141,797 research outputs found
Parallelizing Quantum Circuits
We present a novel automated technique for parallelizing quantum circuits via
forward and backward translation to measurement-based quantum computing
patterns and analyze the trade off in terms of depth and space complexity. As a
result we distinguish a class of polynomial depth circuits that can be
parallelized to logarithmic depth while adding only polynomial many auxiliary
qubits. In particular, we provide for the first time a full characterization of
patterns with flow of arbitrary depth, based on the notion of influencing paths
and a simple rewriting system on the angles of the measurement. Our method
leads to insightful knowledge for constructing parallel circuits and as
applications, we demonstrate several constant and logarithmic depth circuits.
Furthermore, we prove a logarithmic separation in terms of quantum depth
between the quantum circuit model and the measurement-based model.Comment: 34 pages, 14 figures; depth complexity, measurement-based quantum
computing and parallel computin
Is Fault-Tolerant Quantum Computation Really Possible?
The so-called "threshold" theorem says that, once the error rate per qubit
per gate is below a certain value, indefinitely long quantum computation
becomes feasible, even if all of the qubits involved are subject to relaxation
processes, and all the manipulations with qubits are not exact. The purpose of
this article, intended for physicists, is to outline the ideas of quantum error
correction and to take a look at the proposed technical instruction for
fault-tolerant quantum computation. It seems that the mathematics behind the
threshold theorem is somewhat detached from the physical reality, and that some
ideal elements are always present in the construction. This raises serious
doubts about the possibility of large scale quantum computations, even as a
matter of principle.Comment: Based on a talk given at the Future Trends in Microelectronics
workshop, Crete, June 2006. 8 pages, 1 figur
Some Remarks on Quantum Coherence
There are many striking phenomena which are attributed to
``quantum coherence''. It is natural to wonder if there are new quantum
coherence effects waiting to be discovered which could lead to interesting
results and perhaps even practical applications. A useful starting point for
such discussions is a definition of ``quantum coherence''. In this article I
give a definition of quantum coherence and use a number of illustrations to
explore the implications of this definition. I point to topics of current
interest in the fields of cosmology and quantum computation where questions of
quantum coherence arise, and I emphasize the impact that interactions with the
environment can have on quantum coherence.Comment: 25 pages plain LaTeX, no figures. More references have been added and
typos have been corrected. Journal of Modern Optics, in press.
Imperial/TP/93-94/1
A quantum computing primer for operator theorists
This is an exposition of some of the aspects of quantum computation and
quantum information that have connections with operator theory. After a brief
introduction, we discuss quantum algorithms. We outline basic properties of
quantum channels, or equivalently, completely positive trace preserving maps.
The main theorems for quantum error detection and correction are presented and
we conclude with a description of a particular passive method of quantum error
correction.Comment: 24 pages, to appear in Lin. Alg. App
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