N. E. Bonesteel

Florida State University, Tallahassee, Florida, United States

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Publications (50)146.82 Total impact

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    Daniel Zeuch, R. Cipri, N. E. Bonesteel
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    ABSTRACT: 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.
    02/2014;
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    Hsin-Hua Lai, Kun Yang, N E Bonesteel
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    ABSTRACT: We show the violation of the entanglement area law for bosonic systems with Bose surfaces. For bosonic systems with gapless factorized energy dispersions on an N^{d} Cartesian lattice in d dimensions, e.g., the exciton Bose liquid in two dimensions, 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.
    Physical Review Letters 11/2013; 111(21):210402. · 7.73 Impact Factor
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    R. Cipri, N. E. Bonesteel
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    ABSTRACT: 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 $\nu_{tot} = 1$. 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.
    11/2013; 89(8).
  • Daniel Zeuch, Robert Cipri, N. E. Bonesteel
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    ABSTRACT: Exchange pulses are local unitary operations obtained by turning on and off the isotropic exchange interaction between pairs of spin-1/2 particles, for example electron spins in quantum dots. We present a procedure for analytically constructing sequences of exchange pulses for carrying out leakage free two-qubit gates on logical three-spin qubits. At each stage of our construction we reduce the problem to that of finding a sequence of rotations for an effective two-level system. The resulting pulse sequences are 39 pulses long, longer than the original 19-pulse sequence of DiVincenzo et al. [1] and the more recent 18-pulse sequence of Fong and Wandzura [2], both of which were obtained numerically. Like the latter sequence, our sequences work regardless of the total spin of the six spins used to encode two qubits. After introducing our method, we prove that any leakage-free sequence of exchange pulses must act on at least five of the six spins to produce an entangling two-qubit gate.[4pt] [1] D.P. DiVincenzo et al., Nature 408, 339 (2000). [2] B.H. Fong & S.M. Wandzura, Quantum Info. Comput., 11, 1003 (2011).
    03/2013;
  • Caitlin Carnahan, Daniel Zeuch, N. E. Bonesteel
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    ABSTRACT: In topological quantum computation, quantum gates are carried out by braiding worldlines of non-Abelian anyons in 2+1 dimensional space-time. The simplest such anyons for which braiding is universal for quantum computation are Fibonacci anyons. Reichardt [1] has shown how to construct nontrivial braids for three Fibonacci anyons which yield 2 x2 unitary operations whose off-diagonal matrix elements (in the appropriate basis) can be made arbitrarily small through a simple and efficient iterative procedure. A great advantage of this construction is that it does not require either brute force search or the Solovay-Kitaev method. There is, however, a downside---the phases of the diagonal matrix elements cannot be directly controlled. Despite this, we show that the resulting braids can be used to construct leakage-free entangling two-qubit gates for qubits encoded using four Fibonacci anyons each. We give two explicit constructions---one based on the ``functional braid" approach of Hu and Wan [2], and another based on the ``effective qubit" approach of Hormozi et al. [3]. [1] B.W. Reichardt, Quant. Inf. and Comp. 12, 876 (2012). [2] H. Xu and X. Wan, PRA 78, 042325 (2008). [3] L. Hormozi et al., PRL 103, 160501 (2009).
    03/2013;
  • Weibo Feng, N. E. Bonesteel, David Divincenzo
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    ABSTRACT: It may be possible to use the ground states of the Levin-Wen model for Fibonacci anyons as a non-Abelian surface code for fault-tolerant quantum computation [1]. To do this, it will be necessary to repeatedly measure the vertex and plaquette operators of the model to check for errors. Recently, two of us have constructed quantum circuits for performing such measurements [2]. Here we present an alternate measurement scheme based on simulating an interference experiment. This ``experiment'' can be thought of, roughly, as first inserting a pair of Fibonacci anyons with trivial total topological charge onto one edge of a plaquette, ``braiding'' one anyon all the way around the plaquette while the other remains fixed, and then either measuring the total topological charge of the two anyons or manipulating their state in a specific way. We construct explicit quantum circuits which can be used to simulate these processes and show how they can be used to measure the Levin-Wen plaquette operator on a quantum computer.[4pt] [1] R. Koenig, G. Kuperberg, and B.W. Reichardt, Ann. Phys. 325, 2707 (2010).[0pt] [2] N.E. Bonesteel and D.P. DiVincenzo, Phys. Rev. B 86, 165113 (2012).
    03/2013;
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    N. E. Bonesteel, D. P. DiVincenzo
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    ABSTRACT: 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.
    Physical review. B, Condensed matter 06/2012; 86(16). · 3.77 Impact Factor
  • K. C.foster, N. E.bonesteel, S. H.simon
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    ABSTRACT: There is compelling theoretical evidence1 that the ν = 5/2 fractional quantum Hall state is a Moore-Read state2 - a state which can be viewed as a spin-polarized p-wave superconductor of composite fermions. The question remains, how can one test this hypothesis experimentally? To address this we have developed a semi-phenomenological description of this state in which the Halperin-Lee-Read3 theory of the half-filled Landau level is modified by adding a p-wave pairing interaction between composite fermions by hand. The electromagnetic response functions for the resulting mean-field p-wave superconducting state are then calculated and used in an RPA calculation of the physical electronic response. In particular, we predict the wave-vector and frequency dependence of the longitudinal conductivity σxx(q,ω) which can be measured in surface-acoustic-wave propagation experiments.4
    International Journal of Modern Physics B 01/2012; 16(20n22). · 0.46 Impact Factor
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    Huan Tran, N E Bonesteel
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    ABSTRACT: 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 that 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.
    Physical Review B 10/2011; 84(14):144420. · 3.66 Impact Factor
  • Robert Cipri, Yafis Barlas, N. E. Bonesteel
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    ABSTRACT: The nu =1/2+1/2 bilayer quantum Hall system exhibits at least two phases as a function of layer spacing, d. For d/l 1, (l is magnetic length), the system decouples into two nu= 1/2 composite fermion (CF) liquids. For d/l sufficiently small, the system enters an incompressible bilayer quantum Hall state. Recently, Alicea et al. [1] have proposed a state which might exist for intermediate layer spacing (d ˜l). In this "interlayer phase coherent" state, CFs tunnel coherently between layers forming well-defined bonding and antibonding Fermi seas, though there is no actual tunneling of physical electrons. Here we show that scattering from gauge fields in the CF liquids leads to strong layer-dependent fluctuations in the Aharonov-Bohm phases seen by CFs which suppress interlayer phase coherence. This suppression appears as a singular contribution to the correlation energy which inhibits any T=0 phase transition into an interlayer phase coherent state, and drives any such transition first order. Work supported by US DOE.[4pt] [1] J. Alicea, O.I. Motrunich, G. Refael, M.P.A. Fisher, PRL 103, 256403 (2009).
    03/2011;
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    Huan Tran, N E Bonesteel
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    ABSTRACT: a b s t r a c t 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. Published by Elsevier B.V.
    Computational Materials Science 04/2010; 49:S395. · 1.88 Impact Factor
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    M. Baraban, N. E. Bonesteel, S. H. Simon
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    ABSTRACT: 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.
    Physical Review A 02/2010; · 3.04 Impact Factor
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    L Hormozi, N E Bonesteel, S H Simon
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    ABSTRACT: 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 not equal 4. 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.
    Physical Review Letters 10/2009; 103(16):160501. · 7.73 Impact Factor
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    M Baraban, G Zikos, N Bonesteel, S H Simon
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    ABSTRACT: We demonstrate numerically that non-Abelian quasihole (qh) excitations of the nu=5/2 fractional quantum Hall state have some of the key properties necessary to support quantum computation. We find that as the qh spacing is increased, the unitary transformation which describes winding two qh's around each other converges exponentially to its asymptotic limit and that the two orthogonal wave functions describing a system with four qh's become exponentially degenerate. We calculate the length scales for these two decays to be xi(U) approximately 2.7l(0) and xi(E) approximately 2.3l(0), respectively. Additionally, we determine which fusion channel is lower in energy when two qh's are brought close together.
    Physical Review Letters 08/2009; 103(7):076801. · 7.73 Impact Factor
  • Huan Tran, Nicholas Bonesteel
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    ABSTRACT: In valence-bond Monte Carlo (VBMC) ootnotetextA. Sandvik, PRL 95, 207203 (2005). the ground state of a quantum spin system is sampled directly from the valence-bond (VB) basis --- a useful basis for visualizing the properties of singlet ground states. For example, the ground state of the uniform AFM spin-12 Heisenberg chain is characterized by strongly fluctuating bonds with power-law length distribution, while in the random-singlet phase (RSP) of a random Heisenberg chain these bonds, while still having a power-law length distribution, lock into a particular VB state on long length scales. ootnotetextD. S. Fisher, PRB 50, 3799 (1994). We use VBMC to directly probe the formation of a RSP by calculating both the average number of bonds nL leaving a block of L spins (the VB entanglement entropy ootnotetextF. Alet, et al., PRL 99, 117204 (2007).), and its fluctuations, sigmanL^2 =
    03/2009;
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    G Zikos, K Yang, N E Bonesteel, L Hormozi, S H Simon
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    ABSTRACT: Certain fractional quantum Hall states, including the experimentally observed ν = 5/2 state, and, possibly, the ν = 12/5 state, may have a sufficiently rich form of topological order (i.e. they may be nonabelian) to be useful for quantum information processing. For example, in some cases they may be used for topological quantum computation, an intrinsically fault tolerant form of quantum computation which is carried out by braiding the world lines of quasiparticle excitations in 2+1 dimensional space time. Here we briefly review the relevant properties of nonabelian quantum Hall states and discuss some of the methods we have found for finding specific braiding patterns which can be used to carry out universal quantum computation using them. Recent work on one-dimensional chains of interacting quasiparticles in nonabelian states is also reviewed.
    International Journal of Modern Physics B 01/2009; 14(13):2727-2736. · 0.46 Impact Factor
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    Wenxin Ding, Nicholas E. Bonesteel, Kun Yang
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    ABSTRACT: In this paper we calculate the block entanglement entropies of spin models whose ground states have perfect antiferromagnetic or ferromagnetic long-range order. In the latter case the definition of entanglement entropy is extended to properly take into account the ground state degeneracy. We find in both cases the entropy grows logarithmically with the block size. Implication of our results on states with general long-range order will be discussed.
    Physical Review A 03/2008; · 3.04 Impact Factor
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    L. Fidkowski, G. Refael, N. E. Bonesteel, J. E. Moore
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    ABSTRACT: Topological insulators supporting non-Abelian anyonic excitations are in the center of attention as candidates for topological quantum computation. In this paper, we analyze the ground-state properties of disordered non-Abelian anyonic chains. The resemblance of fusion rules of non-Abelian anyons and real-space decimation strongly suggests that disordered chains of such anyons generically exhibit infinite-randomness phases. Concentrating on the disordered golden chain model with nearest-neighbor coupling, we show that Fibonacci anyons with the fusion rule tau[direct-product]tau=1[direct-sum]tau exhibit two infinite-randomness phases: a random-singlet phase when all bonds prefer the trivial fusion channel and a mixed phase which occurs whenever a finite density of bonds prefers the tau fusion channel. Real-space renormalization-group (RG) analysis shows that the random-singlet fixed point is unstable to the mixed fixed point. By analyzing the entanglement entropy of the mixed phase, we find its effective central charge and find that it increases along the RG flow from the random-singlet point, thus ruling out a c theorem for the effective central charge.
    Physical review. B, Condensed matter 01/2008; · 3.77 Impact Factor
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    N E Bonesteel, Kun Yang
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    ABSTRACT: 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-->infinity). 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) approximately lnd/3 log(2)L for large L, where d is the quantum dimension of the particles.
    Physical Review Letters 10/2007; 99(14):140405. · 7.73 Impact Factor
  • Huan Tran, Nicholas Bonesteel
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    ABSTRACT: We present the results of a quantum Monte Carlo study of the S=1/2 Heisenberg chain with random antiferromagnetic nearest-neighbor coupling. Using the method of ground state projection in the singlet-bond basis, recently introduced by Sandvik, we are able to directly confirm the expected freezing of the ground state into a random singlet phase at long length scales, while at the same time exactly capturing the nonuniversal (i.e. detail dependent) short-range bond fluctuations. By computing the bond-length distribution in the random singlet phase we are then able to determine the mean entanglement entropy, SN, associated with a segment of N 1 spins, both by self-averaging over segments for a particular realization of disorder, and by averaging over many distinct realizations of disorder. Our results confirm the SN˜23 2N scaling found by Refael and Moore using real space RG, showing that the ``effective central charge" of the critical random S=1/2 Heisenberg chain is c = 2. Work supported by US DOE. A. Sandvik, PRL 95, 207203 (2005). G. Refael and J. E. Moore, PRL 93, 260602 (2004).
    03/2007;

Publication Stats

638 Citations
146.82 Total Impact Points

Institutions

  • 1997–2013
    • Florida State University
      • Department of Physics
      Tallahassee, Florida, United States
  • 2009
    • National Institute of Standards and Technology
      Maryland, United States
    • Yale University
      • Department of Physics
      New Haven, CT, United States
  • 1996–2001
    • National High Magnetic Field Laboratory
      Tallahassee, Florida, United States