4,256 research outputs found
Simulation of many-qubit quantum computation with matrix product states
Matrix product states provide a natural entanglement basis to represent a
quantum register and operate quantum gates on it. This scheme can be
materialized to simulate a quantum adiabatic algorithm solving hard instances
of a NP-Complete problem. Errors inherent to truncations of the exact action of
interacting gates are controlled by the size of the matrices in the
representation. The property of finding the right solution for an instance and
the expected value of the energy are found to be remarkably robust against
these errors. As a symbolic example, we simulate the algorithm solving a
100-qubit hard instance, that is, finding the correct product state out of ~
10^30 possibilities. Accumulated statistics for up to 60 qubits point at a slow
growth of the average minimum time to solve hard instances with
highly-truncated simulations of adiabatic quantum evolution.Comment: 5 pages, 4 figures, final versio
Renormalization group transformations on quantum states
We construct a general renormalization group transformation on quantum
states, independent of any Hamiltonian dynamics of the system. We illustrate
this procedure for translational invariant matrix product states in one
dimension and show that product, GHZ, W and domain wall states are special
cases of an emerging classification of the fixed points of this
coarse--graining transformation.Comment: 5 pages, 2 figur
Entanglement and Quantum Phase Transition Revisited
We show that, for an exactly solvable quantum spin model, a discontinuity in
the first derivative of the ground state concurrence appears in the absence of
quantum phase transition. It is opposed to the popular belief that the
non-analyticity property of entanglement (ground state concurrence) can be used
to determine quantum phase transitions. We further point out that the
analyticity property of the ground state concurrence in general can be more
intricate than that of the ground state energy. Thus there is no one-to-one
correspondence between quantum phase transitions and the non-analyticity
property of the concurrence. Moreover, we show that the von Neumann entropy, as
another measure of entanglement, can not reveal quantum phase transition in the
present model. Therefore, in order to link with quantum phase transitions, some
other measures of entanglement are needed.Comment: RevTeX 4, 4 pages, 1 EPS figures. some modifications in the text.
Submitted to Phys. Rev.
Quantum simulation of an extra dimension
We present a general strategy to simulate a D+1-dimensional quantum system
using a D-dimensional one. We analyze in detail a feasible implementation of
our scheme using optical lattice technology. The simplest non-trivial
realization of a fourth dimension corresponds to the creation of a bivolume
geometry. We also propose single- and many-particle experimental signatures to
detect the effects of the extra dimension.Comment: 5 pages, 3 figures, revtex style;v2 minor changes, references adde
Violation of area-law scaling for the entanglement entropy in spin 1/2 chains
Entanglement entropy obeys area law scaling for typical physical quantum
systems. This may naively be argued to follow from locality of interactions. We
show that this is not the case by constructing an explicit simple spin chain
Hamiltonian with nearest neighbor interactions that presents an entanglement
volume scaling law. This non-translational model is contrived to have couplings
that force the accumulation of singlet bonds across the half chain. Our result
is complementary to the known relation between non-translational invariant,
nearest neighbor interacting Hamiltonians and QMA complete problems.Comment: 9 pages, 4 figure
Violation of the entropic area law for Fermions
We investigate the scaling of the entanglement entropy in an infinite
translational invariant Fermionic system of any spatial dimension. The states
under consideration are ground states and excitations of tight-binding
Hamiltonians with arbitrary interactions. We show that the entropy of a finite
region typically scales with the area of the surface times a logarithmic
correction. Thus, in contrast to analogous Bosonic systems, the entropic area
law is violated for Fermions. The relation between the entanglement entropy and
the structure of the Fermi surface is discussed, and it is proven, that the
presented scaling law holds whenever the Fermi surface is finite. This is in
particular true for all ground states of Hamiltonians with finite range
interactions.Comment: 5 pages, 1 figur
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