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Paper 1

Improved error thresholds for measurement-free error correction

Daniel Crow, Robert Joynt, Mark Saffman

Year

2015

Journal

arXiv preprint

DOI

arXiv:1510.08359

arXiv

1510.08359

Motivated by limitations and capabilities of neutral atom qubits, we examine whether measurement-free error correction can produce practical error thresholds. We show that this can be achieved by extracting redundant syndrome information, giving our procedure extra fault tolerance and eliminating the need for ancilla verification. The procedure is particularly favorable when multi-qubit gates are available for the correction step. Simulations of the bit-flip, Bacon-Shor, and Steane codes indicate that coherent error correction can produce threshold error rates that are on the order of $10^{-3}$ to $10^{-4}$---comparable with or better than measurement-based values, and much better than previous results for other coherent error correction schemes. This indicates that coherent error correction is worthy of serious consideration for achieving protected logical qubits.

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Paper 2

Semiclassical evolution of correlations between observables

Alfredo M. Ozorio de Almeida, Olivier Brodier

Year

2015

Journal

arXiv preprint

DOI

arXiv:1507.04707

arXiv

1507.04707

The trace of an arbitrary product of quantum operators with the density operator is rendered as a multiple phase space integral of the product of their Weyl symbols with the Wigner function. Interspersing the factors with various evolution operators, one obtains an evolving correlation. The kernel for the matching multiple integral that evolves within the Weyl representation is identified with the trace of a single compound unitary operator. Its evaluation within a semiclassical approximation then becomes a sum over the periodic trajectories of the corresponding classical compound canonical transformation. The search for periodic trajectories can be bypassed by an exactly equivalent initial value scheme, which involves a change of integration variable and a reduced compound unitary operator. Restriction of all the operators to observables with smooth non-oscillatory Weyl symbols reduces the evolving correlation to a single phase space integral. If each observable undergoes independent Heisenberg evolution, the overall correlation evolves classically. Otherwise, the kernel acquires a nonclassical phase factor, though it still depends on a purely classical compound trajectory: e.g. the fase for a double return of the quantum Loschmidt echo does not coincide with twice the phase for a single echo.

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