54 research outputs found
Noise-tolerant quantum speedups in quantum annealing without fine tuning
Quantum annealing is a powerful alternative model for quantum computing,
which can succeed in the presence of environmental noise even without error
correction. However, despite great effort, no conclusive proof of a quantum
speedup (relative to state of the art classical algorithms) has been shown for
these systems, and rigorous theoretical proofs of a quantum advantage generally
rely on exponential precision in at least some aspects of the system, an
unphysical resource guaranteed to be scrambled by random noise. In this work,
we propose a new variant of quantum annealing, called RFQA, which can maintain
a scalable quantum speedup in the face of noise and modest control precision.
Specifically, we consider a modification of flux qubit-based quantum annealing
which includes random, but coherent, low-frequency oscillations in the
directions of the transverse field terms as the system evolves. We show that
this method produces a quantum speedup for finding ground states in the Grover
problem and quantum random energy model, and thus should be widely applicable
to other hard optimization problems which can be formulated as quantum spin
glasses. Further, we show that this speedup should be resilient to two
realistic noise channels (-like local potential fluctuations and local
heating from interaction with a finite temperature bath), and that another
noise channel, bath-assisted quantum phase transitions, actually accelerates
the algorithm and may outweigh the negative effects of the others. The
modifications we consider have a straightforward experimental implementation
and could be explored with current technology.Comment: 21 pages, 7 figure
Localization of interacting fermions at high temperature
We suggest that if a localized phase at nonzero temperature exists for
strongly disordered and weakly interacting electrons, as recently argued, it
will also occur when both disorder and interactions are strong and is very
high. We show that in this high- regime the localization transition may be
studied numerically through exact diagonalization of small systems. We obtain
spectra for one-dimensional lattice models of interacting spinless fermions in
a random potential. As expected, the spectral statistics of finite-size samples
cross over from those of orthogonal random matrices in the diffusive regime at
weak random potential to Poisson statistics in the localized regime at strong
randomness. However, these data show deviations from simple one-parameter
finite-size scaling: the apparent mobility edge ``drifts'' as the system's size
is increased. Based on spectral statistics alone, we have thus been unable to
make a strong numerical case for the presence of a many-body localized phase at
nonzero
Theory of dissipationless Nernst effects
We develop a theory of transverse thermoelectric (Peltier) conductivity,
\alpha_{xy}, in finite magnetic field -- this particular conductivity is often
the most important contribution to the Nernst thermopower. We demonstrate that
\alpha_{xy} of a free electron gas can be expressed purely and exactly as the
entropy per carrier irrespective of temperature (which agrees with seminal Hall
bar result of Girvin and Jonson). In two dimensions we prove the universality
of this result in the presence of disorder which allows explicit demonstration
of a number features of interest to experiments on graphene and other
two-dimensional materials. We also exploit this relationship in the low field
regime and to analyze the rich singularity structure in \alpha_{xy}(B, T) in
three dimensions; we discuss its possible experimental implications.Comment: 4.5 pages, 2 figure
Phenomenology of fully many-body-localized systems
We consider fully many-body localized systems, i.e. isolated quantum systems
where all the many-body eigenstates of the Hamiltonian are localized. We define
a sense in which such systems are integrable, with localized conserved
operators. These localized operators are interacting pseudospins, and the
Hamiltonian is such that unitary time evolution produces dephasing but not
"flips" of these pseudospins. As a result, an initial quantum state of a
pseudospin can in principle be recovered via (pseudospin) echo procedures. We
discuss how the exponentially decaying interactions between pseudospins lead to
logarithmic-in-time spreading of entanglement starting from nonentangled
initial states. These systems exhibit multiple different length scales that can
be defined from exponential functions of distance; we suggest that some of
these decay lengths diverge at the phase transition out of the fully many-body
localized phase while others remain finite.Comment: 5 pages. Some of this paper has already appeared in: Huse and
Oganesyan, arXiv:1305.491
- …