arXiv subjects

Gilad Ben-Shach

Publications and source records attributed to Gilad Ben-Shach.

6 recordsLinked to original sources

arXiv2024

How to Build a Quantum Supercomputer: Scaling from Hundreds to Millions of Qubits

In the span of four decades, quantum computation has evolved from an intellectual curiosity to a potentially realizable technology. Today, small-scale demonstrations have become possible for quantum algorithmic primitives on hundreds of physical qubits. Nevertheless, there are significant outstanding challenges in quantum hardware, fabrication, software architecture, and algorithms on the path towards a full-stack scalable quantum computing technology. Here, we provide a comprehensive review of these scaling challenges. We show how to facilitate scaling by adopting existing semiconductor technology to build much higher-quality qubits, employing systems engineering approaches, and performing distributed heterogeneous quantum-classical computing. We provide a detailed resource and sensitivity analysis for quantum applications on surface-code error-corrected quantum computers given current, target, and desired hardware specifications based on superconducting qubits, accounting for a realistic distribution of errors. We provide comprehensive resource estimates for several utility-scale applications including quantum chemistry calculations, catalyst design, NMR spectroscopy, and Fermi-Hubbard simulation. We show that orders of magnitude enhancement in performance could be obtained by a combination of hardware improvements and tight quantum-HPC integration. Furthermore, we introduce high-performance architectures for quantum-probabilistic computing with custom-designed accelerators to tackle today's industry-scale classical optimization, machine learning, and quantum simulation tasks in a cost-effective manner.

quant-ph↗

arXiv2023

Simulating spectroscopy experiments with a superconducting quantum computer

We present a novel method for solving eigenvalue problems on a quantum computer based on spectroscopy. The method works by coupling a "probe" qubit to a set of system simulation qubits and then time evolving both the probe and the system under Hamiltonian dynamics. In this way, we simulate spectroscopy on a quantum computer. We test our method on the IBM quantum hardware for a simple single spin model and an interacting Kitaev chain model. For the Kitaev chain, we trace out the pseudo-topological phase boundary for a two-site model.

quant-ph↗

arXiv2015

Controlled Finite Momentum Pairing and Spatially Varying Order Parameter in Proximitized HgTe Quantum Wells

Conventional $s$-wave superconductivity is understood to arise from singlet pairing of electrons with opposite Fermi momenta, forming Cooper pairs whose net momentum is zero [1]. Several recent studies have focused on structures where such conventional $s$-wave superconductors are coupled to systems with an unusual configuration of electronic spin and momentum at the Fermi surface. Under these conditions, the nature of the paired state can be modified and the system may even undergo a topological phase transition [2, 3]. Here we present measurements and theoretical calculations of several HgTe quantum wells coupled to either aluminum or niobium superconductors and subject to a magnetic field in the plane of the quantum well. By studying the oscillatory response of Josephson interference to the magnitude of the in-plane magnetic field, we find that the induced pairing within the quantum well is spatially varying. Cooper pairs acquire a tunable momentum that grows with magnetic field strength, directly reflecting the response of the spin-dependent Fermi surfaces to the in-plane magnetic field. In addition, in the regime of high electron density, nodes in the induced superconductivity evolve with the electron density in agreement with our model based on the Hamiltonian of Bernevig, Hughes, and Zhang [4]. This agreement allows us to quantitatively extract the value of $\tilde{g}/v_{F}$, where $\tilde{g}$ is the effective g-factor and $v_{F}$ is the Fermi velocity. However, at low density our measurements do not agree with our model in detail. Our new understanding of the interplay between spin physics and superconductivity introduces a way to spatially engineer the order parameter, as well as a general framework within which to investigate electronic spin texture at the Fermi surface of materials.

cond-mat.mes-hall↗

arXiv2014

Detecting Majoranas in 1D wires by charge sensing

The electron number-parity of the ground state of a semiconductor narowire proximity-coupled to a bulk superconductor can alternate between the quantised values $\pm 1$ if parameters such as the wire length $L$, the chemical potential $μ$ or the magnetic field $B$ are varied inside the topological superconductor phase. % The parity jumps, which may be interpreted as changes in the occupancy of the fermion state formed from the pair of Majorana modes at opposite ends of the wire, are accompanied by jumps $δN$ in the charge of the nanowire, whose values decrease exponentially with the wire length. % We study theoretically the dependence of $δN$ on system parameters, and compare the locations in the $μ$-$B$ plane of parity jumps when the nanowire is or is not proximity-coupled to a bulk superconductor. % We show that, despite the fact that the wave functions of the Majorana modes are localised near the two ends of the wire, the charge-density jumps have spatial distributions that are essentially uniform along the wire length, being proportional to the product of the two Majorana wave functions. % We explain how charge measurements, say by an external single-electron transistor, could reveal these effects. % Whereas existing experimental methods require direct contact to the wire for tunneling measurements, charge sensing avoids this issue and provides an orthogonal measurement to confirm recent experimental developments. % Furthermore, by comparing density of states measurements which show Majorana features at the wire ends with the uniformly-distributed charge measurements, one can rule out alternative explanations for earlier results. % We shed light on a new parameter regime for these wire-superconductor hybrid systems, and propose a related experiment to measure spin density.

cond-mat.mes-hall↗

arXiv2012

Detecting Non-Abelian Anyons by Charging Spectroscopy

Observation of non-Abelian statistics for the e/4 quasiparticles in the ν=5/2 fractional quantum Hall state remains an outstanding experimental problem. The non-Abelian statistics are linked to the presence of additional low energy states in a system with localised quasiparticles, and hence an additional low-temperature entropy. Recent experiments, which detect changes in the number of quasiparticles trapped in a local potential well as a function of an applied gate voltage, V_G, provide a possibility for measuring this entropy, if carried out over a suitable range of temperatures, T. We present a microscopic model for quasiparticles in a potential well and study the effects of non-Abelian statistics on the charge stability diagram in the V_G-T plane, including broadening at finite temperature. We predict a measurable slope for the first quasiparticle charging line, and an even-odd effect in the diagram, which is a signature of non-Abelian statistics.

cond-mat.mes-hall↗

arXiv2009

The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums

We present a method which enables one to construct isospectral objects, such as quantum graphs and drums. One aspect of the method is based on representation theory arguments which are shown and proved. The complementary part concerns techniques of assembly which are both stated generally and demonstrated. For that purpose, quantum graphs are grist to the mill. We develop the intuition that stands behind the construction as well as the practical skills of producing isospectral objects. We discuss the theoretical implications which include Sunada's theorem of isospectrality arising as a particular case of this method. A gallery of new isospectral examples is presented and some known examples are shown to result from our theory.

math-ph↗