Coogee’17

Sydney Quantum Information Theory Workshop

Robin Blume-Kohout

(Sandia, USA)

Gauge

Quantum computation is a gauge theory.  As-built quantum information processors (QIPs) are described by "gate sets" that associate a quantum process matrix to each logic gate that can appear in a quantum circuit.  But these descriptions are not unique.  For any given QIP, there is an infinite set of equivalent gatesets that look quite different, but are experimentally indistinguishable.  This is surprisingly inconvenient for characterizing QIPs -- i.e., for tomography, randomized benchmarking, and any other attempt to infer properties of the gate set from experimental data.  I will present what is known about the gauge freedom, survey the problems that it presents, and issue a challenge to the audience to slay this dragon by developing a gauge-free theory of QIPs.

Courtney Brell

(Perimeter Institute, Canada)

TBA

Abstract:  TBA. 

Ben Brown

(Niels Bohr Institute, Copenhagen, Denmark)

Picking holes and cutting corners to achieve Clifford gates with the surface code

Abstract: The surface code is currently the leading proposal to achieve fault-tolerant quantum computation. Among its strengths are the plethora of known ways in which fault-tolerant Clifford operations can be performed, namely, by deforming the topology of the surface, by the fusion and splitting of codes and even by braiding engineered Majorana modes using twist defects. Here we present a unified framework to describe these methods, which is required to better compare different schemes, and to facilitate the design of hybrid schemes. Novel to our unification is the identification of twist defects with the corners of the planar code. This identification enables us to find new ways of performing single-qubit Clifford gates by exchanging the corners of the planar code via code deformation. We analyse the ways in which all of the different schemes can be combined, and propose a novel hybrid encoding. We also show how all of the Clifford gates can be implemented on a single code without loss of distance, thus offering an attractive alternative to ancilla-mediated schemes to complete the Clifford group with lattice surgery.

Nicolas Delfosse

(Caltech, USA)

Contextuality and negativity of the Wigner function in quantum computation

Abstract:  Contextuality and negativity of the Wigner function are two notions of

non-classicality for quantum systems.  In this talk, I will review these two notions and their role in quantum computing. I will show that they coincide for systems of qudits with odd local dimension. Then, I will consider the case of qudits, which is surprisingly different, due to the presence of state independent contextuality.

Based on joint work with J. Bermejo-Vega, D. E. Browne, C. Okay, R. Raussendorf.

https://arxiv.org/abs/1610.07093

https://arxiv.org/abs/1610.08529

https://arxiv.org/abs/1511.08506

David Gross

(Cologne, Germany)

Quantum Non-Locality and Latent Causal Structures

Abstract: It's a recent trend to cast problems of quantum non-locality into the language of causal analysis, a subfield of statistics (or, if you want to get funding, of machine learning). Indeed, both fields face the problem of deciding whether observed data is compatible with a presumed causal relationship between the variables. In physics, Bell inequalities have been used to describe the restrictions imposed by causal structures on marginal distributions. However, some structures give rise to non-convex constraints on the accessible data, and surprisingly little is known about how to test compatibility with such causal assumptions. I'll give an introduction to these problems and explain our approaches based on information theory and semi-definite programming.

Tomas Jochym-O’Connor

(Caltech, USA)

Fault-tolerant universality for planar quantum error correction

Abstract: Stabilizer codes defined on planar geometries are among the most promising architectures for quantum fault-tolerance. However, despite recent alternative proposals to magic state distillation, implementing universal logical gates remains a challenge. This talk will review the code conversion techniques of doubled/stacked codes and explore a new scheme inspired by state-teleportation for implementing a non-Clifford gate on a planar stabilizer code.

Richard Kueng

(Cologne, Germany)

The Clifford group fails gracefully to be a unitary 4-design with

applications to quantum state discrimination

Abstract: We have achieved a new analysis of the representation theory of the Clifford group. The result allows us to prove new results for state discrimination under stabilizer measurements; entropic uncertainty relations; problems from compressed sensing with structured measurements; and (as others have shown) randomized benchmarking. In this talk, we will focus on a variant of quantum state

discrimination: the task of correctly distinguishing two arbitrary quantum states with a fixed POVM-measurement. Several near-optimal measurement schemes have been identified (e.g. the uniform POVM, or spherical 4-designs). In contrast, most structured measurements – such as MUBs and SICs - perform much worse. We show that multi-qubit stabilizer measurements are an exception: although highly structured, they are essentially optimal for distinguishing pure quantum states. This result follows from a more general insight about the symmetry group of stabilizer states: the 4th tensor power of the Clifford group affords only one more invariant subspace than the 4th tensor power of the unitary group. In this sense, the Clifford group fails “gracefully” to be a unitary 4-design (i.e. a set of unitaries that is “evenly distributed” in the sense that the average of any 4th order polynomial over the design equals the average over the entire unitary group)..

Naomi Nickerson

(PsiQuantum, USA)

Adaptive decoding for distinguishing noise models in topological codes

Abstract: Many experimental systems for QIP are rapidly progressing towards a state where quantum error-correcting codes may soon be realised. These codes will suffer from environmental noise, and in many systems it is likely that this will include some sort of correlated errors, not the purely i.i.d. Pauli noise that is generally used to analyse schemes for error correction. If the structure of the correlations is known it is often possible to adapt the decoding process to handle them effectively. If they are not known, however, correlations can very quickly reduce the threshold of a code. 

This talk will consider how we can handle this case in which the structure of the correlations are not known in advance.  I will discuss a new method that can be used to analyse correlated errors by making use of a parameterised family of decoding algorithms. With this approach, by using only classical syndrome and decoding information it is still possible to identify structure in the noise, and adapt the decoder to reduce the rate of logical failure. I will show some numerical results for the specific case of a diffusive noise model in the surface code.

David Poulin

(Sherbrooke, Canada)

Surprising facts about quantum error correction

Abstract: While many studies have analyzed the fault-tolerant threshold, surprisingly little is known about the sub-threshold behavior. Given a physical noise rate, how much of an overhead do I actually need to achieve desired logical accuracy? We have devised numerical simulations platforms for the surface code and for concatenated codes that can take as input a wide range of noise models, including non-Pauli and correlated noise, and outputs a logical noise model after some amount of error correction. In this talk, I will briefly describe these numerical tools and present surprising results that we have obtained using them. This wors is in collaboration with Pavithran Iyer and Andrew Darmawan. Some of the results are presented in http://arxiv.org/abs/arXiv:1607.06460

Joel Wallman

(IQC, Waterloo, Canada)

Characterizing quantum gates and circuits

Abstract: Quantum computers promise to revolutionize information processing, provided they can be implemented with sufficiently small errors for the output to be reliable with an efficient overhead. For quantum computers to be useful and reliable, estimating errors in quantum circuits has to use fewer classical computational resources than simulating an ideal quantum computer.

In this talk, I will discuss the primary ways of quantifying errors in quantum circuits, namely, the average gate infidelity and the diamond distance from the identity,

and how they can be used to estimate the total error rate in a given circuit. I will then discuss how these parameters can be estimated using randomized

benchmarking and purity benchmarking by averaging outcome probabilities over random circuits. I will conclude by discussing how ideas from randomized benchmarking can be used to reduce the error rate in quantum circuits. 

Michael Walker

(Stanford, USA)

Multipartite Entanglement in Stabilizer Tensor Networks

Abstract: Tensor network models reproduce important structural features of holography, including the Ryu-Takayanagi formula for the entanglement entropy and quantum error correction in the entanglement wedge. In contrast, only little is known about their multipartite entanglement structure, which has been of considerable recent interest. In this work, we study random stabilizer tensor networks and show that here the tripartite entanglement question has a sharp answer: The average number of GHZ triples that can be extracted from a stabilizer tensor network is small, implying that the entanglement is predominantly bipartite. As a consequence, we obtain a new operational interpretation of the monogamy of the Ryu-Takayanagi mutual information and an entropic diagnostic for higher-partite entanglement. Our technical contributions include a spin model for evaluating the average GHZ content of stabilizer tensor networks and a novel formula for the third moment of random stabilizer states. As time permits, I will also present new results on their higher moments and discuss possible applications in quantum information theory and signal recovery.

This is based on joint work with Sepehr Nezami.

Stephanie Wehner

(Delft, The Netherlands)

Testing quantum devices

Abstract: We present two new results on estimating the performance of quantum devices. The first concerns the estimation of a quantum device's capacity to store or transmit quantum informtion. Such capacities have been studied for arbitrary kinds of quantum channels, but their practical estimation has so far been limited to devices that implement independent and identically distributed (i.i.d.) quantum channels, where each qubit is a_ected by the same noise process. Real devices, however, typically exhibit correlated errors. 

Here, we overcome this limitation by presenting protocols that estimate a channel’s one-shot quantum capacity for the case where the device acts on (an arbitrary number of) qubits. The one-shot quantum capacity quantifies a device’s ability to store or communicate quantum information, even if there are correlated errors across the di_erent qubits. 

We present a protocol which is easy to implement and which comes in two versions. The first version estimates the one-shot quantum capacity by preparing and measuring in two di_erent bases, where all involved qubits are used as test qubits. The second version verifies on-the-fly that a channel’s one-shot quantum capacity exceeds a minimal tolerated value while storing or communicating data, therefore combining test qubits and data qubits in one protocol. We discuss the performance of our method using simple examples, such as the dephasing channel for which our method is asymptotically optimal. We apply our method to estimate the one-shot capacity in an experiment using a transmon qubit.

Second, we briefly highlight a new result on randomized benchmarking that dramatically reduces the required number of samples allowing the procedure to be applied to many qubit quantum computers (see also talk Joel Wallman on friday).

Based on:

https://arxiv.org/abs/1611.05411

https://arxiv.org/abs/1701.04299

https://arxiv.org/abs/1609.08188

Dominic Williamson

(Vienna, Austria)

Two dimensional symmetry enriched topological order in tensor networks

Abstract: I will outline a tensor network description of two dimensional, nonchiral, symmetry enriched topological order that relies heavily on matrix product operators. An important aspect of this description is the defect tube (dube) algebra which facilitates the construction of all extrinsic symmetry defects. If time permits I will also mention implications for transversal gates in two dimensional topological codes..

Huan Qiang Zhou

(Chongqing, China)

Fidelity Mechanics: Analogues of four thermodynamic laws and Landauer’s principle

Abstract: Fidelity mechanics, a scheme to investigate critical phenomena in quantum many-body physics, is formulated as an analogue of four laws in thermodynamics and black hole mechanics, thus unveiling a formal connection between critical points and black holes.

Rich physics is unveiled even for simple, or say, prototypical models in quantum many-body systems, such as one-dimensional quantum XY model and quantum transverse Ising chain in a longitudinal field. This enables us to clarify a confusing point for the so-called long-range entanglement driven order. The latter is believed to be present in the disordered regime for quantum XY chain.