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Turning Gate Synthesis Errors into Incoherent Errors · Around

2016

Turning Gate Synthesis Errors into Incoherent Errors

Hastings, M. B.

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Using error correcting codes and fault tolerant techniques, it is possible, at least in theory, to produce logical qubits with significantly lower error rates than the underlying physical qubits.

Suppose, however, that the gates that act on these logical qubits are only approximation of the desired gate.
This can arise, for example, in synthesizing a single qubit unitary from a set of Clifford and $T$ gates; for a generic such unitary, any finite sequence of gates only approximates the desired target.
In this case, errors in the gate can add coherently so that, roughly, the error $\epsilon$ in the unitary of each gate must scale as $\epsilon \lesssim 1/N$, where $N$ is the number of gates.

Built on

P. W. Shor, “Fault-tolerant quantum computation”, in Proceedings of the 37th Symposium on the Foundations of Computer Science, Los Alamitos, California, 1996, IEEE press, p. 56-65
1996
Earlier work this paper cites.
S. Lloyd, “Universal quantum simulators”, Science 273
1996
Earlier work this paper cites.
D. Aharonov and M. Ben-Or, “Fault-tolerant quantum computation with constant error”, in STOC ’97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing, 1997
1997
Earlier work this paper cites.

Similar

J. Preskill, “Reliable quantum computers”, Proc. R. Soc. Lond. A, 454
1998
Cited alongside, same era.
E. Knill, R. Laflamme, and W. H. Zurek, “Resilient quantum computation: Error models and thresholds”, Phil. Trans. R. Soc. Lond. A, 454
1998
Cited alongside, same era.
A. Kitaev, A. Shen, and M. Vyalyi, Classical and quantum computation
2002
Cited alongside, same era.
E. Knill, “Fault-Tolerant Postselected Quantum Computation: Threshold Analysis”, arXiv:quant-ph/0404104
Cited in the paper.
D. Wecker, unpublished numerical simulations
Cited in the paper.

Then

S. Bravyi and A. Kitaev, “Universal quantum computation with ideal Clifford gates and noisy ancillas”, Phys. Rev. A 71
2005
Later among the works it cites.
E. Knill, “Quantum computing with realistically noisy devices”, Nature 434
2005
Later among the works it cites.
N. J. Ross and P. Selinger, “Optimal ancilla-free Clifford+T approximation of z-rotations”, QIC 16
2016
Closest in time.

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