Talks

In the one-way model of measurement based quantum computing, unlike the quantum circuit model, a computation is driven not by unitary gates but by successive adaptive single-qubit measurements on an entangled resource state. So-called flow properties ensure that a one-way computation, described by a measurement pattern, is deterministic overall (up to Pauli corrections on output qubits). Translations between quantum circuits and measurement patterns have been used to show universality of the one-way model, verify measurement patterns, optimise quantum circuits, and more. Yet while it is straightforward to translate a circuit into a measurement pattern, the question of algorithmic "circuit extraction" -- how to translate general measurement patterns with flow to ancilla-free circuits -- had long remained open for all but the simplest type of flow. In this talk, we will recap the one-way model of quantum computing and then explain how the problem of circuit extraction was resolved using the ZX-calculus as a common language for circuits and measurement patterns. We also discuss applications.

There are well established conjectures about the symmetries of SIC-POVMs, and the number fields needed to construct them. If the dimension is of the form n^2 + 3 there is also an algorithm that allows us to calculate them, making use of Stark units in a subfield of the full number field. The algorithm works in the 72 dimensions where it has been tested. Joint work with (among others) Markus Grassl and Gary McConnell

The Heisenberg limit (HL) and the standard quantum limit (SQL) are two fundamental quantum metrological limits, which describe the scalings of estimation precision of an unknown parameter with respect to N, the number of one-parameter quantum channels applied. In the first part, we show the HL (1/N) is achievable using quantum error correction (QEC) strategies when the ``Hamiltonian-not-in-Kraus-span'' (HNKS) condition is satisfied; and when HNKS is violated, the SQL (1/N^1/2) is optimal and can be achieved with repeated measurements. In the second part, we identify modified metrological limits for estimating one-parameter qubit channels in settings of restricted controls where QEC cannot be performed. We prove unattainability of the HL and further show a ``rotation-generators-not-in-Kraus-span'' (RGNKS) condition that determines the achievability of the SQL.

Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distribution of two-dimensional quantum circuits. Many attempts to close this gap have utilized classical simulations based on tensor network techniques, and their limitations shed light on the improvements to quantum hardware required to inhibit classical simulability. In particular, state of the art quantum computers having in excess of ~50 qubits are primarily vulnerable to classical simulation due to restrictions on their gate fidelity and their connectivity, the latter determining how many gates are required (and therefore how much infidelity is suffered) in generating highly-entangled states. Here, we describe numerical evidence for the difficulty of random circuit sampling in highly connected geometries.

Quantum computers operate by manipulating quantum systems that are particularly susceptible to noise. Classical redundancy-based error correction schemes cannot be applied as quantum data cannot be copied. These challenges can be overcome by using a variation of the quantum teleportation protocol to implement those operations which cannot be easily done fault-tolerantly. This process consumes expensive resources called 'magic states'. The vast quantity of these resources states required for achieving fault-tolerance is a significant bottleneck for experimental implementations of universal quantum computers. I will discuss a program of finding and classifying those quantum operations which can be performed with efficient use of magic state resources. I will focus on the understanding of not just qubits but also the higher-dimensional 'qudit' case. This is motivated by both practical reasons and for the resulting theoretical insights into the ultimate origin of quantum computational advantages. Research into these quantum operations has remained active from their discovery twenty-five years ago to the present. Our approach introduces the novel use of tools from algebraic geometry. The results in this talk will include joint work with Chen, Lautsch, and Bampounis-Barbosa.

The concept of symmetries is crucial in our comprehension of modern theoretical physics. The Corner Proposal introduces a novel framework where symmetries are reinstated as foundational principles in our understanding of gravity. This aims to describe gravity using a language that is more adapted to quantization. In this presentation, I will start by providing an overview of the essential results leading to the main ideas the proposal. This will then allow me to state the proposal in the general case to then specialize to 1+1 dimensional gravity.

Finally, I will present elements of our recent research applying the proposal to the case of 1+1 dimensional gravity. I will demonstrate the framework's promising potential by calculating the entanglement entropy between two spatial regions—a significant challenge in quantum gravity. The result is the 1+1 dimensional equivalent of the well-established Bekenstein-Hawking area law governing the entropy of gravitational systems with the expected behavior of the quantum corrections.

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This colloquium is presented in collaboration with the Foundations of Quantum Computational Advantage conference. 

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Binary constraint system games are a generalization of the Mermin-Peres magic square game introduced by Cleve and Mittal. Thanks to the recent MIP*=RE theorem of Ji, Natarajan, Vidick, Wright, and Yuen, BCS games can be used to construct a proof system for any language in MIP*, the class of languages with a multiprover interactive proof system where the provers can share entanglement. This means that we can apply logical reductions for binary constraint systems to MIP* protocols, and also raises the question: how complicated do our constraint systems have to be to describe all of MIP*? In this talk, I'll give a general overview of this subject, including an application of logical reductions to showing that all languages in MIP* have a perfect zero knowledge proof system (joint work with Kieran Mastel), and one obstacle to expressing all of MIP* with linear constraints (joint work with Connor Paddock).

I will present some recent work on the interplay between contextuality, entanglement, and magic in multiqubit systems. Taking a foundational inquiry into entanglement in the Kochen-Specker theorem as our point of departure, I will proceed to outline some questions this raises about the role of these resources in models of multiqubit quantum computation. The purpose of this talk is to raise questions that can hopefully feed into the discussion sessions.

Integrable field theories in two dimensions are known to originate as defect theories of 4d Chern-Simons theory and as symmetry reductions of the 4d anti-self-dual Yang-Mills equations. Based on ideas of Costello, it has been proposed in work of Bittleston and Skinner that these two approaches can be unified starting from holomorphic Chern-Simons theory in 6 dimensions. In this talk I will introduce the first complete description of this diamond of integrable theories for a family of deformed sigma models, going beyond the Dirichlet boundary conditions that have been considered thus far. The talk is based on the recent work https://arxiv.org/abs/2311.17551.

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A universal and well-motivated notion of classicality for an operational theory is explainability by a generalized-noncontextual ontological model. I will here explain what notion of classicality this implies within the framework of generalized probabilistic theories. I then prove that for any locally tomographic theory, every such classical model is given by a complete frame representation. Using this powerful constraint on the space of possible classical representations, I will then prove that the stabilizer subtheory has a unique classical representation—namely Gross's discrete Wigner function. This provides deep insights into the relevance of Gross's representation within quantum computation. It also implies that generalized contextuality is also a necessary resource for universal quantum computation in the state injection model.