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 $\omega$ give a synchronization accuracy that scales as $(\omega\sqrt{N})^{-1}$, i.e., as the standard quantum limit. We introduce a protocol that makes use of N coherent exchanges of a single qubit at frequency $\omega$, leading to an accuracy that scales as $(\omega N)^{-1}\log N$. 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