Talks

Quantum mechanics forbids the creation of ideal identical copies of unknown quantum systems and, as a result, copying quantum information. This fundamental and non-classical 'unclonability' feature of nature has played a central role in quantum cryptography, quantum communication and quantum computing ever since its discovery. However, unclonability is a broader concept than just the no-cloning theorem. In this talk, I will go over different notions of quantum unclonability and show how they link to many important questions and topics in quantum applications both in quantum machine learning and quantum cryptography. I will also broadly cover the link between unclonability and other fundamental concepts, such as randomness, pseudorandomness and contextuality.

This talk will present work-in-progress towards a new programming methodology for Cliffords, where n-ary Clifford unitaries over qudits can be expressed as functions on compact Pauli. Inspired by the fact that projective Cliffords correspond to center-fixing automorphisms on the Pauli group, we develop a type system where well-typed expressions correspond to symplectic morphisms---that is, linear transformations that respect the symplectic form. This language is backed up by a robust categorical and operational semantics, and well-typed functions can be efficiently simulated and synthesized into circuits via Pauli tableaus.

Fault-tolerant protocols and quantum error correction (QEC) are essential to building reliable quantum computers from imperfect components that are vulnerable to errors. Optimizing the resource and time overheads needed to implement QEC is one of the most pressing challenges that will facilitate a transition from NISQ to the fault tolerance era. In this talk, I will discuss two intriguing ideas that can significantly reduce these overheads. The first idea, erasure qubits, relies on an efficient conversion of the dominant noise into erasure errors at known locations, greatly enhancing the performance of QEC protocols. The second idea, single-shot QEC, guarantees that even in the presence of measurement errors one can perform reliable QEC without repeating measurements, incurring only constant time overhead.

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Whilst tomography has dominated the theory behind reconstructing/approximating quantum objects, such as states or channels, conducting full tomography is often not necessary in practice. If one is interested in learning properties of a quantum system, side-stepping the exponential lower bounds of tomography is then possible. In this talk, we will introduce various learning models for approximating quantum objects, survey the literature of quantum learning theory and explore instances where learning can be fully time- and sample efficient.

Characterizing metastable states and saddle points in complex systems can shed light on a variety of equilibrium and out-of-equilibrium behaviors. In this talk, I will discuss the most versatile theoretical technique for this, the Kac–Rice method, and its application to a family of mean-field models, the spherical spin glasses. I will draw connections from this technique to random matrix theory and Faddeev–Popov gauge fixing. For the spherical models, writing down an effective action is straightforward but finding physical saddle points can be challenging. I will show how, for the lowest-energy states, a BRST supersymmetry can be used to simplify the action and map it to a more tractable equilibrium problem. Finally, I will discuss challenges to using these techniques in inference problems with non-Gaussian energy functions, and current work being done to address them.