Quantum Cambridge-Oxford-Warwick Colloquium 2: Talk abstracts

Learning and Diagnosing Quantum Many-Body Dynamics (Susanne Yelin)

Recent advances in quantum platforms make it increasingly possible to learn, characterize, and interpret many-body dynamics directly from data. In this talk, I will discuss recent results on learning quantum dynamics with minimal prior assumptions, in both closed and open systems, and on using these ideas to probe broader physical behavior. More broadly, these developments suggest new approaches to benchmarking, validating, and understanding quantum simulators.

The Randomized Measurement Toolbox (Richard Küng)

The state of testing and learning stabilizer-like states (Srinivasan Arunachalam)

This will be an overview talk wherein I go over the recent works in the last few years on testing and learning stabilizer states (and their generalizations). I will discuss a couple of recent works wherein we give testing protocols for these states as well as applications to learning states with bounded stabilizer rank.

Resources for quantum learning (Zhenhuan Liu)

Quantum learning broadly refers to the task of extracting information or learning properties of quantum objects, such as quantum states, measurements, channels, or dynamical processes, from limited access to them. A central question in this context is to understand what resources can fundamentally reduce the complexity of such learning tasks. By a resource for quantum learning, we mean any operational ingredient whose availability can substantially enhance learning power, so that a task that is otherwise intractable or highly costly may become achievable with polynomially, or even exponentially, fewer samples or measurements. In this talk, I will first give a brief introduction to the mathematical tool for analyzing the complexity of quantum learning problems. I will then review some of the broader research directions on learning resources and the ways in which different operational primitives can change the learnability of quantum information. Finally, I will focus on our recent works, explaining why joint measurements, pure dilation states, and post-measurement states can serve as important resources for quantum learning, and discuss several related results and connections to the existing literature.

[1] Ye Q*, Liu Z, Deng D-L*. Exponential Advantage from One More Replica in Estimating Nonlinear Properties of Quantum States. arXiv preprint, 2025, arXiv:2509.24000.

[2] Liu Z*, Gong W*, Du Z*, Cai Z*. Exponential Separations between Quantum Learning with and without Purification. arXiv preprint, 2024, arXiv:2410.17718, 2024.

[3] Liu Z*, Ye Q*, Cai Z*, Eisert J*. Exponential speedup in measurement property learning with post-measurement states. arXiv preprint arXiv:2602.22126, 2026.

[4] Du Z, Tang Y, Elben A, Ingo R, Jens E, Liu Z*. Optimal Randomized Measurements for a Family of Non-linear Quantum Properties. arXiv preprint, 2025, arXiv:2505.09206, 2025.

[5] Liu Z*, Du Z*, Cai Z*, Liu Z-W*. No Universal Purification in Quantum Mechanics. arXiv preprint, 2025, arXiv:2509.21111, 2025.

Hamiltonian Learning (Ainesh Bakshi)

Hamiltonian Decoded Quantum Interferometry (Yihui Quek)

In 2009, Oded Regev introduced a way to reduce the problem of finding a short lattice vector to a decoding problem known as Learning with Errors. Building on these techniques and the subsequent work of Decoded Quantum Interferometry (Jordan et al, Nature 2025), we introduce Hamiltonian Decoded Quantum Interferometry (HDQI), a quantum algorithm that utilizes coherent Bell measurements and the symplectic representation of the Pauli group to reduce Gibbs sampling and Hamiltonian optimization to classical decoding. For a signed Pauli Hamiltonian 𝐻 and any degree-ℓ polynomial 𝒫, HDQI prepares a purification of the density matrix 𝜌𝒫 (𝐻) = 𝒫 2 (𝐻)/ Tr[︀ 𝒫 2 (𝐻) ]︀ by solving a combination of two tasks: decoding ℓ errors on a classical code defined by 𝐻, and preparing a pilot state that encodes the anti-commutation structure of 𝐻. Choosing 𝒫(𝑥) to approximate exp(−𝛽𝑥/2) yields Gibbs states at inverse temperature 𝛽; other choices of 𝒫 prepare approximate ground states, microcanonical ensembles, and other spectral filters. The decoding problem inherits structural properties of 𝐻; in particular, local Hamiltonians map to LDPC codes. Preparing the pilot state is always efficient for commuting Hamiltonians, but highly non-trivial for non-commuting Hamiltonians. Nevertheless, we prove that this state admits an efficient matrix product state representation for Pauli Hamiltonians whose anti-commutation graph decomposes into connected components of logarithmic size. HDQI efficiently prepares Gibbs states at arbitrary temperatures for a class of physically motivated commuting Hamiltonians – including the toric code, color code, and Haah’s cubic code – but we also develop a matching efficient classical algorithm for this task, thereby delineating the boundary of efficient classical simulation. For a non-commuting semiclassical spin glass and commuting stabilizer Hamiltonians with quantum defects, HDQI provably prepares Gibbs states up to a constant inverse-temperature threshold using polynomial quantum resources and quasi-polynomial classical pre-processing. These results position HDQI as a versatile new algorithmic primitive and the first extension of Regev’s reduction to non-abelian groups.