Professional Education

  • Bachelor of Science, Fudan University (2016)
  • Doctor of Philosophy, University of California Santa Barbara (2022)
  • PhD, University of California, Santa Barbara, Physics (2022)
  • BSc, Fudan University, Computer Science (2016)

Stanford Advisors

All Publications

  • Operator Relaxation and the Optimal Depth of Classical Shadows. Physical review letters Ippoliti, M., Li, Y., Rakovszky, T., Khemani, V. 2023; 130 (23): 230403


    Classical shadows are a powerful method for learning many properties of quantum states in a sample-efficient manner, by making use of randomized measurements. Here we study the sample complexity of learning the expectation value of Pauli operators via "shallow shadows," a recently proposed version of classical shadows in which the randomization step is effected by a local unitary circuit of variable depth t. We show that the shadow norm (the quantity controlling the sample complexity) is expressed in terms of properties of the Heisenberg time evolution of operators under the randomizing ("twirling") circuit-namely the evolution of the weight distribution characterizing the number of sites on which an operator acts nontrivially. For spatially contiguous Pauli operators of weight k, this entails a competition between two processes: operator spreading (whereby the support of an operator grows over time, increasing its weight) and operator relaxation (whereby the bulk of the operator develops an equilibrium density of identity operators, decreasing its weight). From this simple picture we derive (i) an upper bound on the shadow norm which, for depth t∼log(k), guarantees an exponential gain in sample complexity over the t=0 protocol in any spatial dimension, and (ii) quantitative results in one dimension within a mean-field approximation, including a universal subleading correction to the optimal depth, found to be in excellent agreement with infinite matrix product state numerical simulations. Our Letter connects fundamental ideas in quantum many-body dynamics to applications in quantum information science, and paves the way to highly optimized protocols for learning different properties of quantum states.

    View details for DOI 10.1103/PhysRevLett.130.230403

    View details for PubMedID 37354418

  • Triviality of quantum trajectories close to a directed percolation transition PHYSICAL REVIEW B Piroli, L., Li, Y., Vasseur, R., Nahum, A. 2023; 107 (22)
  • Cross Entropy Benchmark for Measurement-Induced Phase Transitions. Physical review letters Li, Y., Zou, Y., Glorioso, P., Altman, E., Fisher, M. P. 2023; 130 (22): 220404


    We investigate prospects of employing the linear cross entropy to experimentally access measurement-induced phase transitions without requiring any postselection of quantum trajectories. For two random circuits that are identical in the bulk but with different initial states, the linear cross entropy χ between the bulk measurement outcome distributions in the two circuits acts as an order parameter, and can be used to distinguish the volume law from area law phases. In the volume law phase (and in the thermodynamic limit) the bulk measurements cannot distinguish between the two different initial states, and χ=1. In the area law phase χ<1. For circuits with Clifford gates, we provide numerical evidence that χ can be sampled to accuracy ϵ from O(1/ϵ^{2}) trajectories, by running the first circuit on a quantum simulator without postselection, aided by a classical simulation of the second. We also find that for weak depolarizing noise the signature of the measurement-induced phase transitions is still present for intermediate system sizes. In our protocol we have the freedom of choosing initial states such that the "classical" side can be simulated efficiently, while simulating the "quantum" side is still classically hard.

    View details for DOI 10.1103/PhysRevLett.130.220404

    View details for PubMedID 37327428

  • Entanglement Domain Walls in Monitored Quantum Circuits and the Directed Polymer in a Random Environment PRX QUANTUM Li, Y., Vijay, S., Fisher, M. A. 2022; 4 (1)
  • Conformal invariance and quantum nonlocality in critical hybrid circuits PHYSICAL REVIEW B Li, Y., Chen, X., Ludwig, A. W., Fisher, M. A. 2021; 104 (10)
  • Entanglement Negativity at Measurement-Induced Criticality PRX QUANTUM Sang, S., Li, Y., Zhou, T., Chen, X., Hsieh, T. H., Fisher, M. A. 2021; 2 (3)
  • Statistical mechanics of quantum error correcting codes PHYSICAL REVIEW B Li, Y., Fisher, M. A. 2021; 103 (10)
  • Measurement-driven entanglement transition in hybrid quantum circuits PHYSICAL REVIEW B Li, Y., Chen, X., Fisher, M. A. 2019; 100 (13)
  • Quantum Zeno effect and the many-body entanglement transition PHYSICAL REVIEW B Li, Y., Chen, X., Fisher, M. A. 2018; 98 (20)