3,977 research outputs found
Recoverable Information and Emergent Conservation Laws in Fracton Stabilizer Codes
We introduce a new quantity, that we term recoverable information, defined
for stabilizer Hamiltonians. For such models, the recoverable information
provides a measure of the topological information, as well as a physical
interpretation, which is complementary to topological entanglement entropy. We
discuss three different ways to calculate the recoverable information, and
prove their equivalence. To demonstrate its utility, we compute recoverable
information for fracton models using all three methods where appropriate. From
the recoverable information, we deduce the existence of emergent
Gauss-law type constraints, which in turn imply emergent conservation
laws for point-like quasiparticle excitations of an underlying topologically
ordered phase.Comment: Added additional cluster model calculation (SPT example) and a new
section discussing the general benefits of recoverable informatio
Topological Entanglement Entropy of Fracton Stabilizer Codes
Entanglement entropy provides a powerful characterization of two-dimensional
gapped topological phases of quantum matter, intimately tied to their
description by topological quantum field theories (TQFTs). Fracton topological
orders are three-dimensional gapped topologically ordered states of matter, but
the existence of a TQFT description for these phases remains an open question.
We show that three-dimensional fracton phases are nevertheless characterized,
at least partially, by universal structure in the entanglement entropy of their
ground state wave functions. We explicitly compute the entanglement entropy for
two archetypal fracton models --- the `X-cube model' and `Haah's code' --- and
demonstrate the existence of a topological contribution that scales linearly in
subsystem size. We show via Schrieffer-Wolff transformations that the
topological entanglement of fracton models is robust against arbitrary local
perturbations of the Hamiltonian. Finally, we argue that these results may be
extended to characterize localization-protected fracton topological order in
excited states of disordered fracton models.Comment: published versio
Graphical Nonbinary Quantum Error-Correcting Codes
In this paper, based on the nonbinary graph state, we present a systematic
way of constructing good non-binary quantum codes, both additive and
nonadditive, for systems with integer dimensions. With the help of computer
search, which results in many interesting codes including some nonadditive
codes meeting the Singleton bounds, we are able to construct explicitly four
families of optimal codes, namely, , ,
and for any odd dimension and a family of nonadditive code
for arbitrary . In the case of composite numbers as
dimensions, we also construct a family of stabilizer codes for odd , whose coding subspace is {\em not} of a dimension
that is a power of the dimension of the physical subsystem.Comment: 12 pages, 5 figures (pdf
Qudit Colour Codes and Gauge Colour Codes in All Spatial Dimensions
Two-level quantum systems, qubits, are not the only basis for quantum
computation. Advantages exist in using qudits, d-level quantum systems, as the
basic carrier of quantum information. We show that color codes, a class of
topological quantum codes with remarkable transversality properties, can be
generalized to the qudit paradigm. In recent developments it was found that in
three spatial dimensions a qubit color code can support a transversal
non-Clifford gate, and that in higher spatial dimensions additional
non-Clifford gates can be found, saturating Bravyi and K\"onig's bound [Phys.
Rev. Lett. 110, 170503 (2013)]. Furthermore, by using gauge fixing techniques,
an effective set of Clifford gates can be achieved, removing the need for state
distillation. We show that the qudit color code can support the qudit analogues
of these gates, and show that in higher spatial dimensions a color code can
support a phase gate from higher levels of the Clifford hierarchy which can be
proven to saturate Bravyi and K\"onig's bound in all but a finite number of
special cases. The methodology used is a generalisation of Bravyi and Haah's
method of triorthogonal matrices [Phys. Rev. A 86 052329 (2012)], which may be
of independent interest. For completeness, we show explicitly that the qudit
color codes generalize to gauge color codes, and share the many of the
favorable properties of their qubit counterparts.Comment: Authors' final cop
Framework for classifying logical operators in stabilizer codes
Entanglement, as studied in quantum information science, and non-local
quantum correlations, as studied in condensed matter physics, are fundamentally
akin to each other. However, their relationship is often hard to quantify due
to the lack of a general approach to study both on the same footing. In
particular, while entanglement and non-local correlations are properties of
states, both arise from symmetries of global operators that commute with the
system Hamiltonian. Here, we introduce a framework for completely classifying
the local and non-local properties of all such global operators, given the
Hamiltonian and a bi-partitioning of the system. This framework is limited to
descriptions based on stabilizer quantum codes, but may be generalized. We
illustrate the use of this framework to study entanglement and non-local
correlations by analyzing global symmetries in topological order, distribution
of entanglement and entanglement entropy.Comment: 20 pages, 9 figure
Quantum memories based on engineered dissipation
Storing quantum information for long times without disruptions is a major
requirement for most quantum information technologies. A very appealing
approach is to use self-correcting Hamiltonians, i.e. tailoring local
interactions among the qubits such that when the system is weakly coupled to a
cold bath the thermalization process takes a long time. Here we propose an
alternative but more powerful approach in which the coupling to a bath is
engineered, so that dissipation protects the encoded qubit against more general
kinds of errors. We show that the method can be implemented locally in four
dimensional lattice geometries by means of a toric code, and propose a simple
2D set-up for proof of principle experiments.Comment: 6 +8 pages, 4 figures, Includes minor corrections updated references
and aknowledgement
Characterization of quantum dynamics using quantum error correction
Characterizing noisy quantum processes is important to quantum computation
and communication (QCC), since quantum systems are generally open. To date, all
methods of characterization of quantum dynamics (CQD), typically implemented by
quantum process tomography, are \textit{off-line}, i.e., QCC and CQD are not
concurrent, as they require distinct state preparations. Here we introduce a
method, "quantum error correction based characterization of dynamics", in which
the initial state is any element from the code space of a quantum error
correcting code that can protect the state from arbitrary errors acting on the
subsystem subjected to the unknown dynamics. The statistics of stabilizer
measurements, with possible unitary pre-processing operations, are used to
characterize the noise, while the observed syndrome can be used to correct the
noisy state. Our method requires at most configurations to
characterize arbitrary noise acting on qubits.Comment: 7 pages, 2 figures; close to the published versio
Density-matrix simulation of small surface codes under current and projected experimental noise
We present a full density-matrix simulation of the quantum memory and
computing performance of the distance-3 logical qubit Surface-17, following a
recently proposed quantum circuit and using experimental error parameters for
transmon qubits in a planar circuit QED architecture. We use this simulation to
optimize components of the QEC scheme (e.g., trading off stabilizer measurement
infidelity for reduced cycle time) and to investigate the benefits of feedback
harnessing the fundamental asymmetry of relaxation-dominated error in the
constituent transmons. A lower-order approximate calculation extends these
predictions to the distance- Surface-49. These results clearly indicate
error rates below the fault-tolerance threshold of surface code, and the
potential for Surface-17 to perform beyond the break-even point of quantum
memory. At state-of-the-art qubit relaxation times and readout speeds,
Surface-49 could surpass the break-even point of computation.Comment: 10 pages + 8 pages appendix, 12 figure
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