455 research outputs found
Asymmetry of bipartite quantum discord
It is known from the analysis of the density matrix for bipartite systems
that the quantum discord (as a measure of quantum correlations) depends on the
particular subsystem chosen for the projective measurements. We study asymmetry
of the discord in a simple physical model of two spin-1/2 particles with the
dipole-dipole interaction governed by the XY Hamiltonian in the inhomogeneous
magnetic field. The dependence of the above discord asymmetry on the Larmour
frequencies at both T=0 (the ground state) and has been investigated. It
is demonstrated, in particular, that the asymmetry is negligible for high
temperatures but it may become significant with the decrease in temperature.Comment: 5 pages 3 figure
Quantum Simulation of Spin Chains Coupled to Bosonic Modes with Superconducting Circuits
We propose the implementation of a digital quantum simulation of spin chains
coupled to bosonic field modes in superconducting circuits. Gates with high
fidelities allows one to simulate a variety of Ising magnetic pairing
interactions with transverse field, Tavis-Cummings interaction between spins
and a bosonic mode, and a spin model with three-body terms. We analyze the
feasibility of the implementation in realistic circuit quantum electrodynamics
setups, where the interactions are either realized via capacitive couplings or
mediated by microwave resonators.Comment: Chapter in R. S. Anderssen et al. (eds.), Mathematics for Industry 11
(Springer Japan, 2015
Quantum Simulation of Tunneling in Small Systems
A number of quantum algorithms have been performed on small quantum
computers; these include Shor's prime factorization algorithm, error
correction, Grover's search algorithm and a number of analog and digital
quantum simulations. Because of the number of gates and qubits necessary,
however, digital quantum particle simulations remain untested. A contributing
factor to the system size required is the number of ancillary qubits needed to
implement matrix exponentials of the potential operator. Here, we show that a
set of tunneling problems may be investigated with no ancillary qubits and a
cost of one single-qubit operator per time step for the potential evolution. We
show that physically interesting simulations of tunneling using 2 qubits (i.e.
on 4 lattice point grids) may be performed with 40 single and two-qubit gates.
Approximately 70 to 140 gates are needed to see interesting tunneling dynamics
in three-qubit (8 lattice point) simulations.Comment: 4 pages, 2 figure
Optical one-way quantum computing with a simulated valence-bond solid
One-way quantum computation proceeds by sequentially measuring individual
spins (qubits) in an entangled many-spin resource state. It remains a
challenge, however, to efficiently produce such resource states. Is it possible
to reduce the task of generating these states to simply cooling a quantum
many-body system to its ground state? Cluster states, the canonical resource
for one-way quantum computing, do not naturally occur as ground states of
physical systems. This led to a significant effort to identify alternative
resource states that appear as ground states in spin lattices. An appealing
candidate is a valence-bond-solid state described by Affleck, Kennedy, Lieb,
and Tasaki (AKLT). It is the unique, gapped ground state for a two-body
Hamiltonian on a spin-1 chain, and can be used as a resource for one-way
quantum computing. Here, we experimentally generate a photonic AKLT state and
use it to implement single-qubit quantum logic gates.Comment: 11 pages, 4 figures, 8 tables - added one referenc
Quantum circuits for spin and flavor degrees of freedom of quarks forming nucleons
We discuss the quantum-circuit realization of the state of a nucleon in the
scope of simple symmetry groups. Explicit algorithms are presented for the
preparation of the state of a neutron or a proton as resulting from the
composition of their quark constituents. We estimate the computational
resources required for such a simulation and design a photonic network for its
implementation. Moreover, we highlight that current work on three-body
interactions in lattices of interacting qubits, combined with the
measurement-based paradigm for quantum information processing, may also be
suitable for the implementation of these nucleonic spin states.Comment: 5 pages, 2 figures, RevTeX4; Accepted for publication in Quantum
Information Processin
Digital Quantum Simulation of the Statistical Mechanics of a Frustrated Magnet
Many interesting problems in physics, chemistry, and computer science are
equivalent to problems of interacting spins. However, most of these problems
require computational resources that are out of reach by classical computers. A
promising solution to overcome this challenge is to exploit the laws of quantum
mechanics to perform simulation. Several "analog" quantum simulations of
interacting spin systems have been realized experimentally. However, relying on
adiabatic techniques, these simulations are limited to preparing ground states
only. Here we report the first experimental results on a "digital" quantum
simulation on thermal states; we simulated a three-spin frustrated magnet, a
building block of spin ice, with an NMR quantum information processor, and we
are able to explore the phase diagram of the system at any simulated
temperature and external field. These results serve as a guide for identifying
the challenges for performing quantum simulation on physical systems at finite
temperatures, and pave the way towards large scale experimental simulations of
open quantum systems in condensed matter physics and chemistry.Comment: 7 pages for the main text plus 6 pages for the supplementary
material
Transverse Ising Model: Markovian evolution of classical and quantum correlations under decoherence
The transverse Ising Model (TIM) in one dimension is the simplest model which
exhibits a quantum phase transition (QPT). Quantities related to quantum
information theoretic measures like entanglement, quantum discord (QD) and
fidelity are known to provide signatures of QPTs. The issue is less well
explored when the quantum system is subjected to decoherence due to its
interaction, represented by a quantum channel, with an environment. In this
paper we study the dynamics of the mutual information , the
classical correlations and the quantum correlations
, as measured by the QD, in a two-qubit state the density matrix
of which is the reduced density matrix obtained from the ground state of the
TIM in 1d. The time evolution brought about by system-environment interactions
is assumed to be Markovian in nature and the quantum channels considered are
amplitude damping, bit-flip, phase-flip and bit-phase-flip. Each quantum
channel is shown to be distinguished by a specific type of dynamics. In the
case of the phase-flip channel, there is a finite time interval in which the
quantum correlations are larger in magnitude than the classical correlations.
For this channel as well as the bit-phase-flip channel, appropriate quantities
associated with the dynamics of the correlations can be derived which signal
the occurrence of a QPT.Comment: 8 pages, 7 figures, revtex4-1, version accepted for publication in
Eur. Phys. J.
Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
The presence of long-range quantum spin correlations underlies a variety of
physical phenomena in condensed matter systems, potentially including
high-temperature superconductivity. However, many properties of exotic strongly
correlated spin systems (e.g., spin liquids) have proved difficult to study, in
part because calculations involving N-body entanglement become intractable for
as few as N~30 particles. Feynman divined that a quantum simulator - a
special-purpose "analog" processor built using quantum particles (qubits) -
would be inherently adept at such problems. In the context of quantum
magnetism, a number of experiments have demonstrated the feasibility of this
approach. However, simulations of quantum magnetism allowing controlled,
tunable interactions between spins localized on 2D and 3D lattices of more than
a few 10's of qubits have yet to be demonstrated, owing in part to the
technical challenge of realizing large-scale qubit arrays. Here we demonstrate
a variable-range Ising-type spin-spin interaction J_ij on a naturally occurring
2D triangular crystal lattice of hundreds of spin-1/2 particles (9Be+ ions
stored in a Penning trap), a computationally relevant scale more than an order
of magnitude larger than existing experiments. We show that a spin-dependent
optical dipole force can produce an antiferromagnetic interaction J_ij ~
1/d_ij^a, where a is tunable over 0<a<3; d_ij is the distance between spin
pairs. These power-laws correspond physically to infinite-range (a=0),
Coulomb-like (a=1), monopole-dipole (a=2) and dipole-dipole (a=3) couplings.
Experimentally, we demonstrate excellent agreement with theory for 0.05<a<1.4.
This demonstration coupled with the high spin-count, excellent quantum control
and low technical complexity of the Penning trap brings within reach simulation
of interesting and otherwise computationally intractable problems in quantum
magnetism.Comment: 10 pages, 10 figures; article plus Supplementary Material
Quantum discord evolution of three-qubit states under noisy channels
We investigated the dissipative dynamics of quantum discord for correlated
qubits under Markovian environments.
The basic idea in the present scheme is that quantum discord is more general,
and possibly more robust and fundamental, than entanglement. We provide three
initially correlated qubits in pure Greenberger-Horne-Zeilinger (GHZ) or W
state and analyse the time evolution of the quantum discord under various
dissipative channels such as:
Pauli channels , , and , as well as
depolarising channels. Surprisingly, we find that under the action of Pauli
channel , the quantum discord of GHZ state is not affected by
decoherence. For the remaining dissipative channels, the W state is more robust
than the GHZ state against decoherence. Moreover, we compare the dynamics of
entanglement with that of the quantum discord under the conditions in which
disentanglement occurs and show that quantum discord is more robust than
entanglement except for phase flip coupling of the three qubits system to the
environment.Comment: 17 pages, 4 figures, accepted for publication in EPJ
Simulating open quantum systems: from many-body interactions to stabilizer pumping
In a recent experiment, Barreiro et al. demonstrated the fundamental building
blocks of an open-system quantum simulator with trapped ions [Nature 470, 486
(2011)]. Using up to five ions, single- and multi-qubit entangling gate
operations were combined with optical pumping in stroboscopic sequences. This
enabled the implementation of both coherent many-body dynamics as well as
dissipative processes by controlling the coupling of the system to an
artificial, suitably tailored environment. This engineering was illustrated by
the dissipative preparation of entangled two- and four-qubit states, the
simulation of coherent four-body spin interactions and the quantum
non-demolition measurement of a multi-qubit stabilizer operator. In the present
paper, we present the theoretical framework of this gate-based ("digital")
simulation approach for open-system dynamics with trapped ions. In addition, we
discuss how within this simulation approach minimal instances of spin models of
interest in the context of topological quantum computing and condensed matter
physics can be realized in state-of-the-art linear ion-trap quantum computing
architectures. We outline concrete simulation schemes for Kitaev's toric code
Hamiltonian and a recently suggested color code model. The presented simulation
protocols can be adapted to scalable and two-dimensional ion-trap
architectures, which are currently under development.Comment: 27 pages, 9 figures, submitted to NJP Focus on Topological Quantum
Computatio
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