arXiv subjects

Steven Herbert

Publications and source records attributed to Steven Herbert.

25 records · Page 2Linked to original sources

arXiv2019

Increasing the classical data throughput in quantum networks by combining quantum linear network coding with superdense coding

This paper shows how network coding and superdense coding can be combined to increase the classical data throughput by a factor $2-ε$ (for arbitrarily small $ε> 0$) compared to the maximum that could be achieved using either network coding or superdense coding alone. Additionally, a general decomposition of a ``mixed'' network (i.e., consisting of classical and quantum links) is given, and it is reasoned that, owing to the inherent hardness of finding network codes, this may well lead to an increase in classical data throughput in practise, should a scenario arise in which quantum networks are used to transfer classical information.

quant-ph↗

arXiv2019

Spectral sparsification of matrix inputs as a preprocessing step for quantum algorithms

We study the potential utility of classical techniques of spectral sparsification of graphs as a preprocessing step for digital quantum algorithms, in particular, for Hamiltonian simulation. Our results indicate that spectral sparsification of a graph with $n$ nodes through a sampling method, e.g.\ as in \cite{Spielman2011resistances} using effective resistances, gives, with high probability, a locally computable matrix $\tilde H$ with row sparsity at most $\mathcal{O}(\text{poly}\log n)$. For a symmetric matrix $H$ of size $n$ with $m$ non-zero entries, a one-time classical runtime overhead of $\mathcal{O}(m||H||t\log n/ε)$ expended in spectral sparsification is then found to be useful as a way to obtain a sparse matrix $\tilde H$ that can be used to approximate time evolution $e^{itH}$ under the Hamiltonian $H$ to precision $ε$. Once such a sparsifier is obtained, it could be used with a variety of quantum algorithms in the query model that make crucial use of row sparsity. We focus on the case of efficient quantum algorithms for sparse Hamiltonian simulation, since Hamiltonian simulation underlies, as a key subroutine, several quantum algorithms, including quantum phase estimation and recent ones for linear algebra. Finally, we also give two simple quantum algorithms to estimate the row sparsity of an input matrix, which achieve a query complexity of $\mathcal{O}(n^{3/2})$ as opposed to $\mathcal{O}(n^2)$ that would be required by any classical algorithm for the task.

quant-ph↗

arXiv2019

Using Reinforcement Learning to find Efficient Qubit Routing Policies for Deployment in Near-term Quantum Computers

This paper addresses the problem of qubit routing in first-generation and other near-term quantum computers. In particular, it is asserted that the qubit routing problem can be formulated as a reinforcement learning (RL) problem, and that this is sufficient, in principle, to discover the optimal qubit routing policy for any given quantum computer architecture. In order to achieve this, it is necessary to alter the conventional RL framework to allow combinatorial action space, and this represents a second contribution of this paper, which is expected to find additional application, beyond the qubit routing problem addressed herein. Numerical results are included demonstrating the advantage of the RL-trained qubit routing policy over using a sorting network.

quant-ph↗

arXiv2014

A Simple Lower Bound on the Noncoherent Capacity of Highly Underspread Fading Channels

Communication channels are said to be underspread if their coherence time is greater than their delay spread. In such cases it can be shown that in the infinite bandwidth limit the information capacity tends to that of a channel with perfect receiver Channel State Information (CSI). This paper presents a lower bound on the capacity of a channel with finite bandwidth, expressed in a form which is mathematically elegant, and computationally simple. The bounding method exploits the fact that most actual channels are highly underspread; and that typically more is known about their impulse response than the channel time variation. The capacity is lower bounded by finding an achievable rate for individual time blocks which are shorter than the channel coherence time, in an orthogonal frequency division multiplexing system model. A highly underspread channel of particular interest is the invehicle channel, and a numerical example is given to verify that the capacity is indeed approximately that of a channel with perfect receiver CSI. The resulting lower bound is shown to be tighter than those previously derived.

cs.IT↗

arXiv2012

A quantitative study of spin-flip co-tunneling transport in a quantum dot

We report detailed transport measurements in a quantum dot in a spin-flip co-tunneling regime, and a quantitative comparison of the data to microscopic theory. The quantum dot is fabricated by lateral gating of a GaAs/AlGaAs heterostructure, and the conductance is measured in the presence of an in-plane Zeeman field. We focus on the ratio of the nonlinear conductance values at bias voltages exceeding the Zeeman threshold, a regime that permits a spin flip on the dot, to those below the Zeeman threshold, when the spin flip on the dot is energetically forbidden. The data obtained in three different odd-occupation dot states show good quantitative agreement with the theory with no adjustable parameters. We also compare the theoretical results to the predictions of a phenomenological form used previously for the analysis of non-linear co-tunneling conductance, specifically the determination of the heterostructure g-factor, and find good agreement between the two.

cond-mat.mes-hall↗

arXiv2011

Magnetic Splitting of the Zero Bias Peak in a Quantum Point Contact with a Variable Aspect Ratio

We report a zero-bias peak in the differential conductance of a Quantum Point Contact (QPC), which splits in an external magnetic field. The peak is observed over a range of device conductance values starting significantly below $2e^2/h$. The observed splitting closely matches the Zeeman energy and shows very little dependence on gate voltage, suggesting that the mechanism responsible for the formation of the peak involves electron spin. Precision Zeeman energy data for the experiment are obtained from a separately patterned single-electron transistor located a short distance away from the QPC. The QPC device has four gates arranged in a way that permits tuning of the longitudinal potential, and is fabricated in a GaAs/AlGaAs heterostructure containing 2-dimenional electron gas. We show that the agreement between the peak splitting and the Zeeman energy is robust with respect to moderate distortions of the QPC potential. We also show that the mechanism that leads to the formation of the ZBP is different from the conventional Kondo effect found in quantum dots.

cond-mat.mes-hall↗

arXiv2009

Magnetic-Field-Induced Crossover to a Nonuniversal Regime in a Kondo Dot

We have measured the magnetic splitting, $Δ_K$, of a Kondo peak in the differential conductance of a Single-Electron Transistor while tuning the Kondo temperature, $T_K$, along two different paths in the parameter space: varying the dot-lead coupling at a constant dot energy, and vice versa. At a high magnetic field, $B$, the changes of $Δ_K$ with $T_K$ along the two paths have opposite signs, indicating that $Δ_K$ is not a universal function of $T_K$. At low $B$, we observe a decrease in $Δ_K$ with $T_K$ along both paths, in agreement with theoretical predictions. Furthermore, we find $Δ_K/Δ<1$ at low $B$ and $Δ_K/Δ>1$ at high $B$, where $Δ$ is the Zeeman energy of the bare spin, in the same system.

cond-mat.mes-hall↗