QSL Seminars

We consider the problem of testing and learning from data in the presence of resource constraints, such as limited memory or weak data access, which place limitations on the efficiency and feasibility of testing or learning. In particular, we ask the following question: Could a resource-constrained learner/tester use interaction with a resource-unconstrained but untrusted party to solve a learning or testing problem more efficiently than they could without such an interaction? In this work, we answer this question both abstractly and for concrete problems, in two complementary ways: For a wide variety of scenarios, we prove that a resource-constrained learner cannot gain any advantage through classical interaction with an untrusted prover. As a special case, we show that for the vast majority of problems in which quantum memory is a meaningful resource, a memory-constrained quantum algorithm cannot overcome its limitations via classical communication with a memory-unconstrained quantum prover. In contrast, when quantum communication is allowed, we construct a variety of interactive proof protocols, for specific learning and testing problems, which allow memory-constrained quantum verifiers to gain significant advantages through delegation to untrusted provers. These results highlight both the limitations and potential of delegating learning and testing problems to resource-rich but untrusted third parties.

Quantum technologies are grounded on the ability to control highly non-classical probability distributions that are inefficient to simulate with conventional computers. I will describe a quantum hardware system to sample a quantum kernel for a support vector machine learning algorithm. The schema is analogue,  not a qubit circuit, and suggests a path to harness quantum analogue computing for efficient machine learning.

We will take a closer look at fault-tolerance, focusing on so called “internal” errors, errors introduced by the correction process itself. We will show how we can investigate and solve this problem using the detector error model formalism - leading to the topic of circuit level decoding. The relevant paper is "Designing fault-tolerant circuits using detector error models".

In this seminar I will aim to provide an accessible overview of current industrial practices for drug discovery. I will then discuss how computational chemistry methodologies are currently used to support the preclinical stages of drug discovery, drawing on examples from my own academic drug discovery activities. I will then discuss opportunities quantum computers might offer to improve the effectiveness of current drug discovery processes, and even perhaps allow to break into new territories.

Locally indistinguishable states are useful to distribute information among spatially separated parties such that the information is locked. This implies that the parties are not able to extract the information completely via local operations and classical communication (LOCC), while it might be possible via LOCC when the parties share entanglement in a particular fashion. Based on this, we design an information locking protocol to securely hide classical information in quantum states with the possibility of extraction to the trusted parties, when needed. We make our protocol resource efficient in terms of information extraction. On the other hand, we use the basic property of indistinguishability of quantum states as a resource in secure hybrid communication protocol. Introduction of quantumness over the classical primitives in the form of state discrimination ensures security for such protocols. We prescribe entanglement-based communication protocols which are easily expandable to multipartite domains.

We study the implementation of fault-tolerant logical Clifford gates on stabilizer quantum error correcting codes based on their symmetries. Our approach is to map the stabilizer code to a binary linear code, compute its automorphism group, and impose constraints based on the Clifford operators permitted. We provide a rigorous formulation of the method for finding automorphisms of stabilizer codes and generalize ZX-dualities to non-CSS codes. We provide a Python package implementing our algorithms which uses the computational algebra system MAGMA. Our algorithms map automorphism group generators to physical circuits, calculate Pauli corrections based on the destabilizers of the code, and determine their logical action. We discuss the fault tolerance of the circuits and include examples of gates through automorphisms for the [[4,2,2]] and perfect [[5,1,3]] codes, bivariate bicycle codes, and the best known distance codes.

We will explore the implementation of universal quantum computation on quantum error-correcting codes (QECCs) through the technique of Magic State Distillation (MSD) technique, originally introduced by Bravyi and Kitaev in 2005. MSD is pivotal for enabling the execution of non-Clifford gates, which are essential for achieving universal quantum computation. We will discuss the process of preparing and purifying magic states, detailing how these states can be utilized alongside Clifford operations to run quantum algorithms. Relevant papers: Bravyi, S. and Kitaev, A., 2005. Universal quantum computation with ideal Clifford gates and noisy ancillas. Physical Review A—Atomic, Molecular, and Optical Physics, 71(2), p.022316. Jochym-O'Connor, T., Yu, Y., Helou, B. and Laflamme, R., 2012. The robustness of magic state distillation against errors in Clifford gates. arXiv preprint arXiv:1205.6715.

The Standard Model of Particle Physics encapsulates the vast majority of our understanding of the fundamental nature of our Universe. Massive theoretical and algorithmic developments in classical computing, as well as hardware advancements, have allowed us to make first-principle predictions about many of its properties. Nevertheless, there remain a plethora of open questions that do not seem amenable to these methods. With a fundamentally different computational strategy, quantum computers hold the potential to address these open questions. In this talk, I will first give a casual overview of how I, as a particle physicist, understand quantum computation. I will then give an introduction to the particular physical systems in which I am interested, namely Quantum Chromodynamics. I will then outline the various hurdles, and some solutions, that must be overcome before quantum simulations of the Standard Model become possible.

In this talk, we introduce optimal quantum algorithms that estimate both the trace distance and the (square root) fidelity between pure states to within additive error ε using Θ(1/ε) queries to their state-preparation circuits. This approach quadratically improves the long-standing folklore O(1/ε^2) based on the SWAP test, challenging the common belief that the SWAP test is already optimal for testing pure states.

Relevant papers: https://quantum-journal.org/papers/q-2020-01-09-218/ (and bonus material: http://arxiv.org/abs/2204.14038).

Denotational semantics is a cornerstone in the study of programming languages. It aims to translate syntax from a specific language into mathematical objects. It helps abstract away, in order to prove some properties of the language. When recursion or loops are involved in the language, the mathematical interpretation must have corresponding fixed points or a similar theory. This is the case for classical and probabilistic languages and also quantum programming languages with classical control. We briefly present the latter, and then focus on recursion with quantum control, i.e. without measurement. We show what problems arise on the mathematical side and why the usual tools do not apply in the desired setting. We end with a positive note with guarded quantum recursion.

The main objective is to explore the simulability of the Quantum Circuit Born Machine (QCBM) from the perspective of k-order correlators. This ongoing work leverages the knowledge of classical shadows, the Lie algebra of a parameterized quantum circuit, and the approximation of loss functions when considering complex quantum and classical data. Our quantum target data is based on the ground states of Hamiltonians in one-dimensional and two-dimensional lattices, while the classical target is constructed from a coherent superposition of the data. Additionally, this k-order correlation approach allows us to evaluate the inductive bias and generalization capabilities of the algorithm.

Lattice surgery is a crucial technique for enabling interactions between logical qubits encoded in surface codes, paving the way for scalable fault-tolerant quantum computing. This journal club will introduce the key concepts and principles of lattice surgery for surface codes. We will begin by reviewing the basics of surface code architecture and logical qubit encoding. The core operations of lattice surgery - merging and splitting code surfaces - will then be explained, demonstrating how they allow controlled interactions between logically-encoded qubits while maintaining error correction properties. Finally, we will see how these fundamental operations can be used to implement logical gates like CNOT.

In this talk, I will give a brief introduction to both classical and quantum learning theory, covering key concepts from fundamental ideas to the latest developments, including our work on learning quantum processes using statistical queries. I will explore fundamental questions such as: What does it mean to learn "quantum stuff"? And how difficult is it to learn them? Finally, I will discuss why quantum learning theory is a powerful framework that not only pushes us towards a better understanding of machine learning but also offers valuable insights into other fields like cryptography.

Quantum modular multiplication, a key subroutine in algorithms like shor's algorithms for factoring and discrete log, if executed naively, would be computationally demanding and memory-intensive. Windowed quantum arithmetic [1] leverages precomputed lookup tables to reduce the complexity of quantum modular multiplication, achieving asymptotic speedups from O(n^2) to O(n^2/log⁡^2 n). In this seminar, we will explore how this technique optimizes quantum modular multiplication and, if time permits, discuss further optimizations to windowing. [1] Gidney, Craig. "Windowed quantum arithmetic." arXiv preprint arXiv:1905.07682 (2019)

Gaussian Boson Sampling (GBS) is a non-universal quantum computation that in recent years has been used to claim experimental quantum advantage. The noise in these experiments may however be exploited to create classical simulation methods that would invalidate these claims. One such method, based on Fourier analysis of the probability distributions of the samples, is currently being developed at the University of Edinburgh. In this talk, Julia will present an analysis of the viability of the method by looking at the behaviour of Fourier coefficients of GBS sample probabilities under specific system parameters. Then, Tom will present a description of a class of classical simulators that make use of the statistics of these Fourier coefficients and the approximation of marginal probabilities.

Quantum computers have progressed to the point where they can now solve some specific mathematical problems that classical computers cannot solve. This talk will present ongoing research on potential applications to machine learning. I will first introduce near-term photonic quantum processors. Although they are not universal for quantum computation, they provide a scalable route to solving some classes of hard sampling problems. I will then describe ways in which current classical neural network architectures may harness these unique computational capabilities for generative modelling and for classification. This talk will highlight both the potential and the limitations of these approaches, as well as opportunities for further research.

Quantum state purification is the functionality that, given multiple copies of an unknown state, outputs a state with increased purity. This will be an essential building block for near- and middle-term quantum ecosystems before the availability of full fault tolerance, where one may want to suppress errors not only in expectation values but also in quantum states. We propose an effective state purification gadget with a moderate quantum overhead by projecting M noisy quantum inputs to their symmetric subspace defined by a set of projectors forming a symmetric subgroup with order M. Our method, applied in every short evolution over M redundant copies of noisy states, can suppress both coherent and stochastic errors by a factor of 1/M, respectively. This reduces the circuit implementation cost M times smaller than the state projection to the full symmetric subspace proposed by Barenco et al. more than two decades ago. We also show that our gadget purifies the depolarised inputs with probability p to asymptotically O(p^{2}) with an optimal choice of M when p is small. The sampling cost scales O(p^{−1}) for small p, which is also shown to be asymptotically optimal. Our method provides flexible choices of state purification depending on the hardware restrictions before fully fault-tolerant computation is available.

When are tensor networks (TN) simulators better than other methods? Which are their bottlenecks? Should I use GPUs?  Can I implement an error model on top of a TN simulator? In this talk I will cover frequently asked questions about quantum circuit simulation using TNs. While doing so, I will describe the taxonomy of TN methods, along with their strengths and weaknesses.

I will introduce DVLOQC and describe how photon loss is an issue for running computations using LO circuits. I will then present the notion of recycled probabilities, describe their construction and methods by which these may be used to construct loss-mitigated outputs. I'll argue why postselection should be the benchmark against which the performance of any such method should be measured and present analysis comparing the performance of recycling mitigation to postselection. Finally I will describe a photonic QCBM and present results indicating a performance improvement when recycling mitigation is applied.

Learning quantum channels is a fundamental problem in quantum information. Unfortunately, this problem is provably hard for arbitrary quantum channels, requiring an exponential amount of data in the system size. A lot of recent work has instead focused on developing efficient algorithms when the channel is guaranteed to be "simple" in some sense. The kinds of channels for which such endeavours have been successful include those with underlying circuits having low depth or few gates, or those affecting a small number of qubits. In this talk, I will present the efficient algorithms for these channels and focus on the currently relevant technical tools used in these works, such as classical shadows, Pauli/Fourier spectrum analysis, and covering nets.

Quantum information promises to revolutionize our world, from the way in which we communicate to the way in which we compute, deriving its power directly from the laws that govern the behavior of nature on extremely small scales - quantum mechanics. In the near future, the hardware of possibly useful quantum computers is expected to remain very expensive and thus out of reach for most interested end users. In such a world, it is an important problem to provide security guarantees for customers who wish to remotely instruct quantum servers, by keeping their data private (blindness) and checking the correctness of the results (verification). This functionality of secure delegated quantum computing received a lot of attention during recent years, but still admits many open questions. We explore the (im)possibility of securing delegated quantum computations in different settings: what is the hardware that the client needs trusted access to, what is the minimum hardware required by the server, and how must the parties communicate? This work is driven by the motivation to break down the barriers that keep us from securing and verifying quantum computations in practice, by identifying and removing unnecessary overheads.

I will begin by introducing Penrose tilings ("PTs") and quantum error correcting codes ("QECCs"). A PT is a remarkable, intrinsically non-periodic way of tiling the plane whose many beautiful and unexpected properties have fascinated physicists, mathematicians, and geometry lovers of all sorts, ever since its discovery in the 1970s. A QECC is a fundamental way of protecting quantum information from noise, by encoding the information with a sophisticated type of redundancy. Such codes play an increasingly important role in physics: in quantum computing (where they protect the delicate quantum state of the computer); in condensed matter physics (where they underpin the notion of topologically-ordered phases); and even in quantum gravity (where the "holographic" or "gauge/gravity" duality may be understood as such a code). Although PTs and QECCs might seem unrelated, I will explain how PTs gives rise to (or, in a sense, *are*) a new type of QECC in which any local errors or erasures in any finite region of the code space, no matter how large, may be diagnosed and corrected. Variants of this code (based on the cousins of the Penrose tiling, called the Ammann-Beenker and Fibonacci tilings) can live in a finite space, in discrete spin systems, and in an arbitrary number of spatial dimensions.

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In this seminar, we will introduce some quantum learning models along with their classical counterparts. We will also discuss the sample complexity of learners for specific problems in these models and ways of characterizing the complexity.

Due to the nanotechnological progress and the increasing interest in quantum systems, heat engines are no longer limited to the size of steam engines from the industrial revolution. Their miniaturisation is currently leading to the emergence of thermal machines that harness quantum effects to operate. Located at the interface between stochastic thermodynamics, quantum mechanics and quantum information, quantum thermodynamics offers an ideal platform to explore and address several challenges, for instance, energy management at the nanoscale, the energetic cost of measurement and quantum computing as well as the impact of quantum features on the operation of quantum thermal devices such as heat engines and refrigerators. Answering these challenges requires an adequate characterisation of heat and work at the quantum level which is essential for the advancement of novel quantum technologies in the future. In this talk, I will be focusing on highlighting the role of quantum resources, mainly quantum coherence, in the performance of quantum thermal machines that rely on the framework of collision models (CM) to study their open quantum system dynamics. we demonstrate that the presence of even small amounts of coherence in the thermal reservoirs powering a three-terminal machine, constitutes an extra resource for allowing otherwise forbidden combined and hybrid modes of operation, where either different resources are combined to perform a single thermodynamic task, or more than one task is performed at the same time. In order to assess the performance of such coherence-enabled modes of operation, we analyse their power and efficiency and discussing the quantum advantage that coherence provides, as well as its detrimental effects.

Quantum computing platforms have been drawing much attention over the past few years in quantum chemistry and condensed matter. In these domains a possibly large number of particles interact and exhibit quantum effects which are hard to tackle classically. Whereas the first prototypical quantum devices that are being built now are still greatly error-prone, the development of variational methods as well as error mitigation strategies has sparked the hope to leverage such devices in the near term to make computations escaping the reach of classical methods. In particular, strongly-correlated many-fermion systems in solids exhibit rich phase diagrams which lend themselves to plenty of applications in the industry. They are now widely studied through the celebrated Dynamical Mean-Field Theory (DMFT). DMFT consists in computing relevant observables regarding the ’spherical cow’ of strongly-correlated systems, namely the Fermi-Hubbard lattice model, by mapping it to a simpler, auxiliary ’impurity’ model. The solving of this latter model constitutes an exponential bottleneck for any classical algorithm to date. The hybrid implementation of the DMFT scheme with near-term quantum computers typically relies on the variational preparation of the impurity model’s ground state. Scaling the variational circuits to tackle richer impurity models is a challenge due to the relatively low gate fidelities and coherence times characterizing quantum hardware as for now, resulting in greatly degraded performances. This talk will be devoted to the presentation of an algorithmic strategy I have set forth during my PhD research to be able to scale the impurity model. The algorithm, dubbed NaturalOrbitalization, greatly reduces the requirements over the variational circuit depth as the size of the proxy impurity model is increased. It consists in interleaving variational runs with tailored rewritings of the impurity model’s Hamiltonian, which enhance the expressivity of the circuit at hand. We show that this strategy coupled to an adaptive state preparation strategy leads to shorter depths.

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I will give an introduction to some elementary concepts of category theory while motivating their application to the foundations of quantum mechanics and quantum information theory. I would also like to impart an intuition for why the categorical way of thinking can be so productive and for which kinds of problems it is useful.

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