit can be reduced to anequivalent, manifestly simulatable circuit (normal form). This provides a simple proofof the Gottesman-Knill theorem without resorting to stabilizer techniques. The normalform highlights why Clifford circuits have such limited computational power in spiteof their high entangling power. At the same time, the normal form shows how theclassical simulation of Clifford circuits fits into the standard way of embedding classicalcomputation into the quantum circuit model. This leads to simple extensions of Cliffordcircuits which are classically simulatable. These circuits can be efficiently simulated byclassical sampling ("weak simulation") even though the problem of exactly computingthe outcomes of measurements for these circuits ("strong simulation") is proved to be#P-complete-thus showing that there is a separation between weak and strong classicalsimulation of quantum computation.