Coogee’20

Sydney Quantum Information Theory Workshop

Richard Jozsa

(DAMTP, University of Cambridge, UK)

Magic states for matchgate computations

Magic states were introduced in the context of Clifford circuits as a resource that elevates classically simulatable computations to quantum universal capability, while maintaining the same gate set. Here we study magic states in the context of matchgate (MG) circuits, where the notion becomes more subtle, as MGs are subject to locality constraints and the SWAP gate is not a matchgate. Nevertheless a similar picture of gate-gadget constructions applies, and we show that every pure fermionic state which is non--Gaussian, i.e. which cannot be generated by MGs from a computational basis state, is a magic state for MG computations. This result has significance for prospective quantum computing implementation in view of the fact that MG circuit evolutions coincide with the quantum physical evolution of non-interacting fermions.

This work is in collaboration with Barbara Kraus, Martin Hebenstreit, Sergii Strelchuk and Mithuna Yoganathan.

Isaac Kim

(University of Sydney, Australia)

Digitizing quantum adiabatic algorithm

We provide a general recipe to convert a quantum adiabatic algorithm into a gate-based model of quantum computation. If both the Hamiltonian and the perturbation can be encoded in a block of a unitary oracle, we can achieve the oracle and the gate complexity that scales optimally with the spectral gap and the inverse precision up to a polylogarithmic factor. In particular, the dependence on the inverse precision is strictly polylogarithmic, as opposed to being subpolynomial.

Joint work with Kianna Wan (Stanford).

Adrian Chapmann

(University of Sydney, Australia)

A graph-theoretic characterization of free-fermion-solvable spin models

Finding exact solutions to spin models is a fundamental problem of many-body physics. A workhorse technique for exact solution methods is mapping to an effective description by noninteracting fermions, the paradigmatic example of this being the Jordan-Wigner transformation and its application for exactly solving the one-dimensional XY model. Another important example is the exact free-fermion solution to the two-dimensional Kitaev honeycomb model. We connect the general problem of recognizing models which can be solved this way to the graph-theoretic problem of recognizing line graphs, which has been solved optimally. This connection gives a strict criterion by which a given spin model has a free-fermion solution generalizing Kitaev’s. We classify the kinds of symmetries which can be present in such models, and we find that the Pauli symmetries correspond to either: (i) gauge qubits, (ii) cycles on the free-fermion hopping graph, or (iii) the fermion parity. Clifford symmetries, except in finitely-many cases, must be symmetries of the free-fermion Hamiltonian itself. We expect these results to motivate a renewed exploration of free-fermion-solvable models. We close with a discussion of applications for error-correction, fermion-to-qubit mappings, and generalizations to other so-called hereditary structures in physics.

Alex Rigby

(University of Tasmania, Australia)

Modified belief propagation decoders for QLDPC codes

Similar to classical LDPC codes, decoding for quantum LDPC (QLDPC) codes can be performed using belief propagation, which is a heuristic message passing algorithm that takes place on a bipartite graph, called a factor graph, defined by the code's stabilizer generators. Unfortunately, the commuting nature of these generators results in unavoidable cycles of length four in the factor graph, which are detrimental to the performance (decoding error rate) of belief propagation. This performance is further degraded by the degenerate nature of quantum errors, which is not accounted for in the component-wise inference of a belief propagation decoder. We present a number of modified decoders that aim to overcome these limitations, at least in part. Central among these is the augmented decoder, which in the case of a decoding error, iteratively reattempts decoding using modified factor graph. Across a range of codes, we show that our decoders perform as well as or better than other modified decoders presented in literature.

Joe Iverson

(Caltech, USA)

Coherence in logical quantum channels

In quantum error correcting codes, noise channels can be classified as either coherent or incoherent. Coherent noise can cause the average infidelity to accumulate quadratically when a fixed channel is applied many times in succession, rather than linearly as in the case of incoherent noise. I will present a proof that unitary single qubit noise in the 2D toric code with minimum weight decoding is mapped to less coherent logical noise. As the code size grows, the coherence of the logical noise channel is suppressed, provided the noise strength decays inversely with the code distance. The result holds even when the single qubit unitary rotation are not by the same angles or in the same directions, so long as the angles are below a threshold, and even when the rotations are correlated. Our proof does not show that coherence is suppressed in the more physically reasonable case where the noise strength is constant as the code size increases, and I will describe the difficulties in extending our proof to that case. In addition, I will describe how to characterize the coherence of noise using either the growth of infidelity or the relation between the diamond distance from identity and the average infidelity, and I will explain how coherence in the noise on physical qubits is transformed by error correction in general stabilizer codes.

Joint work with John Preskill.

Sisi Zhou

(Yale University, USA)

The theory of entanglement-assisted quantum metrology

The quantum Fisher information (QFI) measures the amount of information that a quantum state carries about an unknown parameter. The one-shot QFI of a quantum channel is defined to be the maximum QFI of the output state assuming an entangled input state over a single probe and an ancilla. Both the one-shot QFI and the optimal input state of a quantum channel could be solved via a semidefinite program. The asymptotic QFI of a quantum channel is defined to be the one-shot QFI of N >> 1 identical copies of the quantum channel. It was known that the asymptotic QFI grows either linearly or quadratically with N. Here we obtain a simple criterion—the HNKS condition—that determines whether the scaling is linear or quadratic. In both cases, we found a quantum error correction protocol achieving the asymptotic QFI and a semidefinite program to solve the optimal code. When the asymptotic QFI is quadratic, the Heisenberg limit, a feature once thought unique to unitary quantum channels, is recovered. When the asymptotic QFI is linear, we show it is still in general larger than N times the one-shot QFI, showing the non-additivity of the QFI of general quantum channels.

Norbert Schuch

(MPQ, Germany)

Order parameters for topological phases from tensor networks

Topological order cannot be characterized through local order parameters but is characterized by a nontrivial global ordering in the quantum correlations (entanglement). Topologically ordered systems display exotic features such as excitations with non-trivial statistics ("anyons") and a topology-dependent ground space structure. Tensor network states form a framework which allows to describe and study quantum many-body systems, including states with complex topological order, in a local way, with direct access to the entanglement degrees of freedom.  In my talk, I will (i) give an introduction to tensor network states, (ii) explain how they can be used to describe states with topological order, giving direct access to ground space and anyonic excitations, and (iii) show how this can be used to define and measure order parameters which directly characterize the behavior of anyons and thus can be used to characterize topological phase transitions through anyonic order parameters, beyond the reach of conventional order parameters.

Raditya Bomantara

(University of Sydney, Australia)

Combating quasiparticle poisoning with multiple Floquet Majorana modes

Majorana fermions are currently considered to be a promising ingredient towards achieving topologically protected quantum computing in the near future. Many theoretical proposals have been made over the years to utilize them for encoding and manipulating qubits in realistic physical systems, and their signatures have been confirmed in various recent experiments. At present, quasiparticle poisoning remains one of the main challenges towards demonstrating the robustness of Majorana qubits for quantum information processing. Quasiparticle poisoning refers to the unwanted flow of Majorana fermions into and out of the system hosting the Majorana qubits, which inevitably occurs when such a system is not completely isolated from its surrounding, thus considerably limiting its computational time. We propose the use of time-periodic driving to generate multiple MFs at each end of a single quantum wire, which naturally provides the necessary resources to implement active quantum error corrections with minimal space overhead. In particular, we present a stabilizer code protocol that can specifically detect and correct any single quasiparticle poisoning event. Such a protocol is implementable via existing proximitized semiconducting nanowire proposals, where all of its stabilizer operators can be measured from an appropriate Majorana parity dependent four-terminal conductance..

Zhengfeng Ji

(UTS, Australia)

Spooky complexity at a distance

In this talk, I will discuss the recent result on the characterisation of the power of quantum multi-prover interactive proof systems, MIP*=RE (arXiv:2001.04383). After a brief setup of the problem, we will highlight its rich connections and implications to problems in computer science, quantum physics, and mathematics, including the Tsirelson's problem and Connes' embedding problem. In the second half of the talk, we will outline the overall proof strategy and introduce several key techniques employed in the proof.

Carolin Wille

(FU Berlin, Germany)

Engineering topological tensor network states

The realization of topological quantum phases is a key challenge for condensed matter physics. In this talk, I demonstrate how concepts from quantum information theory, in particular tensor network states and Hamiltonian gadgets, can be used to make progress in this direction. As an example I present a simple blueprint for a synthetic double semion string-net model built from tunnel coupled mesoscopic units which is based on perturbative parent Hamiltonians and MPO-injectve PEPS. I further investigate how this construction can be combined with additional Hamiltonian gadgets providing a route towards realizing more complex topologically ordered systems such as the double Fibonacci model. 

Michael Gullans

(Princeton University, USA)

The measurement-induced phase transition and nearly random stabilizer codes

In this talk, I will present evidence that the physics of quantum error correction is also a generic, emergent property of quantum many-body systems subject to continuous monitoring of their environment.  Using toy models based on random unitary dynamics interspersed with projective measurements, I will describe precise connections that arise between fundamental notions of quantum error correction, such as the channel capacity, and the existence of a phase transition in these models as one tunes the measurement rate.  I will then show how to define a local order parameter for this transition that is defined by the ability of the system to protect initially local quantum information for exponentially long times.  An immediate consequence of these results is that the many-body dynamics in the ordered phase self-consistently generates new families of finite-rate, quantum error correcting codes.  I will discuss some of our progress in understanding the properties of these codes when the underlying dynamics corresponds to a stabilizer circuit.

Jeongwan Haah

(Microsoft, USA)

On locality preserving automorphisms on lattices

A constant depth quantum circuit on a lattice maps every local operator to a local operator by conjugation, and hence is an example of locality preserving automorphism of operator algebra on lattices. However, it is recently found that not every locality preserving automorphism comes from shallow quantum circuits; such an automorphism is termed “nontrivial QCA.” I will present an example of nontrivial QCA and different ways to think about it: the first is in terms of associated local Hamiltonian whose spectrum splits the Hilbert space, the second is a nontrivial decomposition of the operator algebra on a spatial boundary, and the third is an induced symmetry action from a higher dimensional symmetry protected topological phase.

Robert Harris and Deniz Stiegemann

(University of Queensland, Australia)

Generalising Holographic Codes

Holographic quantum error correcting codes have been proposed as a model for the AdS/CFT correspondence. They are formed by tessellation of smaller error correcting seed codes on a negatively curved surface, creating a finite rate code with potential for practical uses. 

In the first half of the talk we show that the original perfect tensor condition for the seed codes can be relaxed. This allows us to create our heptagon code, a CSS holographic code based on the Steane code, and another variant based on the surface code. We demonstrate that the some holographic codes have promising thresholds against both erasure and pauli noise. Additionally we discuss different distances we can analyse for finite rate codes, and how these scale for holographic codes.

In the second, we discuss necessary properties that these seed tensors ought to have. In the original proposal, Pastawski et al. used so-called perfect tensors to capture a notion of invariance under the underlying symmetry group of the tessellation. We argue that the notion of perfect tensor can be generalised, that is, there are non-perfect tensors which satisfy weaker constraints and still give rise to viable holographic states.