14 research outputs found
Eigenstate Thermalization in Systems with Spontaneously Broken Symmetry
A strongly non-integrable system is expected to satisfy the eigenstate
thermalization hypothesis, which states that the expectation value of an
observable in an energy eigenstate is the same as the thermal value. This must
be revised if the observable is an order parameter for a spontaneously broken
symmetry, which has multiple thermal values. We propose that in this case the
system is unstable towards forming nearby eigenstates which yield each of the
allowed thermal values. We provide strong evidence for this from a numerical
study of the 2D transverse-field quantum Ising model.Comment: 4 pages, 5 figure
The Discrete Noise Approximation in Quantum Circuits
When modeling the effects of noise on quantum circuits, one often makes the
assumption that these effects can be accounted for by individual decoherence
events following an otherwise noise-free gate. In this work, we address the
validity of this model. We find that under a fairly broad set of assumptions,
this model of individual decoherence events provides a good approximation to
the true noise processes occurring on a quantum device during the
implementation of a quantum circuit. However, for gates which correspond to
sufficiently large rotations of the qubit register, we find that the
qualitative nature of these noise terms can vary significantly from the nature
of the noise at the underlying hardware level. The bulk of our analysis is
directed towards analyzing what we refer to as the separability ansatz, which
is an ansatz concerning the manner in which individual quantum operations
acting on a quantum system can be approximated. In addition to the primary
motivation of this work, we identify several other areas of open research which
may benefit from the results we derive here.Comment: 14 pages, 3 figures main text; 15 pages, 1 figure appendix. This
updated version contains some minor notational changes, as well as a few
additional clarifying remark
Describing Trotterized Time Evolutions on Noisy Quantum Computers via Static Effective Lindbladians
We consider the extent to which a noisy quantum computer is able to simulate
the time evolution of a quantum spin system in a faithful manner. Given a
specific set of assumptions regarding the manner in which noise acting on such
a device can be modelled at the circuit level, we show how the effects of noise
can be reinterpreted as a modification to the dynamics of the original system
being simulated. In particular, we find that this modification corresponds to
the introduction of static Lindblad noise terms, which act in addition to the
original unitary dynamics. The form of these noise terms depends not only on
the underlying noise processes occurring on the device, but also on the
original unitary dynamics, as well as the manner in which these dynamics are
simulated on the device, i.e., the choice of quantum algorithm. We call this
effectively simulated open quantum system the noisy algorithm model. Our
results are confirmed through numerical analysis.Comment: 13 pages, 11 figures main text; 3 pages, 2 figures appendix. This
updated version removes two of the previous appendices, with the submission
arXiv:2311.00135 now addressing these ideas in their own separate article.
This version also contains some clarifying remarks, some notational changes,
and some minor corrections, as well as a new subsection considering the case
of gate cancellatio
A quantum algorithm for solving open system dynamics on quantum computers using noise
In this paper we present a quantum algorithm that uses noise as a resource.
The goal of our quantum algorithm is the calculation of operator averages of an
open quantum system evolving in time. Selected low-noise system qubits and
noisy bath qubits represent the system and the bath of the open quantum system.
All incoherent qubit noise can be mapped to bath spectral functions. The form
of the spectral functions can be tuned digitally, allowing for the time
evolution of a wide range of open-system models at finite temperature. We study
the feasibility of this approach with a focus on the solution of the spin-boson
model and assume intrinsic qubit noise that is dominated by damping and
dephasing. We find that classes of open quantum systems exist where our
algorithm performs very well, even with gate errors as high as 1%. In general
the presented algorithm performs best if the system-bath interactions can be
decomposed into native gates.Comment: 19 pages, 8 figures in total: 10 pages main text with 7 figure
Imaging signatures of the local density of states in an electronic cavity
We use Scanning Gate Microscopy to study electron transport through an open,
gate-defined resonator in a Ga(Al)As heterostructure. Raster-scanning the
voltage-biased metallic tip above the resonator, we observe distinct
conductance modulations as a function of the tip-position and voltage. Quantum
mechanical simulations reproduce these conductance modulations and reveal their
relation to the partial local density of states in the resonator. Our
measurements illustrate the current frontier between possibilities and
limitations in imaging the local density of states in buried electron systems
using scanning gate microscopy
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Eigenstate thermalization in systems with spontaneously broken symmetry.
A strongly nonintegrable system is expected to satisfy the eigenstate thermalization hypothesis, which states that the expectation value of an observable in an energy eigenstate is the same as the thermal value. This must be revised if the observable is an order parameter for a spontaneously broken symmetry, which has multiple thermal values. We propose that in this case the system is unstable towards forming nearby eigenstates which yield each of the allowed thermal values. We provide strong evidence for this from a numerical study of the two-dimensional transverse-field quantum Ising model