29,179 research outputs found
Finite correlation length implies efficient preparation of quantum thermal states
Preparing quantum thermal states on a quantum computer is in general a
difficult task. We provide a procedure to prepare a thermal state on a quantum
computer with a logarithmic depth circuit of local quantum channels assuming
that the thermal state correlations satisfy the following two properties: (i)
the correlations between two regions are exponentially decaying in the distance
between the regions, and (ii) the thermal state is an approximate Markov state
for shielded regions. We require both properties to hold for the thermal state
of the Hamiltonian on any induced subgraph of the original lattice. Assumption
(ii) is satisfied for all commuting Gibbs states, while assumption (i) is
satisfied for every model above a critical temperature. Both assumptions are
satisfied in one spatial dimension. Moreover, both assumptions are expected to
hold above the thermal phase transition for models without any topological
order at finite temperature. As a building block, we show that exponential
decay of correlation (for thermal states of Hamiltonians on all induced
subgraph) is sufficient to efficiently estimate the expectation value of a
local observable. Our proof uses quantum belief propagation, a recent
strengthening of strong sub-additivity, and naturally breaks down for states
with topological order.Comment: 16 pages, 4 figure
Simulation of Classical Thermal States on a Quantum Computer: A Transfer Matrix Approach
We present a hybrid quantum-classical algorithm to simulate thermal states of
a classical Hamiltonians on a quantum computer. Our scheme employs a sequence
of locally controlled rotations, building up the desired state by adding qubits
one at a time. We identify a class of classical models for which our method is
efficient and avoids potential exponential overheads encountered by Grover-like
or quantum Metropolis schemes. Our algorithm also gives an exponential
advantage for 2D Ising models with magnetic field on a square lattice, compared
with the previously known Zalka's algorithm.Comment: 5 pages, 3 figures; (new in version 2: added new figure, title
changed, rearranged paragraphs
Investigation of commuting Hamiltonian in quantum Markov network
Graphical Models have various applications in science and engineering which
include physics, bioinformatics, telecommunication and etc. Usage of graphical
models needs complex computations in order to evaluation of marginal
functions,so there are some powerful methods including mean field
approximation, belief propagation algorithm and etc. Quantum graphical models
have been recently developed in context of quantum information and computation,
and quantum statistical physics, which is possible by generalization of
classical probability theory to quantum theory. The main goal of this paper is
preparing a primary generalization of Markov network, as a type of graphical
models, to quantum case and applying in quantum statistical physics.We have
investigated the Markov network and the role of commuting Hamiltonian terms in
conditional independence with simple examples of quantum statistical physics.Comment: 11 pages, 8 figure
Preparing thermal states of quantum systems by dimension reduction
We present an algorithm that prepares thermal Gibbs states of one dimensional
quantum systems on a quantum computer without any memory overhead, and in a
time significantly shorter than other known alternatives. Specifically, the
time complexity is dominated by the quantity , where is the
size of the system, is a bound on the operator norm of the local terms
of the Hamiltonian (coupling energy), and is the temperature. Given other
results on the complexity of thermalization, this overall scaling is likely
optimal. For higher dimensions, our algorithm lowers the known scaling of the
time complexity with the dimension of the system by one.Comment: Published version. Minor editorial changes, one new reference added.
4 pages, 1 figur
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