28 March 2023, 3pm London time - Video of Talk

Andrew Childs (University of Maryland)

Title: Quantum divide and conquer

Abstract: The divide-and-conquer framework, used extensively in classical algorithm design, recursively breaks a problem into smaller subproblems, along with some auxiliary work, to give a recurrence relation for the classical complexity. We describe a quantum divide-and-conquer framework that, in certain cases, yields quantum speedup through an analogous recurrence relation for the quantum query complexity. We apply this framework to obtain near-optimal quantum query complexities for various string problems, such as (i) recognizing regular languages; (ii) decision versions of String Rotation and String Suffix; and natural parameterized versions of (iii) Longest Increasing Subsequence and (iv) Longest Common Subsequence. Based on joint work with Robin Kothari, Matt Kovacs-Deak, Aarthi Sundaram, and Daochen Wang (arXiv:2210.06419).

28 February 2023, 4pm London time - Video of talk

Matt Hastings (Microsoft Research)

Title: The sum-of-squares for fermionic systems, and the SYK model

Abstract: The central problem in physics and quantum chemistry is to determine properties of the ground state of an interacting system of fermions. As a quantum mechanical problem, there may be no efficient classical witness to the ground state energy, or even to an approximation of that energy. A commonly considered witness is a so-called "Gaussian state", or free fermion wavefunction. As a prominent example , the Sachdev-Ye-Kitaev (SYK) model has no Gaussian state which achieves a good approximation to the energy; this model is sometimes considered as one of the "most entangled" or "most strongly interacting" models possible. I will discuss applications of the sum-of-squares method to this model. Sum-of-squares is a semidefinite programming relaxation. I will show that this method can give classically efficient constant-factor lower bounds on the energy, and it inspires a quantum algorithm which gives constant-factor upper bounds. Joint work with R. O'Donnell.

25 October 2022, 2pm London time - Video of talk

Bill Fefferman (University of Chicago)

Title: Quantum pseudoentanglement

Abstract: Quantum pseudorandom states are efficiently preparable states that are indistinguishable from truly Haar random states to an efficient observer. First defined by Ji, Liu and Song, such states have found a wide variety of applications in areas such as cryptography and quantum gravity. A fundamental question is exactly how much entanglement is required to create such states. Haar-random states, as well as t-designs, exhibit near-maximal entanglement. Here we provide the first construction of pseudorandom states with only polylogarithmic entanglement entropy across an equipartition of the qubits, which is the minimum possible. Our construction can be based on any one-way function secure against quantum attack. We additionally show that the entanglement in our construction is fully "tunable". More fundamentally, our work calls into question to what extent entanglement is a "feelable" quantity of quantum systems. Inspired by recent work of Gheorghiu and Hoban, we define a new notion which we call "pseudoentanglement", which are ensembles of efficiently constructable quantum states which hide their entanglement entropy. We show such states exist in the strongest form possible while simultaneously being pseudorandom states. Based on joint work with Adam Bouland, Soumik Ghosh, Umesh Vazirani and Zixin Zhou.

19 August 2022, 2pm London time - Video of talk

Ryan O'Donnell (CMU)

Title: Mean Estimation When You Have The Source Code; or, Quantum Monte Carlo Methods

Abstract: Suppose y is a real random variable, and one is given access to "the code" that generates it (for example, a randomized or quantum circuit whose output is y). We give a quantum procedure that runs the code O(n) times and returns an estimate for E[y] with optimal dependence on n for quantum algorithms. The central subroutine for our result is essentially Grover's algorithm but with complex phases. Joint work with Robin Kothari (Microsoft).

1 July 2022, 2pm London time - Video of talk

Ronald de Wolf (QuSoft, CWI)

Title: Quantum machine learning from a theoretical perspective

Abstract: Machine learning can be enhanced by quantum computing, both by allowing quantum data and by having quantum speedups for the optimization process that finds a good model for given data. This talk will examine both aspects, from the perspective of theoretical computer science.