Coogee’18

Sydney Quantum Information Theory Workshop

David Aasen

(Caltech, USA)

Fermion condensation and superconducting string-nets

A great deal of progress has been made toward a classification of bosonic topological orders whose microscopic constituents are bosons. Much less is known about the classification of their fermionic counterparts. In this talk I will describe a systematic way of producing fermionic topological orders using the technique of fermion condensation. Roughly, this can be understood as binding a physical fermion to an emergent fermion and condensing the pair. I will discuss the `super pivotal categories' that describe universal properties of these phases and use them to construct exactly solvable string-net models. These string-net models feature conventional anyons and two flavours of vortices. I will show that one of the vortex types is similar to a vortex in a p+ip superconductor binding a Majorana zero mode, and will mention some possible applications.

Victor Albert

(Caltech, USA)

Filling cavities to prevent decay: bosonic quantum error correction

Continuous-variable quantum information processing is a field concerned with using one or more harmonic oscillators to protect, manipulate, and transport quantum information. As opposed to building systems out of two-level components (qubits), here the minimal component is the phase space associated with a canonical pair of continuous variables — position and momentum for a mechanical oscillator or quadrature components for an electromagnetic field mode. The large Hilbert space describing this phase space allows one to encode information such that recovery from errors is possible, thereby providing competitive alternatives to encoding into a register of qubits. Moreover, we are at the point of realizing full-fledged protocols utilizing such encodings due to significant advances in microwave cavity, atomic ensemble, and trapped ion control. This presentation overviews continuous-variable quantum error-correcting codes, from theoretical capabilities to experimental realizations.

Juan Bermejo-Vega

(FU Berlin, Germany)

Architectures for quantum simulation showing a quantum speedup

Joint work with Dominik Hangleiter, Martin Schwarz, Robert Raussendorf, Jens Eisert

Abstract: An important near-term goal in the field of quantum simulation is to demonstrate a large quantum speedup (these days sometimes called "quantum computational supremacy") by performing a simple experiment whose outcome cannot efficiently be predicted on a classical computer. Here, we propose new simple quantum simulations that show a quantum speedup. Specifically, we give strong evidence that efficiently classically simulating the dynamics of translation-invariant Ising models on the 2D square lattice is impossible, even for constant times and allowing for constant additive errors. Specifically, we prove that such a classical simulation is impossible assuming plausible complexity-theoretic conjectures analogous to those in the famous boson sampling problem, or in the quantum experiments being put forward by Google AI. Our proposal is tailored to optical-lattice cold-atom quantum simulator hardware and relies on realistic resources. Finally and remarkably, the correctness of our quantum devices can be efficiently certified using tested single-qubit measurements and classical post-processing. Thus, our proposal puts a convincing falsifiable experimental demonstration of a quantum speedup within reach in the near term.

Based on:

https://arxiv.org/abs/1703.00466
https://arxiv.org/abs/1706.03786

Michael Beverland

(Microsoft Research, USA)

Statistical physics and quantum error correction

Abstract: There are deep connections between statistical physics toy models and quantum error correcting codes. In particular, topological error correcting codes, which are compelling candidates for quantum hardware due to their their geometrically local implementations and high tolerance to local errors can be thought of as geometrically local Hamiltonians. The critical noise strength that can be tolerated by an error correcting code (its "threshold") corresponds to a phase transition in the Hamiltonian. I will two extensions of these connections. Firstly, we can find the error correction thresholds for exotic models such as the three-dimensional color code (work with Kubica, Brandao, Preskill, and Svore https://arxiv.org/pdf/1708.07131.pdf) by mapping to interesting statistical mechanics models with local symmetries. Secondly, in addition to identifying asymptotic features such as error thresholds, we can develop statistical physics models to understand finite system error correction behavior which are the use cases (work with Brown, Marolleau and Kastoryano). We can then address practical questions such as: "which parameter regimes is it better to use the standard toric code compared with that rotated by 45 degrees?" (The rotated toric code has a lower distance using the same number of qubits, but more low-weight error configurations). I will also discuss challenges and open questions for this ongoing work. 

Adam Brown

(Stanford, USA)

Spacetime and Computational Complexity

Abstract:  I will explain why high-energy physicists have recently gotten so interested in quantum information theory. As an example, I will discuss the `holographic complexity conjecture', that seeks to relate the size of the wormhole that lies behind a black hole horizon to quantum computational complexity.

Elizabeth Crosson

(Caltech, USA)

Universal quantum computation in thermal equilibrium

Abstract: Adiabatic quantum computation (AQC) is a method for performing universal quantum computation in the ground state of a slowly evolving local Hamiltonian, and in an ideal setting AQC is known to capture all of the computational power of the  quantum circuit model.  However, despite having an inherent robustness to noise as a result of the adiabatic theorem and the spectral gap of the Hamiltonian, it has been a longstanding theoretical challenge to show that fault-tolerant AQC can in principle be performed below some fixed noise threshold.  There are many aspects to this challenge, including the difficulty of adapting known ideas from circuit model fault-tolerance as well as the need to develop an error model that is appropriately tailored for open system AQC.  In this talk I will introduce a scheme for combining Feynman-Kitaev history state Hamiltonians with topological quantum error correction, in order to show that universal quantum computation can be encoded not only in the ground state but also in the finite temperature Gibbs state of a local Hamiltonian.  Using only local interactions with bounded strength and a polynomial overhead in the number of qubits, the scheme is intended to serve as a proof of principle that universal AQC can be performed at non-zero temperature, and also to further our understanding of the complexity of highly entangled quantum systems in thermal equilibrium.

David Gosset

(IBM, USA)

Classical simulation of quantum circuits via stabilizer rank

Abstract: Stabilizer states are a rich class of quantum states which can be efficiently classically represented and manipulated. In this talk I will describe some ways in which they can help us to represent and manipulate more general quantum states. In the first part I will present classical simulation algorithms for quantum circuits which are based on expressing a quantum state as a superposition of (as few as possible) stabilizer states. In the second part I will describe how a quantum state stored in classical computer memory (i.e. a normalized complex vector) can be compressed by roughly a square root factor using a representation consisting of its inner products with random stabilizer states. 

The first part of the talk is based on arXiv:1601.07601 (with Sergey Bravyi) and work in progress with Sergey Bravyi, Dan Browne, Padraic Calpin, Earl Campbell and Mark Howard. The second part is based on joint work with John Smolin (arXiv:1801.05721).

Jonas Helsen

(TU Delft, The Netherlands)

Recognising Cliffordness: Conjectures, Ideas and a Few Proofs

Abstract: Given a quantum circuit composed of Clifford+T gates, is it classically easy to tell whether this circuit represents a unitary in the Clifford group? Is it easy given access to a quantum computer? What if I relax the question to only requiring that the output state (on inputting the all zero state) is (close to) a stabilizer state? Relying on recent results by Gross et al. (2017) and Amy & Mosca (2016) I partially answer these questions in this talk and define several more 'natural' questions involving the complexity of recognising stabilizer states and Clifford elements. I conjecture an analogy between this array of problems and a similar array of problems involving separability testing (as discussed in Gutoski et al. (2013)).

Christina Knapp

(UCSB, USA)

Anyonic Entanglement and Topological Entanglement Entropy

Abstract: In this talk, I will discuss the results of Bonderson, Knapp, Patel, Annals of Physics 385 (2017).  In this work, we study the properties of entanglement in two-dimensional topologically ordered phases of matter. Such phases support anyons, quasiparticles with exotic exchange statistics. The emergent nonlocal state spaces of anyonic systems admit a particular form of entanglement that does not exist in conventional quantum mechanical systems. We study this entanglement by adapting standard notions of entropy to anyonic systems.  We find a general formula for the entanglement entropy for general system configurations of a topological phase, including surfaces of arbitrary genus, punctures, and quasiparticle content. Our results recover and extend prior results for anyonic entanglement and the topological entanglement entropy.

Dax Koh

(MIT, USA)

Classifying the simulation complexities of extended Clifford circuits

Abstract: Extended Clifford circuits straddle the boundary between classical and quantum computational power. Whether such circuits are efficiently classically simulable seems to depend delicately on the ingredients of the circuits. While some combinations of ingredients lead to efficiently classically simulable circuits, other combinations, which might just be slightly different, lead to circuits which are likely not. We extend the results of Jozsa and Van den Nest [Quantum Inf. Comput. 14, 633 (2014)] by studying various further extensions of Clifford circuits. First, we consider how the classical simulation complexity changes when we allow for more general measurements. Second, we investigate different notions of what it means to "classically simulate" a quantum circuit. Third, we consider the class of conjugated Clifford circuits, where one conjugates every qubit in a Clifford circuit by the same single-qubit gate. Our results provide more examples where seemingly modest changes to the ingredients of Clifford circuits lead to "large" changes in the classical simulation complexities of the circuits, and also include new examples of extended Clifford circuits that exhibit "quantum advantage”, in the sense that it is not possible to efficiently classically sample from the output distributions of such circuits, unless the polynomial hierarchy collapses. Based on https://arxiv.org/abs/1512.07892 and https://arxiv.org/abs/1709.01805.

David Poulin

(Sherbrooke, Canada)

Fast Quantum Algorithm for Hamiltonian Spectral Properties

Abstract: We present two techniques that can greatly reduce the number of gates required for ground state preparation in quantum simulations. The first technique realizes that to prepare the ground state of some Hamiltonian, it is not necessary to implement the time-evolution operator: any unitary operator which is a function of the Hamiltonian will do. We propose one such unitary operator which can be implemented exactly, circumventing any Taylor or Trotter approximation errors. The second technique is tailored to lattice models, and is targeted at reducing the use of generic single-qubit rotations, which are very expensive to produce by distillation and synthesis fault-tolerantly. In particular, the number of generic single-qubit rotations used by our method scales with the number of parameters in the Hamiltonian, which contrasts with a growth proportional to the lattice site required by other techniques.

Norbert Schuch

(MPQ, Germany)

Studying topological spin liquids with PEPS

Abstract: Topological spin liquids form an exotic phase of matter where spins do not order magnetically due to strong frustration effects, yet order globally in their entanglement. Systems with such behavior are notoriously difficult to identify, as one needs to verify both the absence of any local ordering and the presence of global topological order in the system.  In my talk, I will discuss how Projected Entangled Pair States (PEPS) -- an ansatz which provides a local description of complex entangled systems, and in which both spin symmetries and topological order can be locally characterized -- allows us to construct and identify topological spin liquids, and to study how they respond to external fields. In particular, I will discuss how to construct and identify spin liquids with SU(2) and SU(3) symmetry with different types of topological order, and how to understand their behavior when subjected to different types of external perturbations. 

Guifre Vidal

(Perimeter Institute, Canada)

Tensor networks as geometry

Abstract: The multiscale entanglement renormalization ansatz (MERA) is a tensor network that can efficiently approximate ground states of critical spin chains --that is, lattice versions of 1+1 CFT ground states. Its network structure extends in an additional dimension corresponding to renormalization group scale. Accordingly, MERA has has been proposed to be a discrete realization of the AdS/CFT correspondence. While a first proposal speculated that "MERA = discrete hyperbolic plane" (time slice of AdS3), a second proposal conjectured instead that "MERA = discrete 1+1 de Sitter spacetime". In this talk I will attach a geometry to MERA from the perspective of a CFT path integral. Surprisingly, the corresponding metric does not have euclidean nor lorentzian signature (as in the above proposals), but is instead degenerate. I will also describe how MERA can be modified to represent either the hyperbolic plane or 1+1 de Sitter spacetime.

Work in preparation with Ash Milsted. 

For "MERA=hyperbolic plane", see Swingle arXiv:0905.1317, arXiv:1209.3304 

For "MERA = de Sitter spacetime", see Beny, arXiv:1110.4872; Czech et al, arXiv:1512.01548; Bao et al, arXiv:1709.03513 

https://quantumfrontiers.com/2015/06/26/holography-and-the-mera/

https://www.quantamagazine.org/tensor-networks-and-entanglement-20150428

http://www.preposterousuniverse.com/blog/2015/05/05/does-spacetime-emerge-from-quantum-information/

Theodore Yoder

(MIT, USA)

The disjointness of stabilizer codes and bounds on fault-tolerant logical gates

Abstract: Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for these codes, the disjointness, which, roughly speaking, is the number of mostly non-overlapping representatives of any given non-trivial logical Pauli operator. We use the disjointness to prove that transversal gates on error-detecting stabilizer codes are necessarily in a finite level of the Clifford hierarchy. We also apply our techniques to topological code families to find similar bounds on the level of the hierarchy attainable by constant depth circuits, regardless of their geometric locality. For instance, we can show that symmetric 2D surface codes cannot have non-geometrically-local constant depth circuits for non-Clifford gates.