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Ben W. Reichardt

Publications and source records attributed to Ben W. Reichardt.

42 records · Page 3Linked to original sources
arXiv2006

Error-detection-based quantum fault tolerance against discrete Pauli noise

A quantum computer -- i.e., a computer capable of manipulating data in quantum superposition -- would find applications including factoring, quantum simulation and tests of basic quantum theory. Since quantum superpositions are fragile, the major hurdle in building such a computer is overcoming noise. Developed over the last couple of years, new schemes for achieving fault tolerance based on error detection, rather than error correction, appear to tolerate as much as 3-6% noise per gate -- an order of magnitude better than previous procedures. But proof techniques could not show that these promising fault-tolerance schemes tolerated any noise at all. With an analysis based on decomposing complicated probability distributions into mixtures of simpler ones, we rigorously prove the existence of constant tolerable noise rates ("noise thresholds") for error-detection-based schemes. Numerical calculations indicate that the actual noise threshold this method yields is lower-bounded by 0.1% noise per gate.

quant-ph↗
arXiv2006

Postselection threshold against biased noise

The highest current estimates for the amount of noise a quantum computer can tolerate are based on fault-tolerance schemes relying heavily on postselecting on no detected errors. However, there has been no proof that these schemes give even a positive tolerable noise threshold. A technique to prove a positive threshold, for probabilistic noise models, is presented. The main idea is to maintain strong control over the distribution of errors in the quantum state at all times. This distribution has correlations which conceivably could grow out of control with postselection. But in fact, the error distribution can be written as a mixture of nearby distributions each satisfying strong independence properties, so there are no correlations for postselection to amplify.

quant-ph↗
arXiv2005

Fault-tolerance threshold for a distance-three quantum code

The quantum error threshold is the highest (model-dependent) noise rate which we can tolerate and still quantum-compute to arbitrary accuracy. Although noise thresholds are frequently estimated for the Steane seven-qubit, distance-three quantum code, there has been no proof that a constant threshold even exists for distance-three codes. We prove the existence of a constant threshold. The proven threshold is well below estimates, based on simulations and analytic models, of the true threshold, but at least it is now known to be positive.

quant-ph↗
arXiv2005

Quantum error correction of systematic errors using a quantum search framework

Composite pulses are a quantum control technique for canceling out systematic control errors. We present a new composite pulse sequence inspired by quantum search. Our technique can correct a wider variety of systematic errors -- including, for example, nonlinear over-rotational errors -- than previous techniques. Concatenation of the pulse sequence can reduce a systematic error to an arbitrarily small level.

quant-ph↗
arXiv2004

Improved magic states distillation for quantum universality

Given stabilizer operations and the ability to repeatedly prepare a single-qubit mixed state rho, can we do universal quantum computation? As motivation for this question, "magic state" distillation procedures can reduce the general fault-tolerance problem to that of performing fault-tolerant stabilizer circuits. We improve the procedures of Bravyi and Kitaev in the Hadamard "magic" direction of the Bloch sphere to achieve a sharp threshold between those rho allowing universal quantum computation, and those for which any calculation can be efficiently classically simulated. As a corollary, the ability to repeatedly prepare any pure state which is not a stabilizer state (e.g., any single-qubit pure state which is not a Pauli eigenstate), together with stabilizer operations, gives quantum universality. It remains open whether there is also a tight separation in the so-called T direction.

quant-ph↗