2,113 research outputs found
Keeping a Quantum Bit Alive by Optimized -Pulse Sequences
A general strategy to maintain the coherence of a quantum bit is proposed.
The analytical result is derived rigorously including all memory and
back-action effects. It is based on an optimized -pulse sequence for
dynamic decoupling extending the Carr-Purcell-Meiboom-Gill (CPMG) cycle. The
optimized sequence is very efficient, in particular for strong couplings to the
environment.Comment: 4 pages, 2 figures; revised version with additional references for
better context, more stringent discussio
Eigenlevel statistics of the quantum adiabatic algorithm
We study the eigenlevel spectrum of quantum adiabatic algorithm for
3-satisfiability problem, focusing on single-solution instances. The properties
of the ground state and the associated gap, crucial for determining the running
time of the algorithm, are found to be far from the predictions of random
matrix theory. The distribution of gaps between the ground and the first
excited state shows an abundance of small gaps. Eigenstates from the central
part of the spectrum are, on the other hand, well described by random matrix
theory.Comment: 8 pages, 10 ps figure
Exponential complexity of an adiabatic algorithm for an NP-complete problem
We prove an analytical expression for the size of the gap between the ground
and the first excited state of quantum adiabatic algorithm for the
3-satisfiability, where the initial Hamiltonian is a projector on the subspace
complementary to the ground state. For large problem sizes the gap decreases
exponentially and as a consequence the required running time is also
exponential.Comment: 5 pages, 2 figures; v3. published versio
Bounds for the adiabatic approximation with applications to quantum computation
We present straightforward proofs of estimates used in the adiabatic
approximation. The gap dependence is analyzed explicitly. We apply the result
to interpolating Hamiltonians of interest in quantum computing.Comment: 15 pages, one figure. Two comments added in Secs. 2 and
Dynamical properties across a quantum phase transition in the Lipkin-Meshkov-Glick model
It is of high interest, in the context of Adiabatic Quantum Computation, to
better understand the complex dynamics of a quantum system subject to a
time-dependent Hamiltonian, when driven across a quantum phase transition. We
present here such a study in the Lipkin-Meshkov-Glick (LMG) model with one
variable parameter. We first display numerical results on the dynamical
evolution across the LMG quantum phase transition, which clearly shows a
pronounced effect of the spectral avoided level crossings. We then derive a
phenomenological (classical) transition model, which already shows some
closeness to the numerical results. Finally, we show how a simplified quantum
transition model can be built which strongly improve the classical approach,
and shed light on the physical processes involved in the whole LMG quantum
evolution. From our results, we argue that the commonly used description in
term of Landau-Zener transitions is not appropriate for our model.Comment: 7 pages, 5 figures; corrected reference
Quantum error correction benchmarks for continuous weak parity measurements
We present an experimental procedure to determine the usefulness of a
measurement scheme for quantum error correction (QEC). A QEC scheme typically
requires the ability to prepare entangled states, to carry out multi-qubit
measurements, and to perform certain recovery operations conditioned on
measurement outcomes. As a consequence, the experimental benchmark of a QEC
scheme is a tall order because it requires the conjuncture of many elementary
components. Our scheme opens the path to experimental benchmarks of individual
components of QEC. Our numerical simulations show that certain parity
measurements realized in circuit quantum electrodynamics are on the verge of
being useful for QEC
Fault-Tolerant Thresholds for Encoded Ancillae with Homogeneous Errors
I describe a procedure for calculating thresholds for quantum computation as
a function of error model given the availability of ancillae prepared in
logical states with independent, identically distributed errors. The thresholds
are determined via a simple counting argument performed on a single qubit of an
infinitely large CSS code. I give concrete examples of thresholds thus
achievable for both Steane and Knill style fault-tolerant implementations and
investigate their relation to threshold estimates in the literature.Comment: 14 pages, 5 figures, 3 tables; v2 minor edits, v3 completely revised,
submitted to PR
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