Featured Papers

This page highlights a small selection of research papers that represent my current interests.
You may also download a full publication list, or find my works directly on the arXiv or on Google Scholar.

Slow Mixing, Spin Glass Order, Error Correction, and Topology

This work establishes topological quantum spin glass (TQSG) order as a low-temperature phase of good quantum LDPC codes, combining ideas from spin-glass physics, topology, and coding theory. TQSGs combine the classical complexity of spin glasses — many ergodic components, not related by symmetries, impossibility of annealing by local algorithms — with the quantum complexity of topological order — that is long-range entanglement in the finite-temperature Gibbs state.

I talked about this work at QEC 2025 at Yale. It has also been discussed in the Journal Club for Condensed Matter Physics.

In this complimentary work, we show that purely classical LDPC codes with good expansion properties already exhibit robust spin-glass order. We provide a simple, rigorous proof of spin class order in models with finite connectivity (where mean-field theory is not exact). We directly characterize the structure of the Gibbs state, without reference to replica symmetry breaking. Together with the quantum work, this establishes expansion as a unifying mechanis underlying glassiness in both classical and quantum LDPC codes.

This work proves a generalization of the bottleneck theorem for classical Markov chains to quantum Channels. This provides a general technical tool to prove meta-stability with respect to a channel, using only properties of its steady state. We use this in our work on topological quantum spin glass to characterize the decomposition of the Gibbs state into such meta-stable dynamic component. However, the theorem has much broader applicability, e.g. in bounding the efficiency of quantum Gibbs samplers (see below).

Note also the concurrent work by Garmanik, Kiani, and Zlokapa.

Towards Practical Quantum Gibbs Sampling

Quantum Gibbs sampling can be thought of as a quantum generalization of Markov chain Monte Carlo methods used extensively in the study of classical many-body physics.
As such, it provides potentially a very clear path to practical quantum advantage. The “problem” of constructing an efficiently implementable and exact quantum Gibbs sampler for general local quantum Hamiltonians has been solved in principle in recent breakthrough work by Chen et al..
However, the proposed protocols still involve significant overheads (e.g. block-encoding the Hamiltonian), which most likely make them prohibitively expensive for near-term devices. In this work, we propose a simple scheme for Lindbladian simulation of an approximate Gibbs sampler. Our protocol only involves ingredients readily available in present day devices: (a) analog simulation of H; (b) strictly local but time-dependent couplings to ancilla qubits; and (c) reset of the ancillas. We give rigorous performance guarantees for our protocol, which are independent of detailed physical knowledge of H beyond its locality.

Discovery-mode Quantum Computing

We propose a new way to use Quantum Computers, that is searching for “interesting” instances of quantum many-body dynamics by combining large scale quantum devices with unsupervised learning. In particular, we propose specifying an “interest function”, which quantifies how interesting a circuit is, that is then optimized by a classical learning agent that controls the quantum device. Beyond its potential utility in finding new ciruit families, the inverse-problem nature of the approach is interesting as it forces us to crisply ask —and formally quantify—what we may find “interesting” about a given family of circuits. We discuss two examples of such interest functions, which lead to the (re)discovery of discrete time crystals and dual unitary circuits by the agent, respectively.