arXiv subjects

Parsa Bonderson

Publications and source records attributed to Parsa Bonderson.

51 records · Page 3Linked to original sources

arXiv2011

Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States

We study the non-Abelian statistics of quasiparticles in the Ising-type quantum Hall states which are likely candidates to explain the observed Hall conductivity plateaus in the second Landau level, most notably the one at filling fraction nu=5/2. We complete the program started in Nucl. Phys. B 506, 685 (1997) and show that the degenerate four-quasihole and six-quasihole wavefunctions of the Moore-Read Pfaffian state are orthogonal with equal constant norms in the basis given by conformal blocks in a c=1+1/2 conformal field theory. As a consequence, this proves that the non-Abelian statistics of the excitations in this state are given by the explicit analytic continuation of these wavefunctions. Our proof is based on a plasma analogy derived from the Coulomb gas construction of Ising model correlation functions involving both order and (at most two) disorder operators. We show how this computation also determines the non-Abelian statistics of collections of more than six quasiholes and give an explicit expression for the corresponding conformal block-derived wavefunctions for an arbitrary number of quasiholes. Our method also applies to the anti-Pfaffian wavefunction and to Bonderson-Slingerland hierarchy states constructed over the Moore-Read and anti-Pfaffian states.

cond-mat.str-el↗

arXiv2010

Numerical Calculation of the Neutral Fermion Gap at $ν=5/2$

We present the first numerical computation of the neutral fermion gap, $Δ_ψ$, in the $ν=5/2$ quantum Hall state, which is analogous to the energy gap for a Bogoliubov-de Gennes quasiparticle in a superconductor. We find $Δ_ψ\approx 0.027 \frac{e^2}{ε\ell_0}$, comparable to the charge gap, and discuss the implications for topological quantum information processing. We also deduce an effective Fermi velocity $v_F$ for neutral fermions from the low-energy spectra for odd numbers of electrons, and thereby obtain a correlation length $ξ_ψ={v_F}/Δ_ψ \approx 1.3\, \ell_0$. We comment on the implications of our results for electronic mechanisms of superconductivity more generally.

cond-mat.str-el↗

arXiv2010

Implementing arbitrary phase gates with Ising anyons

Ising-type non-Abelian anyons are likely to occur in a number of physical systems, including quantum Hall systems, where recent experiments support their existence. In general, non-Abelian anyons may be utilized to provide a topologically error-protected medium for quantum information processing. However, the topologically protected operations that may be obtained by braiding and measuring topological charge of Ising anyons are precisely the Clifford gates, which are not computationally universal. The Clifford gate set can be made universal by supplementing it with single-qubit pi/8-phase gates. We propose a method of implementing arbitrary single qubit phase gates for Ising anyons by running a current of anyons with interfering paths around computational anyons. While the resulting phase gates are not topologically protected, they can be combined with "magic state distillation" to provide error-corrected pi/8-phase gates with a remarkably high threshold.

cond-mat.str-el↗

arXiv2010

Coulomb Blockade Doppelgangers in Quantum Hall States

In this paper, we ask the question: How well can Coulomb blockade experiments correctly identify and distinguish between different topological orders in quantum Hall states? We definitively find the answer to be: Quite poorly. In particular, we write the general expression for the spacing of resonance peaks in a simple form that explicitly displays its dependence on the conformal scaling dimensions of the systems' edge modes. This form makes transparent the general argument that the Coulomb blockade peak spacings do not provide a strongly indicative signature of the topological order of the system, since it is only weakly related to the braiding statistics. We bolster this general argument with examples for all the most physically relevant non-Abelian candidate states, demonstrating that they have Coulomb blockade doppelgangers -- candidate states at the same filling fraction with identical Coulomb blockade signatures, but dramatically different topological orders and braiding statistics.

cond-mat.str-el↗

arXiv2010

A Blueprint for a Topologically Fault-tolerant Quantum Computer

The advancement of information processing into the realm of quantum mechanics promises a transcendence in computational power that will enable problems to be solved which are completely beyond the known abilities of any "classical" computer, including any potential non-quantum technologies the future may bring. However, the fragility of quantum states poses a challenging obstacle for realization of a fault-tolerant quantum computer. The topological approach to quantum computation proposes to surmount this obstacle by using special physical systems -- non-Abelian topologically ordered phases of matter -- that would provide intrinsic fault-tolerance at the hardware level. The so-called "Ising-type" non-Abelian topological order is likely to be physically realized in a number of systems, but it can only provide a universal gate set (a requisite for quantum computation) if one has the ability to perform certain dynamical topology-changing operations on the system. Until now, practical methods of implementing these operations were unknown. Here we show how the necessary operations can be physically implemented for Ising-type systems realized in the recently proposed superconductor-semiconductor and superconductor-topological insulator heterostructures. Furthermore, we specify routines employing these methods to generate a computationally universal gate set. We are consequently able to provide a schematic blueprint for a fully topologically-protected Ising based quantum computer using currently available materials and techniques. This may serve as a starting point for attempts to construct a fault-tolerant quantum computer, which will have applications to cryptanalysis, drug design, efficient simulation of quantum many-body systems, solution of large systems of linear equations, searching large databases, engineering future quantum computers, and -- most importantly -- those applications which no one in our classical era has the prescience to foresee.

quant-ph↗

arXiv2009

The non-Abelian Interferometer

We consider the tunneling current through a double point-contact Fabry-Perot interferometer such as used in recent experimental studies of the fractional quantum Hall plateau at filling fraction nu=5/2. We compare the predictions of several different models of the state of the electrons at this plateau: the Moore-Read, anti-Pfaffian, SU(2)_2 NAF, K=8 strong pairing, and (3,3,1) states. All of these predict the existence of charge e/4 quasiparticles, but the first three are non-Abelian while the last two are Abelian. We give explicit formulas for the scaling of charge e/2 and charge e/4 quasiparticle contributions to the current as a function of temperature, gate voltage and distance between the two point contacts for all three models. Based on these, we analyze several possible explanations of two phenomena reported for recent experiments by Willett et al., namely halving of the period of the observed resistance oscillations with rising temperature and alternation between the same two observed periods at low temperatures as the area of the interference loop is varied with a side gate. We conclude that the most likely explanation is that the observed alternation is due to switching between even and odd numbers of charge e/4 quasiparticles enclosed within the loop as a function of side gate voltage, which is a clear signature of the presence of non-Abelian anyons. However, there are important features of the data which do not have a simple explanation within this picture. We suggest further experiments which could help rule out some possible scenarios. We make the corresponding predictions for future tunneling and interference experiments at the other observed second Landau level fractional quantum Hall states.

cond-mat.mes-hall↗

arXiv2009

Splitting the Topological Degeneracy of non-Abelian Anyons

We examine tunneling of topological charge between non-Abelian anyons as a perturbation of the long-range effective theory of a topologically ordered system. We obtain energy corrections in terms of the anyons' universal algebraic structure and non-universal tunneling amplitudes. We find that generic tunneling completely lifts the topological degeneracy of non-Abelian anyons. This degeneracy splitting is exponentially suppressed for long distances between anyons, but leaves no topological protection at shorter distances. We also show that general interactions of anyons can be expressed in terms of the transfer of topological charge, and thus can be treated effectively as tunneling interactions.

quant-ph↗

arXiv2008

Measurement-Only Topological Quantum Computation via Anyonic Interferometry

We describe measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge. We demonstrate how anyonic teleportation can be achieved using "forced measurement" protocols for both types of measurement. Using this, it is shown how topological charge measurements can be used to generate the braiding transformations used in topological quantum computation, and hence that the physical transportation of computational anyons is unnecessary. We give a detailed discussion of the anyonics for implementation of topological quantum computation (particularly, using the measurement-only approach) in fractional quantum Hall systems.

quant-ph↗

arXiv2008

Fractional Quantum Hall Hierarchy and the Second Landau Level

We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the nu = 5/2 Moore-Read state, we construct new explicit trial wavefunctions to describe the fractional quantum Hall effect in the second Landau level. The resulting hierarchy of states, which reproduces the filling fractions of all observed Hall conductance plateaus in the second Landau level, is characterized by electron pairing in the ground state and an excitation spectrum that includes non-Abelian anyons of the Ising type. We propose this as a unifying picture in which p-wave pairing characterizes the fractional quantum Hall effect in the second Landau level.

cond-mat.mes-hall↗

arXiv2008

Measurement-Only Topological Quantum Computation

We remove the need to physically transport computational anyons around each other from the implementation of computational gates in topological quantum computing. By using an anyonic analog of quantum state teleportation, we show how the braiding transformations used to generate computational gates may be produced through a series of topological charge measurements.

quant-ph↗

arXiv2008

Interferometry of non-Abelian Anyons

We develop the general quantum measurement theory of non-Abelian anyons through interference experiments. The paper starts with a terse introduction to the theory of anyon models, focusing on the basic formalism necessary to apply standard quantum measurement theory to such systems. This is then applied to give a detailed analysis of anyonic charge measurements using a Mach-Zehnder interferometer for arbitrary anyon models. We find that, as anyonic probes are sent through the legs of the interferometer, superpositions of the total anyonic charge located in the target region collapse when they are distinguishable via monodromy with the probe anyons, which also determines the rate of collapse. We give estimates on the number of probes needed to obtain a desired confidence level for the measurement outcome distinguishing between charges, and explicitly work out a number of examples for some significant anyon models. We apply the same techniques to describe interferometry measurements in a double point-contact interferometer realized in fractional quantum Hall systems. To lowest order in tunneling, these results essentially match those from the Mach-Zehnder interferometer, but we also provide the corrections due to processes involving multiple tunnelings. Finally, we give explicit predictions describing state measurements for experiments in the Abelian hierarchy states, the non-Abelian Moore-Read state at $ν=5/2$ and Read-Rezayi state at $ν= 12/5$.

quant-ph↗

arXiv2007

Decoherence of Anyonic Charge in Interferometry Measurements

We examine interferometric measurements of the topological charge of (non-Abelian) anyons. The target's topological charge is measured from its effect on the interference of probe particles sent through the interferometer. We find that superpositions of distinct anyonic charges a and a' in the target decohere (exponentially in the number of probes particles used) when the probes have nontrivial monodromy with the charges that may be fused with a to give a'.

quant-ph↗

arXiv2006

Probing Non-Abelian Statistics with QuasiParticle Interferometry

We examine interferometric experiments in systems that exhibit non-Abelian braiding statistics, expressing outcomes in terms of the modular S-matrix. In particular, this result applies to FQH interferometry, and we give a detailed treatment of the Read-Rezayi states, providing explicit predictions for the recently observed nu=12/5 plateau.

cond-mat.mes-hall↗

arXiv2006

Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State

In this letter we propose an interferometric experiment to detect non-Abelian quasiparticle statistics -- one of the hallmark characteristics of the Moore-Read state expected to describe the observed FQHE plateau at nu=5/2. The implications for using this state for constructing a topologically protected qubit as has been recently proposed by Das Sarma et. al. are also addressed.

cond-mat.mes-hall↗

arXiv2004

Decay Modes of Unstable Strings in Plane-Wave String Field Theory

The cubic interaction vertex of light-cone string field theory in the plane-wave background has a simple effective form when considering states with only bosonic excitations. This simple effective interaction vertex is used in this paper to calculate the three string interaction matrix elements for states of arbitrary bosonic excitation and these results are used to examine certain decay modes on the mass-shell. It is shown that the matrix elements of one string to two string decays involving only bosonic excitations will vanish to all orders in 1/mu on the mass-shell when the number of excitations on the initial string is less than or equal to two, but in general will not vanish when the number of excitations is greater than two. Also, a truncated calculation of the mass-shell matrix elements for one string to three string decays of two excitation states is performed and suggests that these matrix elements do not vanish on the mass-shell. There is, however, a quantitative discrepancy between this last result and its (also non-vanishing) gauge theory prediction from the BMN correspondence.

hep-th↗