# Melbourne Quantum Summit

[Edition 2024: Theoretical Quantum Information]

February 12-13, 2024 @ Ormond College

Directions and Registration: As accepted participant you received a confirmation email titled "Details - Melbourne Quantum Summit" with further instructions. Please aim to arrive around 9:00am at the entrance gate of Ormond College to complete registration in time to start the event at 9:30am.

## Strengthening the Melbourne Quantum Community

There will be ample opportunity to discuss with other researchers during the coffee breaks, over lunch and during dinner. We want to further develop connections between the various institutions in Melbourne.

## Giving early career researchers the opportunity to showcase their work

We will have a number of sessions dedicated to young researchers presenting their work and exchanging idea. We will also have a poster session to facilitate discussions, which may continue over dinner.

## Developing a strategic vision for quantum science in Melbourne

We want to brainstorm as a community how we can strengthen Melbourne as location of world-class quantum science. We can coordinate initiatives, joint funding applications and position ourselves for the future.

## Event Schedule (as of 2024-02-10)

## Lectures

### Lecture 1 - Margaret Reid (RMIT): The Einstein-Podolsky-Rosen paradox

It is well known that Einstein was not convinced of the completeness of quantum mechanics, in particular of the Copenhagen interpretation. In 1935, Einstein, Podolsky and Rosen (EPR) presented a compelling argument (known as the EPR paradox) to demonstrate that quantum mechanics is an incomplete theory. Their argument was based on a set of seemingly well-justified premises, referred to as “local realism”. EPR’s paper motivated immediate responses from both Bohr and Schrodinger, who pointed out that quantum mechanics also seemed inconsistent with realism at a macroscopic level. Schrodinger identified “entanglement” as the property leading to the EPR paradox. The EPR argument later inspired Bell to derive his famous Bell inequalities. Surprisingly, the EPR’s premises could be falsified, if the quantum predictions of certain entangled states which predict a violation of Bell inequalities could be verified in experiment. Experiments have only recently rigorously confirmed violations of Bell’s inequalities.

This talk will review the history behind the pioneering work of EPR and Bell, and closely associated papers and experiments, exploring the relationship to entanglement and steering. We discuss the consequences of violations of Bell inequalities that can be predicted for systems in macroscopic superposition states, called cat states. In doing so, we summarise the relationship to inequalities derived by Leggett and Garg that are designed to negate forms of macroscopic realism, called macrorealism. Bell was concerned with resolving the measurement problem, and we present a recent approach using phase-space methods that suggest a subset of EPR’s premises may be valid, based on hidden causal loops.

It is important to realise that the work of EPR has been important not only for foundational physics, but for the field of quantum information: EPR states provide the resource for quantum cryptography and quantum teleportation. We give a brief outline of applications.

### Lecture 2 - Muhammad Usman (CSIRO Data 61): Quantum Computing and Machine Learning

Quantum computing and machine learning are presently amongst the most rapidly progressing areas of research with the possibility of revolutionary impact for a broad range of applications such as in digital health, climate science, materials science, cybersecurity, and transport/logistics optimisation. In this lecture, you will learn how the integration of quantum computing and machine learning leads to new possibilities to address key challenges in both disciplines. I will first talk about the application of classical machine learning in the characterisation of qubit devices, the design of quantum control, optimal mapping of quantum circuits on a quantum process, and efficient decoding of quantum errors, and argue that classical machine learning tools can have significant impact in advancing the field of quantum computing. In the second part of the lecture, I will describe the superior performance of quantum machine learning models – machine learning models which are specifically designed to benefit from the unique quantum properties such as superposition and entanglement – over their classical counterparts in particular for applications in transport and Defence systems where robustness and reliability of machine learning is of key parameter of interest. The lecture aims to provide a high-level overview of key research outcomes from the literature, highlighting some of the recent advancements at the intersection of quantum computing and machine learning.

### Lecture 3 - Nicolas Menicucci (RMIT): Introduction to continuous variable quantum information

TBA

## Talks

### Talk 1 - Alexander Dellios (Swinburne): Gaussian boson sampling: Phase-space simulations of grouped probabilities

In the past few years, an increasing number of Gaussian boson sampling (GBS) quantum computers have claimed quantum advantage. These devices are linear photonic networks with squeezed vacuum state inputs whose outputs are photon count patterns with probabilities that are #P-hard to compute. The current generation of GBS has been implemented on both programmable and static networks, observing large enough photon counts to be well beyond the realm of direct classical computation. This leads to an interesting problem: How does one verify experimental outputs when they are intractably hard to calculate? To answer this, we use grouped probabilities simulated using the positive-P phase-space representation. These have the same moments as experimental outputs, but are computable. Such methods allow one to simulate all correlations generated in the network, within sampling error. We present comparisons of theory versus experiment for data from recent experiments, where differences are quantified using chi-square tests. Our results show theoretical agreement is increased once decoherence is added to the inputs and the transmission efficiency is corrected.

### Talk 2 - Lucky Antonopoulous (RMIT University): Connections between Discrete Wigner Functions

Wigner functions (WF) are a useful tool in quantum mechanics to represent both states and operators in phase space. Another useful feature is that for states, the negativity of the WF can be a resource for quantum computing, leading to the possibility of a quantum advantage. In the continuous domain, there exists a unique, well defined continuous WF (CWF). In quantum systems however, one typically deals with discrete systems, and so the question of defining a discrete WF (DWF) arises. Unfortunately, this question does not have a simple conclusion as there currently exists a number of DWF definitions, each with slightly different properties, differing phase space sizes, and the bigger issue what dimension the DWF are considered useful. In this work, we try to find a connection between formalisms by first defining a DWF using a 2dx2d sized unit cell of phase space of the CWF of the Gottesman-Kitaev-Preskill (GKP) encoding of an operator. We then use a convolution mapping method to derive dxd sized DWFs and find that some of these match existing definitions in the literature, meaning we have reproduced them. We finally employ the Weyl-Heisenberg displacement operators to show that a number of these dxd DWFs are related to each other, further finding common ground amongst definitions and so providing a stepping stone towards a more unified framework.

### Talk 3 - Philipp Frey (University of Melbourne): Observing time crystals on a quantum computer

Time crystals have been proposed as a novel, stable phase of matter that defies conventional expectations due to ergodicity breaking. We simulate the dynamics of a spin-1/2 chain with nearest neighbour Ising interactions, quenched disorder and periodic driving over 57 qubits on a quantum computer. Based on the ynamics of local spin depolarisation we observe discrete time crystalline behaviour due to many body localisation. In order to extract the signal from the noisy data produced by current quantum computer devices, we develop a strategy for error mitigation. A transition between DTC and a thermal phase is observed via critical fluctuations in the sub-harmonic frequency response of the system, as well as a significant speed-up of spin depolarisation.

### Talk 4 - Karen Bayros (RMIT University): Modelling charge transport in Al/AlOx/Al Josephson junctions

Josephson junctions are key elements of quantum computers based on superconducting qubits. Although superconducting qubits are one of the most promising candidates to realise large-scale quantum computing, the materials science of Josephson junctions still limits their performance. Imperfections in Josephson junctions are thought to be a source of dissipation, decoherence, parameter drift, and uncertainty. As an example, inhomogeneities in the barrier thickness can result in a non-ideal current-phase response. Using molecular dynamics and a tight-binding description, we develop a numerical model of Al/AlOx/Al Josephson junctions to investigate the influence of atomic structure on the electrical response of these junctions. Pairing this with a non-equilibrium Green’s function (NEGF) approach to study transport, we find that the disordered nature of the oxide barrier results in regions with higher transparency which can facilitate quasiparticle current flow through the barrier. These models will help improve the design and fabrication of superconducting qubits.

### Talk 5 - Michael A. Jones (University of Melbourne): Moments-based ground state energy estimation for chemical systems on a quantum computer

The accurate computation of properties of large molecular systems is classically infeasible and is one of the applications in which it is hoped that quantum computers will demonstrate an advantage over classical devices. However, variational-hybrid algorithms introduced to tackle these problems on present day hardware struggle to meet the accuracy and precision requirements for chemical applications. On the other hand, quantum phase estimation requires large resource overheads in order to implement fully fault-tolerant operations. I will discuss a method based on computation of the Hamiltonian moments, including recent experimental results, that suggest a middle-ground on the path to quantum utility.

### Talk 6 - Hugh Sullivan (RMIT University): Modelling quantum mechanical systems with the finite element method

There are a variety of nanostructures today that have been demonstrated to serve quantum information purposes. However, accurately modelling many of the structures, such as quantum dots, is challenging due to their complicated structures. We overcome this difficulty by employing the finite element method (FEM) which solves differential equations on arbitrary geometries. Using the FEM we have investigated quantum dots, quantum dot molecules and quantum rings in the presence of electromagnetic fields.

### Talk 7 - Jean-Emile Bourgine (University of Melbourne): A Calogero model for the non-Abelian quantum Hall effect

The non-Abelian fractional quantum Hall effect is an interesting quantum phenomenon that exhibits topologically protected states, a key feature for the realization of fault-tolerant quantum computing devices. In this talk, I will introduce a new model for this quantum effect obtained from the diagonalization of a matrix model proposed by Dorey, Tong, and Turner (DTT). The Hamiltonian is reminiscent of a spin Calogero-Moser model but involves higher-order symmetric representations of the non-Abelian symmetry. I will discuss its energy spectrum, and its action on a certain class of wave functions with a free fermion expression. I will also explain the emergence of Kac-Moody symmetries in the large N limit using the level-rank duality.

### Talk 8 - Max West (University of Melbourne): Provably Trainable Rotationally Equivariant Quantum Machine Learning

Max West Exploiting the power of quantum computation to realise superior machine learning algorithms has been a major research focus of recent years, but the prospects of quantum machine learning (QML) remain dampened by considerable technical challenges. A particularly significant issue is that generic QML models suffer from so-called barren plateaus in their training landscapes – large regions where cost function gradients vanish exponentially in the number of qubits employed, rendering large models effectively untrainable. A leading strategy for combating this effect is to build problem-specific models which take into account the symmetries of their data in order to focus on a smaller, relevant subset of Hilbert space. In this work, we introduce a family of rotationally equivariant QML models built upon the quantum Fourier transform, and leverage recent insights from the Lie-algebraic study of QML to prove that (a subset of) our models do not exhibit barren plateaus. We additionally conduct numerical tests in which we find that our symmetry-informed models can dramatically outperform their generic counterparts in practice.

### Talk 9 - Jacob Cybulski (Deakin University): Strategies for dealing with barren plateaus in training quantum machine learning models

Quantum machine learning involves development of models, such as quantum neural networks or quantum support vector machines, which commonly consist of parameterised quantum circuits that can be trained using a hybrid quantum-classical process. The process uses a sample of data to guide an optimisation process, which is performed on a classical computer and which is responsible for varying the circuit parameters to reduce the cost function. Typically, the cost function is a classical computation estimating the difference between the circuit measurements taking place on a quantum machine and the expected values specified by the data sample. Such a hybrid process can be affected by the emergence of barren plateaus – flat areas in the landscape of the cost function, which prevent effectiveness of the quantum model optimisation. In this short presentation we will explain the main causes of barren plateaus, outline some strategies for dealing with them, and assess the impact of these strategies on the model’s capacity to learn.

### Talk 10 - Fakhar Zaman (CSIRO): Quantum-enhanced Reinforcement Learning for Robotic Systems

Reinforcement learning has emerged as potent tool in computer science, which focuses on data analysis and patterns recognition to speed up the learning capabilities and decision-making tasks in robotic systems. In recent years, quantum computing has been introduced in reinforcement learning, so called quantum reinforcement learning, leveraging resources such as quantum superposition and quantum correlations to enhance the learning capabilities. This work demonstrates the advantage of single-qubit and multi-qubit quantum reinforcement learning algorithm over classical methods in robotic systems. We provide strong evidence of performance enhancement in reinforcement learning tasks using hybrid quantum-classical neural networks, primarily in terms of sample efficiency and size of the machine learning model. The proposed hybrid model requires fewer training data points and trainable parameters in comparison to its classical counterpart. We show that the proposed hybrid model successfully stabilizes an inverted pendulum and outperforms its classical counterpart, offering a promising avenue for addressing complex tasks more efficiently. In addition, we demonstrate that the single-qubit model learns faster in comparison to multi-qubit hybrid model, which shows the feasibility of the implementation of the proposed algorithm on small scale real quantum devices.

### Talk 11 - Ned Goodman (Swinburne): Classical Approximate Gaussian Boson Sampling: Has Quantum Advantage been Achieved?

A Gaussian Boson Sampler (GBS) is a non-universal optical quantum computer designed to demonstrate quantum advantage without error correction by efficiently sampling from a #P-hard distribution. Experiments have claimed quantum advantage using these devices, and in response, multiple groups have developed classical algorithms to approximately sample from the GBS output distribution. These classical samplers were found to outperform the current experiments on a wide variety of metrics, calling the experimentalist's claims of quantum advantage into question. However, these comparisons used inaccurate ground-truth models of the experiment, undermining their veracity. To address this, we have used quantum phase space methods to simulate the GBS experiments and find more experimentally accurate ground-truth models. Using this realistic ground truth, we have begun a thorough comparison between all currently competitive samplers, including two novel phase-space-based classical samplers of our own, and the experimental data.

### Talk 12 - Brae Vaughan-Hankinson (University of Melbourne): Generalised symmetries in quantum systems

We present a high-level overview of generalised symmetries implemented by topological defects. The consistency conditions between different defects leads to the mathematical structure of a higher group. We then consider the dualities of the transverse field Ising model in light of this formalism.

### Talk 13 - Dominic Lewis (RMIT University): Band-Limited Quantum Field Theory

The likely presence of a fundamental minimum length scale to the universe (motivated by generalised uncertainty principles and UV divergences in quantum field theory to name a few) has led to the application of information theoretic techniques such as bandlimitation to quantum field theory. For example; an ultraviolet cut-off to quantum field theory provides a natural minimum length scale and gives an isomorphism between continuous and discrete representations of a quantum field through Shannon's sampling theorem. A QFT discretised in such a way will still possess the translational symmetries and conserved Noether charges generally associated with fundamentally continuous systems.

We extend on this notion by showing that non-bandlimited quantum field theories can be decomposed into bandlimited ones using Shannon wavelets. Each scale of the wavelet decomposition gives a field theory possessing an ultraviolet cut-off and, as a result, an equivalent discrete theory. As such, one can use wavelets to decompose an N+1 dimensional continuous field theory into a 2N+1 dimensional discrete theory (where the scale of the wavelet decomposition is treated as a spatial dimension). We show that for non-interacting quantum fields (and certain engineered interacting ones) the physics of the field at one scale is entirely isolated from that of other scales, meaning that no events at one scale can have any effect on the field at any other scale. For fields that can self-interact we find that despite non-zero couplings between the scales of the field, quantities such as the Feynman propagator between scales remain zero.

### Talk 14 - Akib Karim (CSIRO): Low Depth Virtual Distillation of Quantum Circuits by Deterministic Circuit Decomposition

Virtual distillation (VD) using measurements of multiple copies of a quantum circuit have recently been proposed as a method of noise mitigation of expectation values. Circuit decompositions known as B gates were found only for single qubit expectation values however practical calculations require multi-qubit expectation values which cannot be corrected with B gates. We discover low depth circuit decompositions for multi-qubit expectation values by combining multiple projections to recover the correct measurement statistics or expectation values. Our method adds linear entangling gates with number of qubits, but requires extra measurements. Furthermore, in applications to find ground states such as the variational quantum eigensolver (VQE) algorithm, the variational principle is required which states the energy cannot go below the ground state energy. We discover that the variational principle is violated if noise is higher on single expectation values than multi-qubit which renders VQE useless. We show this occurs when using B gates and is preserved if using our low depth decomposition on all expectation values. We perform experiments on real devices and demonstrate our technique can mitigate real experimental noise in VQE for the H2 molecule with a two qubit tapered mapping, H3 with three qubits, and H2 with four qubits. Our technique provides a way to perform duplicate circuit virtual distillation on real devices at significantly lower depth and for arbitrary observables.

### Talk 15 - Isobel Aloisio (Monash University): Sampling complexity of open quantum systems

With the rapid development of quantum computing technologies, there is increasing interest in identifying problems that will demonstrate useful quantum advantage over classical methods. One of the most promising candidates is the simulation of complex quantum dynamics, of which open quantum systems form an important subclass. Open quantum systems provide an interesting test bed for applications of quantum computers: these are systems of interest whose size is nominally small enough to classically simulate, but whose interaction with an environment can result in evolution that is unwieldy. Understanding the computational complexity of these systems is a fundamental step towards precisely identifying which problems are beyond the reach of classical computation. Here, we formally explore the complexity of simulating open quantum systems as a dynamic sampling problem: a system coupled to an environment can be probed at successive points in time -- accessing multi-time correlations. We identify several open quantum systems, including circuit models and Hamiltonian dynamics, whose multi-time sampling is as hard as sampling from a complex many-body state, and go further to examine foundational properties of system-environment interactions that result in complex temporal behaviour of the system, such as the connection between spatial and temporal entanglement. Fundamentally, we prove that quantum processes, not just quantum states, can be complex and intricate objects in their own right. Our results pave the way for studying open quantum systems from a complexity-theoretic perspective, highlighting the role quantum computers will play in our understanding of quantum dynamics.

### Talk 16 - Manushan Thenabadu (Swinburne): Quest for Quantum Computing: Monte Carlo Wavefunction Method simulations of the Coherent Ising Machine

The Ising machine, initially designed to model phase transitions in magnetic materials, has found diverse applications beyond its original scope. The Ising machine proves effective in solving NP-hard optimization problems, showcasing its relevance in various industries, including computer science, medicine, telecommunications, and logistics. This study focuses on the Coherent Ising Machine (CIM), a system comprised of a network of optical parametric oscillators (OPOs). The CIM leverages a coherent coupling approach, introducing a quantum regime to enhance its performance. To explore and understand the CIM, we employ numerical simulations due to the inherent complexity of the system. Our investigation demonstrates a quantum advantage by achieving improved simulation times and success rates.While master equation methods are available for such systems, their scalability diminishes for larger systems. Previous attempts utilized positive-P methods, which exhibit better scalability but pose chal- lenges in sampling within the quantum regime. In this study, we use Monte Carlo wavefunction methods, which scales as the wavefunction, and we minimize sampling errors by taking large number of samples. Additionally, Monte Carlo methods are employed to illustrate the generation of Schrödinger cat-type states from OPO. The simulations conducted involve Hilbert spaces exceeding 10^7 dimensions, we make use of quadrature mapping in evaluating success probabilities, using quadrature probabilities. This approach is a balance between computer memory efficiency and computation time, and provides valuable insights into the quantum dynamics and capabilities of the Coherent Ising Machine.

### Talk 17 - Caesnan Leditto (Monash University): Topological Signal Processing on Quantum Computers for Higher-Order Network Analysis

Deciphering the intricate dynamics of complex systems is a formidable task. Recent advancements in modeling such systems involve higher-order networks (HON), particularly simplicial complexes. These networks capture multiway interactions among nodes, offering a more nuanced representation. Simplicial complexes, notable for their topological structures and links to Hodge theory, have gained attention in this context. Our work introduces a novel quantum algorithm designed for topological signal processing (TSP) filtering processes, which employs a Hodge Laplacian for analyzing and manipulating data on HON. In this proof-of-concept, our quantum algorithm outperforms classical counterparts, exhibiting a super-polynomial improvement, hence unlocking potential applications of quantum computers for investigating high-dimensional complex systems in various fields.

### Talk 18 - Kelvin Li (Deakin University): Quantum Fourier Transform: Implications and Applications for Post-Quantum Cryptography

The Quantum Fourier Transform (QFT) is a crucial component of many known quantum algorithms, most notably Shor's algorithm for factoring. Shor's algorithm demonstrates exponential speedup compared to classical factoring algorithms. Its construction motivated the exploration of a new research area known as post-quantum cryptography (PQC), with the goal of developing cryptographic schemes resilient to quantum attacks. Despite the impact of quantum computing, PQC research also leverages QFT to establish hardness proofs, such as the hybrid reductions (combining classical and quantum approaches) for proving the difficulty of the learning with errors (LWE) problem. In this brief presentation, I will outline the role of QFT in Shor's factoring algorithm. Additionally, I will provide a high-level description of how QFT contributes to achieving LWE reductions from lattice problems. I will discuss the efforts and challenges involved in basing LWE reductions on weaker classical computing assumptions without utilising any quantum techniques.

## Posters

Krzysztof Giergiel (CSIRO): Time Crystals

Mike Klymenko (CSIRO): Architectural patterns in hybrid quantum-classical software

Fakhar Zaman (CSIRO): Quantum-enhanced Reinforcement Learning for Robotic Systems

Moe Hdaib (Deakin University): Quantum Machine Learning for Network Anomaly Detection

Lucky K. Antonopoulos (RMIT University): Discrete Wigner function formalisms from the Gottesman-Kitaev-Preskil encoding

Nicholas Funai (RMIT University): Phase sensitive Fock representations of unitary squeezing operators

Takaya Matsuura (RMIT University): From decoders for classical information to a decoder for quantum information

Jesse A. Vaitkus (RMIT University): Quantum algorithm for solving open-system dynamics on quantum computers using noise

Channa Hatharasinghe (Swinburne University of Technology): The measurement problem, two-mode cat state and the Q function

Christopher McGuigan (Swinburne University of Technology): Resolving Schrödinger’s paradoxical analysis of the EPR argument

Vivek Katial (University of Melbourne): On the Instance Dependence of Optimal Parameters for the Quadratic Approximate Optimisation Algorithm: Insights via Instance Space Analysis

Alex Kerin (University of Melbourne): Divergences in Interacting Few-Body Systems

Eric Mascot (University of Melbourne): Majorana braiding without an exponential Hilbert space

Chris Nakhl (University of Melbourne): Calibrating the role of entanglement in variational quantum circuits

Harish Vallury (University of Melbourne): Estimating ground state properties of spin models using quantum computed moments

Leting Zhouli (University of Melbourne): Impact of Data Augmentation on QCNN

Read the workshop proposal. The organizing committee wrote a comprehensive proposal for the workshop in 2024, but also with a long-term vision to establish regular events to bring the Melbourne Quantum Community (also beyond theoretical quantum information) together. Please reach out to us if you have any questions.

Organizing Committee:

Ben Baragiola (RMIT)

Neil Dowling (Monash University)

Lucas Hackl (University of Melbourne)

Harini Hapuarachchi (RMIT)

Ria Rushin Joseph (Deakin University)

Gary Mooney (University of Melbourne)

Behnam Tonekaboni (CSIRO Data 61)

Jia Wang (Swinburne University)

Advisory Committee:

Jared Cole (RMIT)

Jan de Gier (University of Melbourne)

Peter Drummond (Swinburne)

Lloyd Hollenberg (University of Melbourne)

Nicolas Menicucci (RMIT)

Kavan Modi (Monash University)

Anna Phan (IBM)

Muhammad Usman (CSIRO Data 61)

This event was made possible by the generous support of the participating institutions through various individual grants. The total event cost is around 10,000 AUD and we are extremely grateful for the following support:

IBM Quantum Network Hub at the University of Melbourne

Sisson Grant from the School of Mathematics and Statistics, University of Melbourne

ARC Centre of Excellence in Exciton Science

Centre for Quantum & Technology Theory, School of Science, Computing and Engineering Technologies, Swinburne University of Technology

School of Physics, Monash University

QuRMIT GRoup, RMIT

CSIRO Data 61

School of Information Technology, Deakin University

supported by: