Error-Resistant Distributed Quantum Computation in Trapped Ion Chain

We consider experimentally feasible chains of trapped ions with pseudo-spin 1/2, and find models that can potentially be used to implement error-resistant quantum computation. Similar in spirit to classical neural networks, the error-resistance of the system is achieved by encoding the qubits distributed over the whole system. We therefore call our system a ''quantum neural network'', and present a ''quantum neural network model of quantum computation''. Qubits are encoded in a few quasi-degenerated low energy levels of the whole system, separated by a large gap from the excited states, and large energy barriers between themselves. We investigate protocols for implementing a universal set of quantum logic gates in the system, by adiabatic passage of a few low-lying energy levels of the whole system. Naturally appearing and potentially dangerous distributed noise in the system leaves the fidelity of the computation virtually unchanged, if it is not too strong. The computation is also naturally resilient to local perturbations of the spins.Comment: 10 pages, 7 figures, RevTeX4; v2: another noise model analysed, published versio

Quantum Annealing - Foundations and Frontiers

We briefly review various computational methods for the solution of optimization problems. First, several classical methods such as Metropolis algorithm and simulated annealing are discussed. We continue with a description of quantum methods, namely adiabatic quantum computation and quantum annealing. Next, the new D-Wave computer and the recent progress in the field claimed by the D-Wave group are discussed. We present a set of criteria which could help in testing the quantum features of these computers. We conclude with a list of considerations with regard to future research.Comment: 22 pages, 6 figures. EPJ-ST Discussion and Debate Issue: Quantum Annealing: The fastest route to large scale quantum computation?, Eds. A. Das, S. Suzuki (2014

Geometric Quantum Computation

We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary transformation can be implemented with arbitrary precision using only single-spin operations and conditional phase shifts. Thus quantum geometrical phases can form the basis of any quantum computation. Moreover, as the induced conditional phase depends only on the geometry of the paths executed by the spins it is resilient to certain types of errors and offers the potential of a naturally fault-tolerant way of performing quantum computation.Comment: 15 pages, LaTeX, uses cite, eepic, epsfig, graphicx and amsfonts. Accepted by J. Mod. Op

What is a quantum computer, and how do we build one?

The DiVincenzo criteria for implementing a quantum computer have been seminal in focussing both experimental and theoretical research in quantum information processing. These criteria were formulated specifically for the circuit model of quantum computing. However, several new models for quantum computing (paradigms) have been proposed that do not seem to fit the criteria well. The question is therefore what are the general criteria for implementing quantum computers. To this end, a formal operational definition of a quantum computer is introduced. It is then shown that according to this definition a device is a quantum computer if it obeys the following four criteria: Any quantum computer must (1) have a quantum memory; (2) facilitate a controlled quantum evolution of the quantum memory; (3) include a method for cooling the quantum memory; and (4) provide a readout mechanism for subsets of the quantum memory. The criteria are met when the device is scalable and operates fault-tolerantly. We discuss various existing quantum computing paradigms, and how they fit within this framework. Finally, we lay out a roadmap for selecting an avenue towards building a quantum computer. This is summarized in a decision tree intended to help experimentalists determine the most natural paradigm given a particular physical implementation

Counteracting systems of diabaticities using DRAG controls: The status after 10 years

The task of controlling a quantum system under time and bandwidth limitations is made difficult by unwanted excitations of spectrally neighboring energy levels. In this article we review the Derivative Removal by Adiabatic Gate (DRAG) framework. DRAG is a multi-transition variant of counterdiabatic driving, where multiple low-lying gapped states in an adiabatic evolution can be avoided simultaneously, greatly reducing operation times compared to the adiabatic limit. In its essence, the method corresponds to a convergent version of the superadiabatic expansion where multiple counterdiabaticity conditions can be met simultaneously. When transitions are strongly crowded, the system of equations can instead be favorably solved by an average Hamiltonian (Magnus) expansion, suggesting the use of additional sideband control. We give some examples of common systems where DRAG and variants thereof can be applied to improve performance.Comment: 7 pages, 2 figure