1,620 research outputs found
A repetition code of 15 qubits
The repetition code is an important primitive for the techniques of quantum
error correction. Here we implement repetition codes of at most qubits on
the qubit \emph{ibmqx3} device. Each experiment is run for a single round
of syndrome measurements, achieved using the standard quantum technique of
using ancilla qubits and controlled operations. The size of the final syndrome
is small enough to allow for lookup table decoding using experimentally
obtained data. The results show strong evidence that the logical error rate
decays exponentially with code distance, as is expected and required for the
development of fault-tolerant quantum computers. The results also give insight
into the nature of noise in the device.Comment: 7 page
Flow Fragmentalism
In this paper, we articulate a version of non-standard A-theory – which we call Flow Fragmentalism – in relation to its take on the issue of supervenience of truth on being. According to the Truth Supervenes on Being (TSB) Principle, the truth of past- and future-tensed propositions supervenes, respectively, on past and future facts. Since the standard presentist denies the existence of past and future entities and facts concerning them that do not obtain in the present, she seems to lack the resources to accept both past and future-tensed truths and the TSB Principle. Contrariwise, positions in philosophy of time that accept an eternalist ontology (e.g., B-theory, moving spotlight, and Fine’s and Lipman’s versions of fragmentalism) allow for a “direct” supervenience base for past- and future-tensed truths. We argue that Flow Fragmentalism constitutes a middle ground, which retains most of the advantages of both views, and allows us to articulate a novel account of the passage of time
Parafermions in a Kagome lattice of qubits for topological quantum computation
Engineering complex non-Abelian anyon models with simple physical systems is
crucial for topological quantum computation. Unfortunately, the simplest
systems are typically restricted to Majorana zero modes (Ising anyons). Here we
go beyond this barrier, showing that the parafermion model of
non-Abelian anyons can be realized on a qubit lattice. Our system additionally
contains the Abelian anyons as low-energetic excitations. We
show that braiding of these parafermions with each other and with the
anyons allows the entire Clifford group to be
generated. The error correction problem for our model is also studied in
detail, guaranteeing fault-tolerance of the topological operations. Crucially,
since the non-Abelian anyons are engineered through defect lines rather than as
excitations, non-Abelian error correction is not required. Instead the error
correction problem is performed on the underlying Abelian model, allowing high
noise thresholds to be realized.Comment: 11+10 pages, 14 figures; v2: accepted for publication in Phys. Rev.
X; 4 new figures, performance of phase-gate explained in more detai
Mesoscopic Effects in the Fractional Quantum Hall Regime: Chiral Luttinger versus Fermi Liquid
We study tunneling through an edge state formed around an antidot in the
fractional quantum Hall regime using Wen's chiral Luttinger liquid theory
extended to include mesoscopic effects. We identify a new regime where the
Aharonov-Bohm oscillation amplitude exhibits a distinctive crossover from
Luttinger liquid power-law behavior to Fermi-liquid-like behavior as the
temperature is increased. Near the crossover temperature the amplitude has a
pronounced maximum. This non-monotonic behavior and novel high-temperature
nonlinear phenomena that we also predict provide new ways to distinguish
experimentally between Luttinger and Fermi liquids.Comment: 13 pages, Revtex, Figure available from [email protected]
Uniform Density Theorem for the Hubbard Model
A general class of hopping models on a finite bipartite lattice is
considered, including the Hubbard model and the Falicov-Kimball model. For the
half-filled band, the single-particle density matrix \uprho (x,y) in the
ground state and in the canonical and grand canonical ensembles is shown to be
constant on the diagonal , and to vanish if and if and
are on the same sublattice. For free electron hopping models, it is shown in
addition that there are no correlations between sites of the same sublattice in
any higher order density matrix. Physical implications are discussed.Comment: 15 pages, plaintex, EHLMLRJM-22/Feb/9
Hybridization and spin decoherence in heavy-hole quantum dots
We theoretically investigate the spin dynamics of a heavy hole confined to an
unstrained III-V semiconductor quantum dot and interacting with a narrowed
nuclear-spin bath. We show that band hybridization leads to an exponential
decay of hole-spin superpositions due to hyperfine-mediated nuclear pair flips,
and that the accordant single-hole-spin decoherence time T2 can be tuned over
many orders of magnitude by changing external parameters. In particular, we
show that, under experimentally accessible conditions, it is possible to
suppress hyperfine-mediated nuclear-pair-flip processes so strongly that
hole-spin quantum dots may be operated beyond the `ultimate limitation' set by
the hyperfine interaction which is present in other spin-qubit candidate
systems.Comment: 7 pages, 3 figure
Effect of strain on hyperfine-induced hole-spin decoherence in quantum dots
We theoretically consider the effect of strain on the spin dynamics of a
single heavy-hole (HH) confined to a self-assembled quantum dot and interacting
with the surrounding nuclei via hyperfine interaction. Confinement and strain
hybridize the HH states, which show an exponential decay for a narrowed nuclear
spin bath. For different strain configurations within the dot, the dependence
of the spin decoherence time on external parameters is shifted and the
non-monotonic dependence of the peak is altered. Application of external strain
yields considerable shifts in the dependence of on external parameters.
We find that external strain affects mostly the effective hyperfine coupling
strength of the conduction band (CB), indicating that the CB admixture of the
hybridized HH states plays a crucial role in the sensitivity of on
strain
Decoding non-Abelian topological quantum memories
The possibility of quantum computation using non-Abelian anyons has been
considered for over a decade. However the question of how to obtain and process
information about what errors have occurred in order to negate their effects
has not yet been considered. This is in stark contrast with quantum computation
proposals for Abelian anyons, for which decoding algorithms have been
tailor-made for many topological error-correcting codes and error models. Here
we address this issue by considering the properties of non-Abelian error
correction in general. We also choose a specific anyon model and error model to
probe the problem in more detail. The anyon model is the charge submodel of
. This shares many properties with important models such as the
Fibonacci anyons, making our method applicable in general. The error model is a
straightforward generalization of those used in the case of Abelian anyons for
initial benchmarking of error correction methods. It is found that error
correction is possible under a threshold value of for the total
probability of an error on each physical spin. This is remarkably comparable
with the thresholds for Abelian models
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