Quantum memories and error correction

Wootton, James R.

doi:10.1080/09500340.2012.737937

Cited by 29 publications

(26 citation statements)

References 133 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While one approach seeks to achieve this by constructing a self-correcting quantum memory (see Ref. [1] for a recent review), an alternative possibility is to dynamically protect the stored quantum information by constantly pumping entropy out of the system. Topological quantum error correction codes [2,3] store one logical qubit in a large number of physical qubits in a way which guarantees that a sufficiently low density of errors on the physical qubits can be detected and undone, without affecting the stored logical qubit.…”

Section: Introductionmentioning

confidence: 99%

Efficient Markov chain Monte Carlo algorithm for the surface code

2014

Self Cite

View full text Add to dashboard Cite

Minimum-weight perfect matching (MWPM) has been the primary classical algorithm for error correction in the surface code, since it is of low runtime complexity and achieves relatively low logical error rates [Phys. Rev. Lett. 108, 180501 (2012)]. A Markov chain Monte Carlo (MCMC) algorithm [Phys. Rev. Lett. 109, 160503 (2012)] is able to achieve lower logical error rates and higher thresholds than MWPM, but requires a classical runtime complexity, which is super-polynomial in L, the linear size of the code. In this work we present an MCMC algorithm that achieves significantly lower logical error rates than MWPM at the cost of a runtime complexity increased by a factor O(L 2 ). This advantage is due to taking correlations between bit-and phase-flip errors (as they appear, for example, in depolarizing noise) as well as entropic factors (i.e., the numbers of likely error paths in different equivalence classes) into account. For depolarizing noise with error rate p, we present an efficient algorithm for which the logical error rate is suppressed as O((p/3) L/2 ) for p → 0-an exponential improvement over all previously existing efficient algorithms. Our algorithm allows for tradeoffs between runtime and achieved logical error rates as well as for parallelization, and can be also used for correction in the case of imperfect stabilizer measurements.

show abstract

Section: Introductionmentioning

confidence: 99%

Efficient Markov chain Monte Carlo algorithm for the surface code

2014

Self Cite

View full text Add to dashboard Cite

show abstract

“…The stability of the toric code systems, as the archetypal topological quantum memory, has been the subject of much research (see Ref. [68] for a recent review). It would be interesting to study whether some of the stabilization schemes, such as local random potentials [75] or couplings to external baths [76], could also be translated to increase the fault tolerance of topological nanowire arrays.…”

Section: Discussionmentioning

confidence: 99%

“…Topological phases of this type, in general known as toric code, are the archetypal topological quantum memories and they have been studied in the presence of numerous competing perturbations (see, e.g., Ref. [68] for a recent review). It would be interesting if some of these results could be translated and applied to quantum computing schemes with topological nanowire arrays.…”

Section: B Implications For the Array As A Quantum Computermentioning

confidence: 99%

Kitaev spin models from topological nanowire networks

2014

View full text Add to dashboard Cite

We show that networks of superconducting topological nanowires can realize the physics of exactly solvable Kitaev spin models on trivalent lattices. This connection arises from the low-energy theory of both systems being described by a tight-binding model of Majorana modes. In Kitaev spin models the Majorana description provides a convenient representation to solve the model, whereas in an array of Josephson junctions of topological nanowires it arises from localized physical Majorana modes tunneling between the wire ends. We explicitly show that an array of junctions of three wires-a setup relevant to topological quantum computing with nanowires-can realize the Yao-Kivelson model, a variant of Kitaev spin models on a decorated honeycomb lattice. Employing properties of the latter, we show that the network can be constructed to give rise to two-dimensional collective topological states characterized by Chern numbers ν = 0, ±1, and ±2, and that defects in the array can be associated with vortex-like quasiparticle excitations. In addition we show that the collective states are stable in the presence of disorder and superconducting phase fluctuations. When the network is operated as a quantum information processor, the connection to Kitaev spin models implies that decoherence mechanisms can in general be understood in terms of proliferation of the vortex-like quasiparticles.

show abstract

“…The first article within this JMO Series, cf. [13], focusses on these kinds of quantum memories. In this article, Wootton asks the question how to best store inherently-fragile quantum states with the help of error-correcting and self-correcting processes.…”

Section: Announcing the Jmo Series On Quantum Memoriesmentioning

confidence: 99%

Announcing the JMO Series on Quantum Memories

Beige

Pachos

2013

Journal of Modern Optics

View full text Add to dashboard Cite

Data show that the presence of women in quantum science is affected by a number of detriments and their percentage decreases even further for higher positions. Beyond data, from our shared personal experiences as female tenured quantum physics professors, we believe that the current model of scientific leadership, funding, and authority fails to represent many of us. It is time for a real change that calls for a different kind of force and for the participation of everyone. Women for quantum calls for a joint effort and aims with this initiative to contribute to such a transformation.

show abstract

Quantum memories and error correction

Cited by 29 publications

References 133 publications

Efficient Markov chain Monte Carlo algorithm for the surface code

Efficient Markov chain Monte Carlo algorithm for the surface code

Kitaev spin models from topological nanowire networks

Announcing the JMO Series on Quantum Memories

Contact Info

Product

Resources

About