Corpus ID: 122053408

Classical simulation of quantum computation, the Gottesman-Knill theorem, and slightly beyond

@article{Nes2010ClassicalSO,
  title={Classical simulation of quantum computation, the Gottesman-Knill theorem, and slightly beyond},
  author={Maarten Van Den Nes},
  journal={Quantum Information & Computation},
  year={2010},
  volume={10},
  pages={258-271}
}
  • Maarten Van Den Nes
  • Published 2010
  • Mathematics
  • Quantum Information & Computation
  • 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… CONTINUE READING
    37 Citations
    Classical simulation complexity of extended Clifford circuits
    • 54
    • PDF
    Simulating quantum computers with probabilistic methods
    • 72
    • PDF
    Commuting quantum circuits with few outputs are unlikely to be classically simulatable
    • 5
    • PDF
    From estimation of quantum probabilities to simulation of quantum circuits
    • 16
    • PDF
    Simulating Quantum Circuits with Sparse Output Distributions
    • 24
    • PDF
    Simulation of quantum circuits by low-rank stabilizer decompositions
    • 65
    • PDF
    Phase space simulation method for quantum computation with magic states on qubits
    • 14
    • Highly Influenced
    • PDF

    References

    SHOWING 1-10 OF 20 REFERENCES
    Quantum Circuits That Can Be Simulated Classically in Polynomial Time
    • L. Valiant
    • Computer Science, Mathematics
    • SIAM J. Comput.
    • 2002
    • 227
    Matchgates and classical simulation of quantum circuits
    • R. Jozsa, A. Miyake
    • Mathematics, Physics
    • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    • 2008
    • 124
    • PDF
    Classical simulation of noninteracting-fermion quantum circuits
    • 169
    • PDF
    Simulating Quantum Computation by Contracting Tensor Networks
    • 201
    • PDF
    On the Role of Hadamard Gates in Quantum Circuits
    • D. Shepherd
    • Computer Science, Physics
    • Quantum Inf. Process.
    • 2006
    • 11
    • PDF
    The Heisenberg Representation of Quantum Computers
    • 544
    • PDF
    On the simulation of quantum circuits
    • 52
    • PDF
    On the role of entanglement in quantum-computational speed-up
    • R. Jozsa, N. Linden
    • Mathematics, Physics
    • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
    • 2003
    • 455
    • PDF