Measurement-induced phase transitions

The interplay between the two fundamental quantum processes --- quantum measurements and quantum unitary time evolution --- can lead to surprisingly rich phenomena, including a continuous phase transition between "entangling" and "disentangling" phases. These new phenomena go beyond the prevailing paradigm of quantum dynamics focusing on thermalization in unitary systems.

These transitions connect ideas across condensed matter, information theory, and non-equilibrium statistical mechanics, offering new universality classes and experimentally testable signatures.

I have made various efforts in identifying and describing such phenomena, as well as their experimental observations.

• Quantum Zeno effect and the many-body entanglement transition

Y. Li, X. Chen, M.P.A. Fisher | arXiv:1808.06134 | Phys. Rev. B 98, 205136 (2018)

• Measurement-driven entanglement transition in hybrid quantum circuits

Y. Li, X. Chen, M.P.A. Fisher | arXiv:1901.08092 | Phys. Rev. B 100, 134306 (2019)

• Statistical mechanics of quantum error correcting code

Y. Li, M.P.A. Fisher | arXiv:2007.03822 | Phys. Rev. B 103, 104306 (2021)

Self-correcting memories and emergent symmetries

• My talk at KITP

• Slow mixing from emergent one-form symmetries in three-dimensional Ising gauge theory

C. Stahl, B. Placke, V. Khemani, Y. Li | (in preparation)

Stability and thresholds of quantum codes

• Perturbative stability and error correction thresholds of quantum codes

Y. Li, N. O'Dea, V. Khemani | arXiv:2406.15757 | PRX Quantum 6, 010327 (2025)

This paper explores the connection between the stability of topologically ordered quantum phases and the error-correcting capabilities of topological quantum codes. Here, we construct classical statistical mechanics models to describe the error-correction process for general quantum error-correcting codes, including those without geometric locality. This allows us to relate the stability of the perturbed code Hamiltonians to the stability of the corresponding disordered Ising gauge theories. The key findings include the following: (1) We define general order parameters for the generalized Z2 lattice-gauge theories and show that they are lower bounded by the success probabilities of error correction. (2) For CSS codes satisfying the low-density parity-check condition and with a sufficiently large code distance, we prove the existence of a low-temperature ordered phase of the corresponding lattice-gauge theories, even in cases where there is no Euclidean spatial locality or a nonzero code rate. (3) We argue that these results provide evidence for the stability of the corresponding perturbed quantum Hamiltonians by distinguishing between spacelike and timelike defects in the lattice-gauge theory. Overall, this work presents a novel synthesis of ideas and techniques that could be of significant importance in the field of quantum error correction and topological quantum computing.

• LDPC stabilizer codes as gapped quantum phases: stability under graph-local perturbations

W. De Roeck, V. Khemani, Y. Li, N. O'Dea, T. Rakovszky | arXiv:2411.02384 | PRX Quantum 6, 030330 (2025)

Phases of matter provide a key organizing concept throughout physics. A major breakthrough in modern condensed matter has been the notion of topological phases that are stable to all local perturbations, making them extremely robust. Our work rigorously proves robustness for a wide family of models that live on graphs rather than in conventional Euclidean space, proving that the concept of phase still exists in this much more general setting. In quantum information theory, there is a similar notion of robustness given by quantum error correction: by encoding quantum information into entangled states, one can track and correct errors to protect the information from local noise. Our proof applies to stabilizer Hamiltonians, which can be associated with the most widely studied family of error-correcting codes. These Hamiltonians include the very best codes, called “good” codes, which have recently been constructed and are an active area of research. Our proof is a generalization of one by Bravyi, Hastings, and Michalakis, where the perturbation is rotated into a simpler form. One of our breakthroughs is a method for stronger control over the locality of the rotated perturbation. We have proven stability of a vast number of phases. But how should we characterize these unusual phases? For example, we have proven that many ground-state spectral properties are maintained under perturbation, but some of these quantum codes are known to have an extremely strict form of topological order that extends to finite energy density. Is this property also maintained under perturbation?

Single-shot error correction (SSEC) in equilibrium?

Single-shot error correction (SSEC) promises the possibility to perform error correction even when the check measurements themselves are noisy—without the need repeating them. That turns time overhead into zero (constant) depth, which is desirable for practical quantum error correction.

In a paper with Curt von Keyserlingk, Guanyu Zhu, and Tomas Jochym-O'Connor, we study a new subsystem code construction in 3D that has recently received much attention. The code is single-shot decodable, making it potentially important in future practices of QEC. We write down a natural physical Hamiltonian for the code, solve for its phase diagram, and show that the quantum phases are not stable at finite temperatures, despite the code being single-shot. Thus, we answer in the negative to a prevailing conjecture relating single-shot and self-correcting memories. Our work also provides a many-body physics perspective on single-shot QEC, and more generally the dynamics of QEC.

• Phase diagram of the three-dimensional subsystem toric code

Y. Li, C.W. von Keyserlingk, G. Zhu, T. Jochym-O'Connor | arXiv:2305.06389 | Phys. Rev. Research 6, 043007 (2024)

Operator relaxation and efficient classical shadows 

Learning properties of many-body states with minimal quantum resources is a near-term priority. Understanding when short-depth protocols suffice has immediate experimental impact.

We analyzed operator relaxation in random circuits and derived bounds that identify when classical-shadow tomography is near-optimal at surprisingly shallow depths. These results inform the design of resource-efficient characterization protocols for noisy devices.

• Operator Relaxation and the Optimal Depth of Classical Shadows

M. Ippoliti, Y. Li, T. Rakovszky, V. Khemani | arXiv:2212.11963 | Phys. Rev. Lett. 130, 230403 (2023)