5,278 research outputs found
Dynamics of Electrons in Graded Semiconductors
I present a theory of electron dynamics in semiconductors with slowly varying
composition. I show that the frequency-dependent conductivity, required for the
description of transport and optical properties, can be obtained from a
knowledge of the band structures and momentum matrix elements of homogeneous
semiconductor alloys. New sum rules for the electronic oscillator strengths,
which apply within a given energy band or between any two bands, are derived,
and a general expression for the width of the intraband absorption peak is
given. Finally, the low-frequency dynamics is discussed, and a correspondence
with the semiclassical motion is established.Comment: 4 pages, Revte
New sum rules for an electron in a periodic or nearly periodic potential
I derive new sum rules for the electronic oscillator strengths in a periodic
or nearly periodic potential, which apply within a single energy band and
between any two bands. The physical origin of these sum rules is quite unlike
that of conventional sum rules, and is shown to be associated with a
solid-state counterpart to the principle of spectroscopic stability known in
atomic physics.Comment: 4 pages, Revte
Noisy intermediate-scale quantum computation with a complete graph of superconducting qubits: Beyond the single-excitation subspace
There is currently a tremendous interest in developing practical applications
of NISQ processors without the overhead required by full error correction.
Quantum information processing is especially challenging within the gate model,
as algorithms quickly lose fidelity as the problem size and circuit depth grow.
This has lead to a number of non-gate-model approaches such as analog quantum
simulation and quantum annealing. These approaches come with specific hardware
requirements that are typically different than that of a universal gate-based
quantum computer. We have previously proposed a non-gate-model approach called
the single-excitation subspace (SES) method, which requires a complete graph of
superconducting qubits. Like any approach lacking error correction, the SES
method is not scalable, but it often leads to algorithms with constant depth,
allowing it to outperform the gate model in a wide variety of applications. A
challenge of the SES method is that it requires a physical qubit for every
basis state in the computer's Hilbert space. This imposes large resource costs
for algorithms using registers of ancillary qubits, as each ancilla would
double the required graph size. Here we show how to circumvent this doubling by
leaving the SES and reintroducing a tensor product structure in the
computational subspace. Specifically, we implement the tensor product of an SES
register holding ``data" with one or more ancilla qubits. This enables a hybrid
form of quantum computation where fast SES operations are performed on the
data, traditional logic gates and measurements are performed on the ancillas,
and controlled-unitaries act between. As an application we give an SES
implementation of the quantum linear system solver of Harrow, Hassidim, and
Lloyd
Quantum Phenomena in Low-Dimensional Systems
A brief summary of the physics of low-dimensional quantum systems is given.
The material should be accessible to advanced physics undergraduate students.
References to recent review articles and books are provided when possible.Comment: EOLSS Encyclopedia Article, 13 pages, Revte
Sampling and scrambling on a chain of superconducting qubits
We study a circuit, the Josephson sampler, that embeds a real vector into an
entangled state of n qubits, and optionally samples from it. We measure its
fidelity and entanglement on the 16-qubit ibmqx5 chip. To assess its
expressiveness, we also measure its ability to generate Haar random unitaries
and quantum chaos, as measured by Porter-Thomas statistics and
out-of-time-order correlation functions. The circuit requires nearest-neighbor
CZ gates on a chain and is especially well suited for first-generation
superconducting architectures.Comment: 11 page
Tunneling into a Fractional Quantum Hall System and the Infrared Catastrophe
We calculate the tunneling density of states of a two-dimensional interacting
electron gas in a quantizing magnetic field. We show that the observed
pseudogap in the density of states can be understood as the result of an
infrared catastrophe in a noninteracting electron model. This catastrophe stems
from the response of an electronic system to the potential produced by the
abruptly added charge during a tunneling event. Our formalism can be applied at
any filling factor without the use of Chern-Simons or composite fermion theory
Fractionally charged impurity states of a fractional quantum Hall system
The single-particle spectral function for an incompressible fractional
quantum Hall state in the presence of a scalar short-ranged attractive impurity
potential is calculated via exact diagonalization within the spherical
geometry. In contrast to the noninteracting case, where only a single bound
state below the lowest Landau level forms, electron-electron interactions
strongly renormalize the impurity potential, effectively giving it a finite
range, which can support many quasi-bound states (long-lived resonances).
Averaging the spectral weights of the quasi-bound states and extrapolating to
the thermodynamic limit, for filling factor we find evidence
consistent with localized fractionally charged quasiparticles. For
, the results are slightly more ambiguous, due to finite size effects
and possible bunching of Laughlin-quasiparticles.Comment: 7 pages and 4 figure
Efficient characterization of correlated SPAM errors
State preparation and measurement (SPAM) errors limit the performance of many
gate-based quantum computing architecures, but are partly correctable after a
calibration step that requires, for an exact implementation on a register of
qubits, additional characterization experiments, as well as classical
post-processing. Here we introduce an approximate but efficient method for SPAM
error characterization requiring the {\it classical} processing of real matrices, but only measurements. The technique
assumes that multi-qubit measurement errors are dominated by pair correlations,
which are estimated with two-qubit experiments, where is a
parameter related to the accuracy. We demonstrate the technique on the IBM and
Rigetti online superconducting quantum computers, allowing comparison of their
SPAM errors in both magnitude and degree of correlation. We also study the
correlations as a function of the register's geometric layout. We find that the
pair-correlation model is fairly accurate on linear arrays of superconducting
qubits. However qubits arranged in more closely spaced two-dimensional
geometries exhibit significant higher-order (such as 3-qubit) SPAM error
correlations.Comment: This manuscript is superseded by 2001.0998
Three-step implementation of any nxn unitary with a complete graph of n qubits
Quantum computation with a complete graph of superconducting qubits has been
recently proposed, and applications to amplitude amplification, phase
estimation, and the simulation of realistic atomic collisions given [Phys. Rev.
A 91, 062309 (2015)]. This single-excitation subspace (SES) approach does not
require error correction and is practical now. Previously it was shown how to
implement symmetric nxn unitaries in a single step, but not general unitaries.
Here we show that any element in the unitary group U(n) can be executed in no
more than three steps, for any n. This enables the implementation of highly
complex operations in constant time, and in some cases even allows for the
compilation of an entire algorithm down to only three operations. Using this
protocol we show how to prepare any pure state of an SES chip in three steps,
and also how to compute, for a given SES state rho, the expectation value of
any nxn Hermitian observable O in a constant number of steps
Friction in nanoelectromechanical systems: Clamping loss in the GHz regime
The performance of a wide variety of ultra-sensitive devices employing
nanoelectromechanical resonators is determined by their mechanical quality
factor, yet energy dissipation in these systems remains poorly understood. Here
we develop a comprehensive theory of friction in high frequency resonators
caused by the radiation of elastic energy into the support substrate, referred
to as clamping loss. The elastic radiation rate is found to be a strong
increasing function of resonator frequency, and we argue that this mechanism
will play an important role in future microwave-frequency devices.Comment: 4 page
- …