182 research outputs found
Simple Pulses for Universal Quantum Computation with a Heisenberg ABAB Chain
Recently Levy has shown that quantum computation can be performed using an
ABAB.. chain of spin-1/2 systems with nearest-neighbor Heisenberg interactions.
Levy notes that all necessary elementary computational `gates' can be achieved
by using spin-resonance techniques involving modulating the spin-spin
interaction strength at high frequency. Here we note that, as an alternative to
that approach, it is possible to perform the elementary gates with simple,
non-oscillatory pulses.Comment: 3 pages including 2 fig
Physical Optimization of Quantum Error Correction Circuits
Quantum error correcting codes have been developed to protect a quantum
computer from decoherence due to a noisy environment. In this paper, we present
two methods for optimizing the physical implementation of such error correction
schemes. First, we discuss an optimal quantum circuit implementation of the
smallest error-correcting code (the three bit code). Quantum circuits are
physically implemented by serial pulses, i.e. by switching on and off external
parameters in the Hamiltonian one after another. In contrast to this, we
introduce a new parallel switching method that allows faster gate operation by
switching all external parameters simultaneously. These two methods are applied
to electron spins in coupled quantum dots subject to a Heisenberg coupling
H=J(t) S_1*S_2 which can generate the universal quantum gate
`square-root-of-swap'. Using parallel pulses, the encoding for three-bit
quantum error correction in a Heisenberg system can be accelerated by a factor
of about two. We point out that parallel switching has potential applications
for arbitrary quantum computer architectures.Comment: 13 pages, 6 figure
Quantum information processing in bosonic lattices
We consider a class of models of self-interacting bosons hopping on a
lattice. We show that properly tailored space-temporal coherent control of the
single-body coupling parameters allows for universal quantum computation in a
given sector of the global Fock space. This general strategy for encoded
universality in bosonic systems has in principle several candidates for
physical implementation.Comment: 4 pages, 2 figs, RevTeX 4; updated to the published versio
Universal quantum control in irreducible state-space sectors: application to bosonic and spin-boson systems
We analyze the dynamical-algebraic approach to universal quantum control
introduced in P. Zanardi, S. Lloyd, quant-ph/0305013. The quantum state-space
encoding information decomposes into irreducible sectors and
subsystems associated to the group of available evolutions. If this group
coincides with the unitary part of the group-algebra \CC{\cal K} of some
group then universal control is achievable over the -irreducible components of . This general strategy is applied to
different kind of bosonic systems. We first consider massive bosons in a
double-well and show how to achieve universal control over all
finite-dimensional
Fock sectors. We then discuss a multi-mode massless case giving the
conditions for generating the whole infinite-dimensional multi-mode
Heisenberg-Weyl enveloping-algebra. Finally we show how to use an auxiliary
bosonic mode coupled to finite-dimensional systems to generate high-order
non-linearities needed for universal control.Comment: 10 pages, LaTeX, no figure
Quantum Computing via The Bethe Ansatz
We recognize quantum circuit model of computation as factorisable scattering
model and propose that a quantum computer is associated with a quantum
many-body system solved by the Bethe ansatz. As an typical example to support
our perspectives on quantum computation, we study quantum computing in
one-dimensional nonrelativistic system with delta-function interaction, where
the two-body scattering matrix satisfies the factorisation equation (the
quantum Yang--Baxter equation) and acts as a parametric two-body quantum gate.
We conclude by comparing quantum computing via the factorisable scattering with
topological quantum computing.Comment: 6 pages. Comments welcom
Storage Qubits and Their Potential Implementation Through a Semiconductor Double Quantum Dot
In the context of a semiconductor based implementation of a quantum computer
the idea of a quantum storage bit is presented and a possible implementation
using a double quantum dot structure is considered. A measurement scheme using
a stimulated Raman adiabatic passage is discussed.Comment: Revised version accepted for publication in Phys.Rev. B. 19 pages, 4
eps figure
Quantum copying: Fundamental inequalities
How well one can copy an arbitrary qubit? To answer this question we consider
two arbitrary vectors in a two-dimensional state space and an abstract copying
transformation which will copy these two vectors. If the vectors are
orthogonal, then perfect copies can be made. If they are not, then errors will
be introduced. The size of the error depends on the inner product of the two
original vectors. We derive a lower bound for the amount of noise induced by
quantum copying. We examine both copying transformations which produce one copy
and transformations which produce many, and show that the quality of each copy
decreases as the number of copies increases.Comment: 5 pages + 1 figure, LaTeX with revtex, epsfig submitted to Phys. Rev.
Computation on a Noiseless Quantum Code and Symmetrization
Let be the state-space of a quantum computer coupled with the
environment by a set of error operators spanning a Lie algebra
Suppose admits a noiseless quantum code i.e., a subspace annihilated by We show that a universal set of
gates over is obtained by any generic pair of -invariant
gates. Such gates - if not available from the outset - can be obtained by
resorting to a symmetrization with respect to the group generated by Any computation can then be performed completely within the coding
decoherence-free subspace.Comment: One result added, to appear in Phys. Rev. A (RC) 4 pages LaTeX, no
figure
Effect of an inhomogeneous external magnetic field on a quantum dot quantum computer
We calculate the effect of an inhomogeneous magnetic field, which is
invariably present in an experimental environment, on the exchange energy of a
double quantum dot artificial molecule, projected to be used as a 2-qubit
quantum gate in the proposed quantum dot quantum computer. We use two different
theoretical methods to calculate the Hilbert space structure in the presence of
the inhomogeneous field: the Heitler-London method which is carried out
analytically and the molecular orbital method which is done computationally.
Within these approximations we show that the exchange energy J changes slowly
when the coupled dots are subject to a magnetic field with a wide range of
inhomogeneity, suggesting swap operations can be performed in such an
environment as long as quantum error correction is applied to account for the
Zeeman term. We also point out the quantum interference nature of this slow
variation in exchange.Comment: 12 pages, 4 figures embedded in tex
Spin Qubits in Multi-Electron Quantum Dots
We study the effect of mesoscopic fluctuations on the magnitude of errors
that can occur in exchange operations on quantum dot spin-qubits. Mid-size
double quantum dots, with an odd number of electrons in the range of a few tens
in each dot, are investigated through the constant interaction model using
realistic parameters. It is found that the constraint of having short pulses
and small errors implies keeping accurate control, at the few percent level, of
several electrode voltages. In practice, the number of independent parameters
per dot that one should tune depends on the configuration and ranges from one
to four.Comment: RevTex, 6 pages, 5 figures. v3: two figures added, more details
provided. Accepted for publication in PR
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