Talks

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.

Quantum Darwinism proposes that the proliferation of redundant information plays a major role in the emergence of objectivity out of the quantum world. Is this kind of objectivity necessarily classical? We show that if one takes Spekkens’s notion of noncontextuality as the notion of classicality and the approach of Brandão, Piani, and Horodecki to quantum Darwinism, the answer to the above question is “‘yes,” if the environment encodes the proliferated information sufficiently well. Moreover, we propose a threshold on this encoding, above which one can unambiguously say that classical objectivity has emerged under quantum Darwinism.

We give a simple description of rectangular matrices that can be implemented by a post-selected stabilizer circuit. Given a matrix with entries in dyadic cyclotomic number fields $\mathbb{Q}(\exp(i\frac{2\pi}{2^m}))$, we show that it can be implemented by a post-selected stabilizer circuit if it has entries in $\mathbb{Z}[\exp(i\frac{2\pi}{2^m})]$ when expressed in a certain non-orthogonal basis. This basis is related to Barnes-Wall lattices. Our result is a generalization to a well-known connection between Clifford groups and Barnes-Wall lattices. We also show that minimal vectors of Barnes-Wall lattices are stabilizer states, which may be of independent interest. Finally, we provide a few examples of generalizations beyond standard Clifford groups. Joint work with Sebastian Schonnenbeck

Ground states as well as Gibbs states of many-body quantum Hamiltonians have been studied extensively since the inception of quantum mechanics. In contrast, the landscape of many-body quantum states that are not in thermal equilibrium is relatively less explored. In this talk I will discuss some of the recent progress in understanding decohered or dissipative quantum many-body states. One of the key ideas I will employ is that of "separability", i.e., whether a mixed state can be expressed as an ensemble of short-range entangled pure states. I will discuss several quantum phase transitions in topological phases of matter subjected to Markovian environmental noise from a separability viewpoint, and argue that such a framework also subsumes our understanding of pure quantum states as well as Gibbs states. Time permitting, I will also provide a brief overview of quantum spin-systems subjected to non-Markovian noise originating from an electronic bath, and discuss a new critical phase of matter where quantum coherence coexists with dissipation.

References: 2307.13889, 2309.11879, 2310.07286

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