4,179 research outputs found
Perfect Sampling with Unitary Tensor Networks
Tensor network states are powerful variational ans\"atze for many-body ground
states of quantum lattice models. The use of Monte Carlo sampling techniques in
tensor network approaches significantly reduces the cost of tensor
contractions, potentially leading to a substantial increase in computational
efficiency. Previous proposals are based on a Markov chain Monte Carlo scheme
generated by locally updating configurations and, as such, must deal with
equilibration and autocorrelation times, which result in a reduction of
efficiency. Here we propose a perfect sampling scheme, with vanishing
equilibration and autocorrelation times, for unitary tensor networks -- namely
tensor networks based on efficiently contractible, unitary quantum circuits,
such as unitary versions of the matrix product state (MPS) and tree tensor
network (TTN), and the multi-scale entanglement renormalization ansatz (MERA).
Configurations are directly sampled according to their probabilities in the
wavefunction, without resorting to a Markov chain process. We also describe a
partial sampling scheme that can result in a dramatic (basis-dependent)
reduction of sampling error.Comment: 11 pages, 9 figures, renamed partial sampling to incomplete sampling
for clarity, extra references, plus a variety of minor change
Complex Networks from Classical to Quantum
Recent progress in applying complex network theory to problems in quantum
information has resulted in a beneficial crossover. Complex network methods
have successfully been applied to transport and entanglement models while
information physics is setting the stage for a theory of complex systems with
quantum information-inspired methods. Novel quantum induced effects have been
predicted in random graphs---where edges represent entangled links---and
quantum computer algorithms have been proposed to offer enhancement for several
network problems. Here we review the results at the cutting edge, pinpointing
the similarities and the differences found at the intersection of these two
fields.Comment: 12 pages, 4 figures, REVTeX 4-1, accepted versio
Variational Monte Carlo with the Multi-Scale Entanglement Renormalization Ansatz
Monte Carlo sampling techniques have been proposed as a strategy to reduce
the computational cost of contractions in tensor network approaches to solving
many-body systems. Here we put forward a variational Monte Carlo approach for
the multi-scale entanglement renormalization ansatz (MERA), which is a unitary
tensor network. Two major adjustments are required compared to previous
proposals with non-unitary tensor networks. First, instead of sampling over
configurations of the original lattice, made of L sites, we sample over
configurations of an effective lattice, which is made of just log(L) sites.
Second, the optimization of unitary tensors must account for their unitary
character while being robust to statistical noise, which we accomplish with a
modified steepest descent method within the set of unitary tensors. We
demonstrate the performance of the variational Monte Carlo MERA approach in the
relatively simple context of a finite quantum spin chain at criticality, and
discuss future, more challenging applications, including two dimensional
systems.Comment: 11 pages, 12 figures, a variety of minor clarifications and
correction
Endurance of quantum coherence due to particle indistinguishability in noisy quantum networks
Quantum coherence, the physical property underlying fundamental phenomena
such as multi-particle interference and entanglement, has emerged as a valuable
resource upon which modern technologies are founded. In general, the most
prominent adversary of quantum coherence is noise arising from the interaction
of the associated dynamical system with its environment. Under certain
conditions, however, the existence of noise may drive quantum and classical
systems to endure intriguing nontrivial effects. In this vein, here we
demonstrate, both theoretically and experimentally, that when two
indistinguishable non-interacting particles co-propagate through quantum
networks affected by non-dissipative noise, the system always evolves into a
steady state in which coherences accounting for particle indistinguishabilty
perpetually prevail. Furthermore, we show that the same steady state with
surviving quantum coherences is reached even when the initial state exhibits
classical correlations.Comment: arXiv admin note: substantial text overlap with arXiv:1709.0433
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