105,256 research outputs found
Universal quantum computation by discontinuous quantum walk
Quantum walks are the quantum-mechanical analog of random walks, in which a
quantum `walker' evolves between initial and final states by traversing the
edges of a graph, either in discrete steps from node to node or via continuous
evolution under the Hamiltonian furnished by the adjacency matrix of the graph.
We present a hybrid scheme for universal quantum computation in which a quantum
walker takes discrete steps of continuous evolution. This `discontinuous'
quantum walk employs perfect quantum state transfer between two nodes of
specific subgraphs chosen to implement a universal gate set, thereby ensuring
unitary evolution without requiring the introduction of an ancillary coin
space. The run time is linear in the number of simulated qubits and gates. The
scheme allows multiple runs of the algorithm to be executed almost
simultaneously by starting walkers one timestep apart.Comment: 7 pages, revte
Efficient discrete-time simulations of continuous-time quantum query algorithms
The continuous-time query model is a variant of the discrete query model in
which queries can be interleaved with known operations (called "driving
operations") continuously in time. Interesting algorithms have been discovered
in this model, such as an algorithm for evaluating nand trees more efficiently
than any classical algorithm. Subsequent work has shown that there also exists
an efficient algorithm for nand trees in the discrete query model; however,
there is no efficient conversion known for continuous-time query algorithms for
arbitrary problems.
We show that any quantum algorithm in the continuous-time query model whose
total query time is T can be simulated by a quantum algorithm in the discrete
query model that makes O[T log(T) / log(log(T))] queries. This is the first
upper bound that is independent of the driving operations (i.e., it holds even
if the norm of the driving Hamiltonian is very large). A corollary is that any
lower bound of T queries for a problem in the discrete-time query model
immediately carries over to a lower bound of \Omega[T log(log(T))/log (T)] in
the continuous-time query model.Comment: 12 pages, 6 fig
Atomic Quantum Simulation of Dynamical Gauge Fields coupled to Fermionic Matter: From String Breaking to Evolution after a Quench
Using a Fermi-Bose mixture of ultra-cold atoms in an optical lattice, we
construct a quantum simulator for a U(1) gauge theory coupled to fermionic
matter. The construction is based on quantum links which realize continuous
gauge symmetry with discrete quantum variables. At low energies, quantum link
models with staggered fermions emerge from a Hubbard-type model which can be
quantum simulated. This allows us to investigate string breaking as well as the
real-time evolution after a quench in gauge theories, which are inaccessible to
classical simulation methods.Comment: 14 pages, 5 figures. Main text plus one general supplementary
material and one basic introduction to the topic. Published versio
Non-local updates for quantum Monte Carlo simulations
We review the development of update schemes for quantum lattice models
simulated using world line quantum Monte Carlo algorithms. Starting from the
Suzuki-Trotter mapping we discuss limitations of local update algorithms and
highlight the main developments beyond Metropolis-style local updates: the
development of cluster algorithms, their generalization to continuous time, the
worm and directed-loop algorithms and finally a generalization of the flat
histogram method of Wang and Landau to quantum systems.Comment: 14 pages, article for the proceedings of the "The Monte Carlo Method
in the Physical Sciences: Celebrating the 50th Anniversary of the Metropolis
Algorithm", Los Alamos, June 9-11, 200
The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
In this Letter we show that an arbitrarily good approximation to the
propagator e^{itH} for a 1D lattice of n quantum spins with hamiltonian H may
be obtained with polynomial computational resources in n and the error
\epsilon, and exponential resources in |t|. Our proof makes use of the finitely
correlated state/matrix product state formalism exploited by numerical
renormalisation group algorithms like the density matrix renormalisation group.
There are two immediate consequences of this result. The first is that the
Vidal's time-dependent density matrix renormalisation group will require only
polynomial resources to simulate 1D quantum spin systems for logarithmic |t|.
The second consequence is that continuous-time 1D quantum circuits with
logarithmic |t| can be simulated efficiently on a classical computer, despite
the fact that, after discretisation, such circuits are of polynomial depth.Comment: 4 pages, 2 figures. Simplified argumen
- …