Quantum Chaos & Quantum Computers

The standard generic quantum computer model is studied analytically and numerically and the border for emergence of quantum chaos, induced by imperfections and residual inter-qubit couplings, is determined. This phenomenon appears in an isolated quantum computer without any external decoherence. The onset of quantum chaos leads to quantum computer hardware melting, strong quantum entropy growth and destruction of computer operability. The time scales for development of quantum chaos and ergodicity are determined. In spite the fact that this phenomenon is rather dangerous for quantum computing it is shown that the quantum chaos border for inter-qubit coupling is exponentially larger than the energy level spacing between quantum computer eigenstates and drops only linearly with the number of qubits n. As a result the ideal multi-qubit structure of the computer remains rather robust against imperfections. This opens a broad parameter region for a possible realization of quantum computer. The obtained results are related to the recent studies of quantum chaos in such many-body systems as nuclei, complex atoms and molecules, finite Fermi systems and quantum spin glass shards which are also reviewed in the paper.Comment: Lecture at Nobel symposium on "Quantum chaos", June 2000, Sweden; revtex, 10 pages, 9 figure

The one-way quantum computer - a non-network model of quantum computation

A one-way quantum computer works by only performing a sequence of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. No non-local operations are required in the process of computation. Any quantum logic network can be simulated on the one-way quantum computer. On the other hand, the network model of quantum computation cannot explain all ways of processing quantum information possible with the one-way quantum computer. In this paper, two examples of the non-network character of the one-way quantum computer are given. First, circuits in the Clifford group can be performed in a single time step. Second, the realisation of a particular circuit --the bit-reversal gate-- on the one-way quantum computer has no network interpretation. (Submitted to J. Mod. Opt, Gdansk ESF QIT conference issue.)Comment: 7 pages, 3 figure

Quantum Spin Dynamics and Quantum Computation

We describe a simulation method for a quantum spin model of a generic, general purpose quantum computer. The use of this quantum computer simulator is illustrated through several implementations of Grover's database search algorithm. Some preliminary results on the stability of quantum algorithms are presented.Comment: 6 pages, 4 figures ; Minor errors corrected and figures update

Parallel Evaluation of Quantum Algorithms for Computational Fluid Dynamics

The development and evaluation of quantum computing algorithms for computational fluid dynamics is described along with a detailed analysis of the parallel performance of a quantum computer simulator developed as part of the present work. The quantum computer simulator is used in the evaluation of the quantum algorithms on a conventional parallel computer, and is applied to quantum lattice-based algorithms as well as the Poisson equation. A key result is a demonstration of how the Poisson equation can be solved effeciently on a quantum computer, while its use within a larger algorithm representing a full CFD solver poses a number of signifi- cant challenges

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

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