arXiv subjects

N. E. Bonesteel

Publications and source records attributed to N. E. Bonesteel.

At least 19 recordsLinked to original sources

arXiv2023

Pairing and Pair Breaking by Gauge Fluctuations in Bilayer Composite Fermion Metals

We study interlayer pairing of composite fermions in the total $ν=1/2+1/2$ quantum Hall bilayer as a possible framework for understanding the experimentally observed transition from a compressible state at large layer spacing to a bilayer quantum Hall state at small layer spacing. We consider a model in which the effective interlayer composite fermion pairing interaction mediated by the Chern-Simons gauge fields in the two layers is singular with both attractive (out-of-phase) and repulsive (in-phase) components diverging at low frequency. If only the more singular attractive interaction is included the pairing gap obtained by solving the gap equation is proportional to the inverse of the layer spacing squared. In the so-called local approximation, we find that when the less singular repulsive interactions are also included the pairing gap still falls off as inverse layer spacing squared, consistent with recent analyses, but is strongly suppressed to a degree that may account for the fact that this predicted inverse square dependence is not observed experimentally. The analytically obtained local approximation solutions are then used as a starting point to numerically iterate the full gap equation to assess the validity of the approximation in this limit.

cond-mat.str-el↗

arXiv2020

Efficient Two-Qubit Pulse Sequences Beyond CNOT

We design efficient controlled-rotation gates with arbitrary angle acting on three-spin encoded qubits for exchange-only quantum computation. Two pulse sequence constructions are given. The first is motivated by an analytic derivation of the efficient Fong-Wandzura sequence for an exact CNOT gate. This derivation, briefly reviewed here, is based on elevating short sequences of SWAP pulses to an entangling two-qubit gate. To go beyond CNOT, we apply a similar elevation to a modified short sequence consisting of SWAPs and one pulse of arbitrary duration. This results in two-qubit sequences that carry out controlled-rotation gates of arbitrary angle. The second construction streamlines a class of arbitrary CPHASE gates established earlier. Both constructions are based on building two-qubit sequences out of subsequences with special properties that render each step of the construction analytically tractable.

quant-ph↗

arXiv2015

Spin Correlations and Topological Entanglement Entropy in a Non-Abelian Spin-1 Spin Liquid

We analyze the properties of a non-Abelian spin-1 chiral spin liquid state proposed by Greiter and Thomale [PRL 102, 207203 (2009)] using variational Monte Carlo. In this state the bosonic $ν= 1$ Moore-Read Pfaffian wave function is used to describe a gas of bosonic spin flips on a square lattice with one flux quantum per plaquette. For toroidal geometries there is a three-dimensional space of these states corresponding to the topological degeneracy of the bosonic Moore-Read state on the torus. We show that spin correlations for different states in this space become indistinguishable for large system size. We also calculate the Renyi entanglement entropy for different system partitions to extract the topological entanglement entropy and provide evidence that the topological order of the lattice spin-liquid state is the same as that of the continuum Moore-Read state from which it is constructed.

cond-mat.str-el↗

arXiv2015

Systematically generated two-qubit anyon braids

Fibonacci anyons are non-Abelian particles for which braiding is universal for quantum computation. Reichardt has shown how to systematically generate nontrivial braids for three Fibonacci anyons which yield unitary operations with off-diagonal matrix elements that can be made arbitrarily small in a particular natural basis through a simple and efficient iterative procedure. This procedure does not require brute force search, the Solovay-Kitaev method, or any other numerical technique, but the phases of the resulting diagonal matrix elements cannot be directly controlled. We show that despite this lack of control the resulting braids can be used to systematically construct entangling gates for two qubits encoded by Fibonacci anyons.

quant-ph↗

arXiv2015

Monte Carlo studies of the properties of the Majorana quantum error correction code: is self-correction possible during braiding?

The Majorana code is an example of a stabilizer code where the quantum information is stored in a system supporting well-separated Majorana Bound States (MBSs). We focus on one-dimensional realizations of the Majorana code, as well as networks of such structures, and investigate their lifetime when coupled to a parity-preserving thermal environment. We apply the Davies prescription, a standard method that describes the basic aspects of a thermal environment, and derive a master equation in the Born-Markov limit. We first focus on a single wire with immobile MBSs and perform error correction to annihilate thermal excitations. In the high-temperature limit, we show both analytically and numerically that the lifetime of the Majorana qubit grows logarithmically with the size of the wire. We then study a trijunction with four MBSs when braiding is executed. We study the occurrence of dangerous error processes that prevent the lifetime of the Majorana code from growing with the size of the trijunction. The origin of the dangerous processes is the braiding itself, which separates pairs of excitations and renders the noise nonlocal; these processes arise from the basic constraints of moving MBSs in 1D structures. We confirm our predictions with Monte Carlo simulations in the low-temperature regime, i.e. the regime of practical relevance. Our results put a restriction on the degree of self-correction of this particular 1D topological quantum computing architecture.

cond-mat.mes-hall↗

arXiv2015

A Simple Derivation of the Fong-Wandzura Pulse Sequence

We give an analytic construction of a class of two-qubit gate pulse sequences that act on five of the six spin-$\frac12$ particles used to encode a pair of exchange-only three-spin qubits. Within this class, the problem of gate construction reduces to that of finding a smaller sequence that acts on four spins and is subject to a simple constraint. The optimal sequence satisfying this constraint yields a two-qubit gate sequence equivalent to that found numerically by Fong and Wandzura. Our construction is sufficiently simple that it can be carried out entirely with pen, paper, and knowledge of a few basic facts about quantum spin. We thereby analytically derive the Fong-Wandzura sequence that has so far escaped intuitive explanation.

quant-ph↗

arXiv2014

Analytic Pulse Sequence Construction for Exchange-Only Quantum Computation

We present pulse sequences for two-qubit gates acting on encoded qubits for exchange-only quantum computation. Previous work finding such sequences has always required numerical methods due to the large search space of unitary operators acting on the space of the encoded qubits. By contrast, our construction can be understood entirely in terms of three-dimensional rotations of effective spin-1/2 pseudospins which allows us to use geometric intuition to determine the required sequence of operations analytically. The price we pay for this simplification is that, at 39 pulses, our sequences are significantly longer than the best numerically obtained sequences.

quant-ph↗

arXiv2013

Gauge Fluctuations and Interlayer Coherence in Bilayer Composite Fermion Metals

We study the effect of the Chern-Simons gauge fields on the possible transition from two decoupled composite fermion metals to the interlayer coherent composite fermion state proposed by Alicea et al. [Phys. Rev. Lett. 103, 256403 (2009)] in a symmetrically doped quantum Hall bilayer with total Landau level filling fraction $ν_{tot} = 1$. In this transition, interlayer Coulomb repulsion leads to excitonic condensation of composite fermions which are then free to tunnel coherently between layers. We find that this coherent tunneling is strongly suppressed by the layer-dependent Aharonov-Bohm phases experienced by composite fermions as they propagate through the fluctuating gauge fields in the system. This suppression is analyzed by treating these gauge fluctuations within the random-phase approximation and calculating their contribution to the energy cost for forming an exciton condensate of composite fermions. This energy cost leads to (1) an increase in the critical interlayer repulsion needed to drive the transition; and (2) a discontinuous jump in the energy gaps to out-of-phase excitations (i.e., excitations involving currents with opposite signs in the two layers) at the transition.

cond-mat.str-el↗

arXiv2013

Violation of Entanglement-Area Law in Bosonic Systems with Bose Surfaces: Possible Application to Bose Metals

We show the violation of the entanglement-area law for bosonic systems with Bose surfaces. For bosonic systems with gapless factorized energy dispersions on a N^d Cartesian lattice in d-dimension, e.g., the exciton Bose liquid in two dimension, we explicitly show that a belt subsystem with width L preserving translational symmetry along d-1 Cartesian axes has leading entanglement entropy (N^{d-1}/3)ln L. Using this result, the strong subadditivity inequality, and lattice symmetries, we bound the entanglement entropy of a rectangular subsystem from below and above showing a logarithmic violation of the area law. For subsystems with a single flat boundary we also bound the entanglement entropy from below showing a logarithmic violation, and argue that the entanglement entropy of subsystems with arbitrary smooth boundaries are similarly bounded.

quant-ph↗

arXiv2012

Quantum Circuits for Measuring Levin-Wen Operators

We construct quantum circuits for measuring the commuting set of vertex and plaquette operators that appear in the Levin-Wen model for doubled Fibonacci anyons. Such measurements can be viewed as syndrome measurements for the quantum error-correcting code defined by the ground states of this model (the Fibonacci code). We quantify the complexity of these circuits with gate counts using different universal gate sets and find these measurements become significantly easier to perform if n-qubit Toffoli gates with n = 3,4 and 5 can be carried out directly. In addition to measurement circuits, we construct simplified quantum circuits requiring only a few qubits that can be used to verify that certain self-consistency conditions, including the pentagon equation, are satisfied by the Fibonacci code.

quant-ph↗

arXiv2011

Valence Bond Entanglement and Fluctuations in Random Singlet Phases

The ground state of the uniform antiferromagnetic spin-1/2 Heisenberg chain can be viewed as a strongly fluctuating liquid of valence bonds, while in disordered chains these bonds lock into random singlet states on long length scales. We show that this phenomenon can be studied numerically, even in the case of weak disorder, by calculating the mean value of the number of valence bonds leaving a block of $L$ contiguous spins (the valence-bond entanglement entropy) as well as the fluctuations in this number. These fluctuations show a clear crossover from a small $L$ regime, in which they behave similar to those of the uniform model, to a large $L$ regime in which they saturate in a way consistent with the formation of a random singlet state on long length scales. A scaling analysis of these fluctuations is used to study the dependence on disorder strength of the length scale characterizing the crossover between these two regimes. Results are obtained for a class of models which include, in addition to the spin-1/2 Heisenberg chain, the uniform and disordered critical 1D transverse-field Ising model and chains of interacting non-Abelian anyons.

cond-mat.dis-nn↗

arXiv2010

Monte Carlo Simulations of Interacting Anyon Chains

A generalized version of the valence-bond Monte Carlo method is used to study ground state properties of the 1+1 dimensional quantum $Q$-state Potts models. For appropriate values of $Q$ these models can be used to describe interacting chains of non-Abelian anyons --- quasiparticle excitations of certain exotic fractional quantum Hall states.

cond-mat.dis-nn↗

arXiv2010

Resources Required for Topological Quantum Factoring

We consider a hypothetical topological quantum computer where the qubits are comprised of either Ising or Fibonacci anyons. For each case, we calculate the time and number of qubits (space) necessary to execute the most computationally expensive step of Shor's algorithm, modular exponentiation. For Ising anyons, we apply Bravyi's distillation method [S. Bravyi, Phys. Rev. A 73, 042313 (2006)] which combines topological and non-topological operations to allow for universal quantum computation. With reasonable restrictions on the physical parameters we find that factoring a 128 bit number requires approximately 10^3 Fibonacci anyons versus at least 3 x 10^9 Ising anyons. Other distillation algorithms could reduce the resources for Ising anyons substantially.

quant-ph↗

arXiv2009

Topological Quantum Computing with Read-Rezayi States

Read-Rezayi fractional quantum Hall states are among the prime candidates for realizing non-Abelian anyons which in principle can be used for topological quantum computation. We present a prescription for efficiently finding braids which can be used to carry out a universal set of quantum gates on encoded qubits based on anyons of the Read-Rezayi states with $k>2$, $k\neq4$. This work extends previous results which only applied to the case $k = 3$ (Fibonacci) and clarifies why in that case gate constructions are simpler than for a generic Read-Rezayi state.

quant-ph↗

arXiv2007

Infinite-Randomness Fixed Points for Chains of Non-Abelian Quasiparticles

One-dimensional chains of non-Abelian quasiparticles described by $SU(2)_k$ Chern-Simons-Witten theory can enter random singlet phases analogous to that of a random chain of ordinary spin-1/2 particles (corresponding to $k \to \infty$). For $k=2$ this phase provides a random singlet description of the infinite randomness fixed point of the critical transverse field Ising model. The entanglement entropy of a region of size $L$ in these phases scales as $S_L \simeq \frac{\ln d}{3} \log_2 L$ for large $L$, where $d$ is the quantum dimension of the particles.

cond-mat.mes-hall↗

arXiv2007

Topological Quantum Compiling

A method for compiling quantum algorithms into specific braiding patterns for non-Abelian quasiparticles described by the so-called Fibonacci anyon model is developed. The method is based on the observation that a universal set of quantum gates acting on qubits encoded using triplets of these quasiparticles can be built entirely out of three-stranded braids (three-braids). These three-braids can then be efficiently compiled and improved to any required accuracy using the Solovay-Kitaev algorithm.

quant-ph↗

arXiv2006

Topological Quantum Computing with Only One Mobile Quasiparticle

In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in 2+1 dimensional space-time. In this paper we show that any such quantum computation that can be done by braiding $n$ identical quasiparticles can also be done by moving a single quasiparticle around n-1 other identical quasiparticles whose positions remain fixed.

quant-ph↗

arXiv2005

Braid Topologies for Quantum Computation

In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particle-like excitations (quasiparticles) around one another in two space dimensions. The resulting quasiparticle trajectories define world-lines in three dimensional space-time, and the corresponding quantum gates depend only on the topology of the braids formed by these world-lines. We show how to find braids that yield a universal set of quantum gates for qubits encoded using a specific kind of quasiparticle which is particularly promising for experimental realization.

quant-ph↗