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achieving quantum computing.
Comment: This is a quite general and introductory review article which doesn t
introduce anything new but which can be used as good bibliographical reference and
short summary of common wisdom.
3.1.2 Emergence of Quantum Chaos in Quantum Computer Core and
How to Manage It
author(s): B.Georgeot, D.L.Shepelyansky
where: quant-ph/0005015, Phys. Rev. E, 62, 6366 (2000)
We study the standard generic quantum computer model, which describes a re-
alistic isolated quantum computer with fluctuations in individual qubit energies
and residual short-range inter-qubit couplings. It is shown that in the limit where
the fluctuations and couplings are small compared to one-qubit energy spacing the
spectrum has a band structure and a renormalized Hamiltonian is obtained which
describes the eigenstate properties inside one band. The studies are concentrated
on the central band of the computer ( core ) with the highest density of states.
We show that above a critical inter-qubit coupling strength, quantum chaos sets in,
leading to quantum ergodicity of the computer eigenstates. In this regime the ideal
qubit structure disappears, the eigenstates become complex and the operability of
the computer is quickly destroyed. We confirm that the quantum chaos border
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decreases only linearly with the number of qubits n, although the spacing between
multi-qubit states drops exponentially with n. The investigation of time-evolution
in the quantum computer shows that in the quantum chaos regime, an ideal (non-
interacting) state quickly disappears and exponentially many states become mixed
after a short chaotic time scale for which the dependence on system parameters
is determined. Below the quantum chaos border an ideal state can survive for
long times and be used for computation. The results show that a broad parameter
region does exist where the efficient operation of a quantum computer is possible.
3.1.3 Quantum Chaos & Quantum Computers
author(s): D.L.Shepelyansky
where: quant-ph/0006073, Physica Scripta, T90, 112-120 (2001)
The standard generic quantum computer model is studied analytically and numer-
ically 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 quan-
tum 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 phe-
nomenon 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.
3.1.4 Hybrid quantum computing
author(s): S.Lloyd
where: quant-ph/0008057, submitted to Physical Review Letters
Necessary and sufficient conditions are given for the construction of a hybrid quan-
tum computer that operates on both continuous and discrete quantum variables.
Such hybrid computers are shown to be more efficient than conventional quantum
computers for performing a variety of quantum algorithms, such as computing
eigenvectors and eigenvalues.
3.1.5 Constructing Qubits in Physical Systems
author(s): L.Viola, E.Knill, R.Laflamme
where: quant-ph/0101090, submitt. J.Phys.A:Math.Gen
The notion of a qubit is ubiquitous in quantum information processing. In spite of
the simple abstract definition of qubits as two-state quantum systems, identifying
qubits in physical systems is often unexpectedly difficult. There are an astonishing
variety of ways in which qubits can emerge from devices. What essential features
are required for an implementation to properly instantiate a qubit? We give three
typical examples and propose an operational characterization of qubits based on
quantum observables and subsystems.
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3.1.6 Encoded Universality in Physical Implementations of a Quantum
Computer
author(s): D.Bacon, J.Kempe, D.A.Lidar, K.B.Whaley, D.P.DiVincenzo
where: quant-ph/0102140, to appear in IQC 01
We revisit the question of universality in quantum computing and propose a new
paradigm. Instead of forcing a physical system to enact a predetermined set of
universal gates (e.g., single-qubit operations and CNOT), we focus on the intrinsic
ability of a system to act as a universal quantum computer using only its naturally
available interactions. A key element of this approach is the realization that the
fungible nature of quantum information allows for universal manipulations using
quantum information encoded in a subspace of the full system Hilbert space, as
an alternative to using physical qubits directly. Starting with the interactions
intrinsic to the physical system, we show how to determine the possible universality
resulting from these interactions over an encoded subspace. We outline a general
Lie-algebraic framework which can be used to find the encoding for universality
and give several examples relevant to solid-state quantum computing.
3.1.7 Non-holonomic Quantum Devices
author(s): V.M.Akulin, V.Gershkovich, G.Harel
where: quant-ph/0012102, report IHES/P/00/01
We analyze the possibility and efficiency of non-holonomic control over quantum
devices with exponentially large number of Hilbert space dimensions. We show that
completely controllable devices of this type can be assembled from elementary units
of arbitrary physical nature, and can be employed efficiently for universal quantum
computations and simulation of quantum field dynamics.
3.2 Theoretical issues
3.2.1 Multi-bit gates for quantum computing
author(s): X.Wang, A.Sorensen, K.Molmer
where: quant-ph/0012055, Phys. Rev. Lett. 86, 3907-3910 (2001)
We present a general technique to implement products of many qubit operators
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