627 research outputs found
Symmetry-protected self-correcting quantum memories
A self-correcting quantum memory can store and protect quantum information
for a time that increases without bound with the system size and without the
need for active error correction. We demonstrate that symmetry can lead to
self-correction in 3D spin-lattice models. In particular, we investigate codes
given by 2D symmetry-enriched topological (SET) phases that appear naturally on
the boundary of 3D symmetry-protected topological (SPT) phases. We find that
while conventional on-site symmetries are not sufficient to allow for
self-correction in commuting Hamiltonian models of this form, a generalized
type of symmetry known as a 1-form symmetry is enough to guarantee
self-correction. We illustrate this fact with the 3D "cluster-state" model from
the theory of quantum computing. This model is a self-correcting memory, where
information is encoded in a 2D SET-ordered phase on the boundary that is
protected by the thermally stable SPT ordering of the bulk. We also investigate
the gauge color code in this context. Finally, noting that a 1-form symmetry is
a very strong constraint, we argue that topologically ordered systems can
possess emergent 1-form symmetries, i.e., models where the symmetry appears
naturally, without needing to be enforced externally.Comment: 39 pages, 16 figures, comments welcome; v2 includes much more
explicit detail on the main example model, including boundary conditions and
implementations of logical operators through local moves; v3 published
versio
Optimizing qubit Hamiltonian parameter estimation algorithms using PSO
We develop qubit Hamiltonian single parameter estimation techniques using a
Bayesian approach. The algorithms considered are restricted to projective
measurements in a fixed basis, and are derived under the assumption that the
qubit measurement is much slower than the characteristic qubit evolution. We
optimize a non-adaptive algorithm using particle swarm optimization (PSO) and
compare with a previously-developed locally-optimal scheme.Comment: 3 pages, 2 figures, presented at 2012 IEEE Congress on Evolutionary
Computation, to be published in the proceeding
Quantum methods for clock synchronization: Beating the standard quantum limit without entanglement
We introduce methods for clock synchronization that make use of the adiabatic
exchange of nondegenerate two-level quantum systems: ticking qubits. Schemes
involving the exchange of N independent qubits with frequency give a
synchronization accuracy that scales as , i.e., as the
standard quantum limit. We introduce a protocol that makes use of N coherent
exchanges of a single qubit at frequency , leading to an accuracy that
scales as . This protocol beats the standard quantum
limit without the use of entanglement, and we argue that this scaling is the
fundamental limit for clock synchronization allowed by quantum mechanics. We
analyse the performance of these protocols when used with a lossy channel.Comment: 9 pages, 1 figure, published versio
Requirement for quantum computation
We identify "proper quantum computation" with computational processes that
cannot be efficiently simulated on a classical computer. For optical quantum
computation, we establish "no-go" theorems for classes of quantum optical
experiments that cannot yield proper quantum computation, and we identify
requirements for optical proper quantum computation that correspond to
violations of assumptions underpinning the no-go theorems.Comment: 11 pages, no figure
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