39 research outputs found
Average Fidelity in n-Qubit systems
This letter generalizes the expression for the average fidelity of single
qubits, as found by Bowdrey et al., to the case of n qubits. We use a simple
algebraic approach with basis elements for the density-matrix expansion
expressed as Kronecker products of n Pauli spin matrices. An explicit
integration over initial states is avoided by invoking the invariance of the
state average under unitary transformations of the initial density matrix. The
results have applications to measurements of quantum information, for example
in ion-trap and NMR experiments.Comment: 4 pages, no figures. Revision includes additional references and a
more detailed symmetry argumen
Compiling gate networks on an Ising quantum computer
Here we describe a simple mechanical procedure for compiling a quantum gate
network into the natural gates (pulses and delays) for an Ising quantum
computer. The aim is not necessarily to generate the most efficient pulse
sequence, but rather to develop an efficient compilation algorithm that can be
easily implemented in large spin systems. The key observation is that it is not
always necessary to refocus all the undesired couplings in a spin system.
Instead the coupling evolution can simply be tracked and then corrected at some
later time. Although described within the language of NMR the algorithm is
applicable to any design of quantum computer based on Ising couplings.Comment: 5 pages RevTeX4 including 4 figures. Will submit to PR
The distribution of quantum fidelities
When applied to different input states, an imperfect quantum operation yields
output states with varying fidelities, defined as the absolute square of their
overlap with the desired states. We present an expression for the distribution
of fidelities for a class of operations applied to a general qubit state, and
we present general expressions for the variance and input-space averaged
fidelities of arbitrary linear maps on finite dimensional Hilbert spaces.Comment: 5 pages, 1 figur
Fidelity of quantum operations
We present a derivation and numerous applications of a compact explicit
formula for the average fidelity of a quantum operation on a finite dimensional
quantum system. The formula can be applied to averages over particularly
relevant subspaces; it is easily generalized to multi-component systems, and as
a special result, we show that when the same completely positive
trace-preserving map is applied to a large number of qubits with one-bit
fidelity F close to unity, the average fidelity of the operation on the full
K-bit register scales as .Comment: 5 pages, no figures. The text has been modified to acknowledge that
our Eq.(1) has appeared already in quant-ph/0503243 and quant-ph/051221
Minimal measurements of the gate fidelity of a qudit map
We obtain a simple formula for the average gate fidelity of a linear map
acting on qudits. It is given in terms of minimal sets of pure state
preparations alone, which may be interesting from the experimental point of
view. These preparations can be seen as the outcomes of certain minimal
positive operator valued measures. The connection of our results with these
generalized measurements is briefly discussed
Effect of noise on geometric logic gates for quantum computation
We introduce the non-adiabatic, or Aharonov-Anandan, geometric phase as a
tool for quantum computation and show how it could be implemented with
superconducting charge qubits. While it may circumvent many of the drawbacks
related to the adiabatic (Berry) version of geometric gates, we show that the
effect of fluctuations of the control parameters on non-adiabatic phase gates
is more severe than for the standard dynamic gates. Similarly, fluctuations
also affect to a greater extent quantum gates that use the Berry phase instead
of the dynamic phase.Comment: 8 pages, 4 figures; published versio
Single qubit gates by selective excitation with Jump and Return sequences
We discuss the implementation of frequency selective rotations using
sequences of hard pulses and delays. These rotations are suitable for
implementing single qubit gates in Nuclear Magnetic Resonance (NMR) quantum
computers, but can also be used in other related implementations of quantum
computing. We also derive methods for implementing hard pulses in the presence
of moderate off-resonance effects, and describe a simple procedure for
implementing a hard 180 degree rotation in a two spin system. Finally we show
how these two approaches can be combined to produce more accurate frequency
selective rotations.Comment: Revised and extended at request of referee; now in press at Physical
Review A. 6 pages RevTex including 3 figure
State transfer in dissipative and dephasing environments
By diagonalization of a generalized superoperator for solving the master
equation, we investigated effects of dissipative and dephasing environments on
quantum state transfer, as well as entanglement distribution and creation in
spin networks. Our results revealed that under the condition of the same
decoherence rate , the detrimental effects of the dissipative
environment are more severe than that of the dephasing environment. Beside
this, the critical time at which the transfer fidelity and the
concurrence attain their maxima arrives at the asymptotic value
quickly as the spin chain length increases. The transfer
fidelity of an excitation at time is independent of when the system
subjects to dissipative environment, while it decreases as increases when
the system subjects to dephasing environment. The average fidelity displays
three different patterns corresponding to , and . For
each pattern, the average fidelity at time is independent of when the
system subjects to dissipative environment, and decreases as increases when
the system subjects to dephasing environment. The maximum concurrence also
decreases as increases, and when , it arrives at an
asymptotic value determined by the decoherence rate and the structure
of the spin network.Comment: 12 pages, 6 figure