Fault-tolerant error correction with the gauge color code

The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a universal set of computational operations with the minimal cost in quantum resources remains an important and ongoing challenge. One proposal of significant recent interest is the gauge color code. Notably, this code may offer a reduced resource cost over other well-studied fault-tolerant architectures using a new method, known as gauge fixing, for performing the non-Clifford logical operations that are essential for universal quantum computation. Here we examine the gauge color code when it is subject to noise. Specifically we make use of single-shot error correction to develop a simple decoding algorithm for the gauge color code, and we numerically analyse its performance. Remarkably, we find threshold error rates comparable to those of other leading proposals. Our results thus provide encouraging preliminary data of a comparative study between the gauge color code and other promising computational architectures.Comment: v1 - 5+4 pages, 11 figures, comments welcome; v2 - minor revisions, new supplemental including a discussion on correlated errors and details on threshold calculations; v3 - Author accepted manuscript. Accepted on 21/06/16. Deposited on 29/07/16. 9+5 pages, 17 figures, new version includes resource scaling analysis in below threshold regime, see eqn. (4) and methods sectio

Qdensity - a Mathematica Quantum Computer Simulation

This Mathematica 5.2 package~\footnote{QDENSITY is available at http://www.pitt.edu/~tabakin/QDENSITY} is a simulation of a Quantum Computer. The program provides a modular, instructive approach for generating the basic elements that make up a quantum circuit. The main emphasis is on using the density matrix, although an approach using state vectors is also implemented in the package. The package commands are defined in {\it Qdensity.m} which contains the tools needed in quantum circuits, e.g. multiqubit kets, projectors, gates, etc. Selected examples of the basic commands are presented here and a tutorial notebook, {\it Tutorial.nb} is provided with the package (available on our website) that serves as a full guide to the package. Finally, application is made to a variety of relevant cases, including Teleportation, Quantum Fourier transform, Grover's search and Shor's algorithm, in separate notebooks: {\it QFT.nb}, {\it Teleportation.nb}, {\it Grover.nb} and {\it Shor.nb} where each algorithm is explained in detail. Finally, two examples of the construction and manipulation of cluster states, which are part of ``one way computing" ideas, are included as an additional tool in the notebook {\it Cluster.nb}. A Mathematica palette containing most commands in QDENSITY is also included: {\it QDENSpalette.nb} .Comment: The Mathematica 5+ package is available at: http://www.pitt.edu/~tabakin/QDENSITY/QDENSITY.htm Minor corrections, accepted in Computer Physics Communication

An efficient quantum circuit analyser on qubits and qudits

This paper presents a highly efficient decomposition scheme and its associated Mathematica notebook for the analysis of complicated quantum circuits comprised of single/multiple qubit and qudit quantum gates. In particular, this scheme reduces the evaluation of multiple unitary gate operations with many conditionals to just two matrix additions, regardless of the number of conditionals or gate dimensions. This improves significantly the capability of a quantum circuit analyser implemented in a classical computer. This is also the first efficient quantum circuit analyser to include qudit quantum logic gates

Qcmpi: A Parallel Environment for Quantum Computing

QCMPI is a quantum computer (QC) simulation package written in Fortran 90 with parallel processing capabilities. It is an accessible research tool that permits rapid evaluation of quantum algorithms for a large number of qubits and for various "noise" scenarios. The prime motivation for developing QCMPI is to facilitate numerical examination of not only how QC algorithms work, but also to include noise, decoherence, and attenuation effects and to evaluate the efficacy of error correction schemes. The present work builds on an earlier Mathematica code QDENSITY, which is mainly a pedagogic tool. In QCMPI, the stress is on state vectors, in order to employ a large number of qubits. The parallel processing feature is implemented by using the Message-Passing Interface (MPI) protocol. Codes for Grover's search and Shor's factoring algorithms are provided as examples. A major feature of this work is that concurrent versions of the algorithms can be evaluated with each version subject to alternate noise effects, which corresponds to the idea of solving a stochastic Schr\"{o}dinger equation.Comment: Package webpage http://www.pitt.edu/~tabakin/QCMP