Resilience to time-correlated noise in quantum computation

Fault-tolerant quantum computation techniques rely on weakly correlated noise. Here I show that it is enough to assume weak spatial correlations: time correlations can take any form. In particular, single-shot error correction techniques exhibit a noise threshold for quantum memories under spatially local stochastic noise.Comment: 16 pages, v3: as accepted in journa

Single-shot fault-tolerant quantum error correction

Conventional quantum error correcting codes require multiple rounds of measurements to detect errors with enough confidence in fault-tolerant scenarios. Here I show that for suitable topological codes a single round of local measurements is enough. This feature is generic and is related to self-correction and confinement phenomena in the corresponding quantum Hamiltonian model. 3D gauge color codes exhibit this single-shot feature, which applies also to initialization and gauge-fixing. Assuming the time for efficient classical computations negligible, this yields a topological fault-tolerant quantum computing scheme where all elementary logical operations can be performed in constant time.Comment: Typos corrected after publication in journal, 26 pages, 4 figure

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

Fault-tolerant gates via homological product codes

A method for the implementation of a universal set of fault-tolerant logical gates is presented using homological product codes. In particular, it is shown that one can fault-tolerantly map between different encoded representations of a given logical state, enabling the application of different classes of transversal gates belonging to the underlying quantum codes. This allows for the circumvention of no-go results pertaining to universal sets of transversal gates and provides a general scheme for fault-tolerant computation while keeping the stabilizer generators of the code sparse.Comment: 11 pages, 3 figures. v2 (published version): quantumarticle documentclass, expanded discussion on the conditions for a fault tolerance threshol

Towards Quantum Repeaters with Solid-State Qubits: Spin-Photon Entanglement Generation using Self-Assembled Quantum Dots

In this chapter we review the use of spins in optically-active InAs quantum dots as the key physical building block for constructing a quantum repeater, with a particular focus on recent results demonstrating entanglement between a quantum memory (electron spin qubit) and a flying qubit (polarization- or frequency-encoded photonic qubit). This is a first step towards demonstrating entanglement between distant quantum memories (realized with quantum dots), which in turn is a milestone in the roadmap for building a functional quantum repeater. We also place this experimental work in context by providing an overview of quantum repeaters, their potential uses, and the challenges in implementing them.Comment: 51 pages. Expanded version of a chapter to appear in "Engineering the Atom-Photon Interaction" (Springer-Verlag, 2015; eds. A. Predojevic and M. W. Mitchell

Encoding qubits into oscillators with atomic ensembles and squeezed light

The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit within an oscillator provides a number of advantages when used in a fault-tolerant architecture for quantum computing, most notably that Gaussian operations suffice to implement all single- and two-qubit Clifford gates. The main drawback of the encoding is that the logical states themselves are challenging to produce. Here we present a method for generating optical GKP-encoded qubits by coupling an atomic ensemble to a squeezed state of light. Particular outcomes of a subsequent spin measurement of the ensemble herald successful generation of the resource state in the optical mode. We analyze the method in terms of the resources required (total spin and amount of squeezing) and the probability of success. We propose a physical implementation using a Faraday-based quantum non-demolition interaction.Comment: (v2) consistent with published version; (v1) 16 pages, 5 figure

Layered architecture for quantum computing

We develop a layered quantum computer architecture, which is a systematic framework for tackling the individual challenges of developing a quantum computer while constructing a cohesive device design. We discuss many of the prominent techniques for implementing circuit-model quantum computing and introduce several new methods, with an emphasis on employing surface code quantum error correction. In doing so, we propose a new quantum computer architecture based on optical control of quantum dots. The timescales of physical hardware operations and logical, error-corrected quantum gates differ by several orders of magnitude. By dividing functionality into layers, we can design and analyze subsystems independently, demonstrating the value of our layered architectural approach. Using this concrete hardware platform, we provide resource analysis for executing fault-tolerant quantum algorithms for integer factoring and quantum simulation, finding that the quantum dot architecture we study could solve such problems on the timescale of days.Comment: 27 pages, 20 figure