A taxonomy of problems with fast parallel algorithms
Information and Control
Information Processing Letters
A note on closure properties of logspace MOD classes
Information Processing Letters
The Invariants of the Clifford Groups
Designs, Codes and Cryptography
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Classical simulation of quantum computation, the Gottesman-Knill theorem, and slightly beyond
Quantum Information & Computation
Quantum Information & Computation
IEEE Transactions on Information Theory
Quantum Information & Computation
Classical simulations of Abelian-group normalizer circuits with intermediate measurements
Quantum Information & Computation
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The stabilizer formalism is a scheme, generalizing well-known techniques developed by Gottesman [1] in the case of qubits, to efficiently simulate a class of transformations (stabilizer circuits, which include the quantum Fourier transform and highly entangling operations) on standard basis states of d-dimensional qudits. To determine the state of a simulated system, existing treatments involve the computation of cumulative phase factors which involve quadratic dependencies. We present a simple formalism in which Pauli operators are represented using displacement operators in discrete phase space, expressing the evolution of the state via linear transformations modulo D ≤ 2d. We thus obtain a simple proof that simulating stabilizer circuits on n qudits, involving any constant number of measurement rounds, is complete for the complexity class coModdL and may be simulated by O(log(n)2)-depth circuits for any constant d ≥ 2.