Emergent Unitary Designs for Encoded Qubits from Coherent Errors and Syndrome Measurements Zihan Cheng, Eric Huang, Vedika Khemani, Michael J. Gullans, Matteo Ippoliti Prx Quantum, 2025 Unitary k-designs are distributions of unitary gates that match the Haar distribution up to its kth statistical moment. They are a crucial resource for randomized quantum protocols. However, their implementation on encoded logical qubits is nontrivial due to the need for magic gates, which can require a large resource overhead. In this work, we propose an efficient approach to generate unitary designs for encoded qubits in surface codes by applying local unitary rotations (“coherent errors”) on the physical qubits followed by syndrome measurement and error correction. We prove that, under some conditions on the coherent errors (notably including all single-qubit unitaries) and on the error-correcting code, this process induces a unitary transformation of the logical subspace. We numerically show that the ensemble of logical unitaries (indexed by the random syndrome outcomes) converges to a unitary design in the thermodynamic limit, provided that the density or strength of coherent errors is above a finite threshold. This “unitary design” phase transition coincides with the code’s coherent error threshold under optimal decoding. Furthermore, we propose a classical algorithm to simulate the protocol based on a “staircase” implementation of the surface code encoder and decoder circuits. This enables a mapping to a (1+1)-dimensional monitored circuit, where we observe an entanglement phase transition (and thus a classical complexity phase transition of the decoding algorithm) coinciding with the aforementioned unitary design phase transition. Our results provide a practical way to realize unitary designs on encoded qubits, with applications including quantum state tomography and benchmarking in error-correcting codes.
Universal structure of measurement-induced information in many-body ground states Zihan Cheng, Rui Wen, Sarang Gopalakrishnan, Romain Vasseur, Andrew C. Potter Physical Review B, 2024 Unlike unitary dynamics, measurements of a subsystem can induce long-range entanglement via quantum teleportation. The amount of measurement-induced entanglement or mutual information depends jointly on the measurement basis and the entanglement structure of the state (before measurement), and has operational significance for whether the state is a resource for measurement-based quantum computing, as well as for the computational complexity of simulating the state using quantum or classical computers. In this work, we examine entropic measures of measurement-induced entanglement (MIE) and information (MII) for the ground-states of quantum many-body systems in one- and two- spatial dimensions. From numerical and analytic analysis of a variety of models encompassing critical points, quantum Hall states, string-net topological orders, and Fermi liquids, we identify universal features of the long-distance structure of MIE and MII that depend only on the underlying phase or critical universality class of the state. We argue that, whereas in $1d$ the leading contributions to long-range MIE and MII are universal, in $2d$, the existence of a teleportation transition for finite-depth circuits implies that trivial $2d$ states can exhibit long-range MIE, and the universal features lie in sub-leading corrections. We introduce modified MIE measures that directly extract these universal contributions. As a corollary, we show that the leading contributions to strange-correlators, used to numerically identify topological phases, are in fact non-universal in two or more dimensions, and explain how our modified constructions enable one to isolate universal components. We discuss the implications of these results for classical- and quantum- computational simulation of quantum materials.
Efficient Sampling of Noisy Shallow Circuits Via Monitored Unraveling Zihan Cheng, Matteo Ippoliti Prx Quantum, 2023 We introduce a classical algorithm for sampling the output of shallow, noisy random circuits on two-dimensional qubit arrays. The algorithm builds on the recently-proposed"space-evolving block decimation"(SEBD) and extends it to the case of noisy circuits. SEBD is based on a mapping of 2D unitary circuits to 1D {\\it monitored} ones, which feature measurements alongside unitary gates; it exploits the presence of a measurement-induced entanglement phase transition to achieve efficient (approximate) sampling below a finite critical depth $T_c$. Our noisy-SEBD algorithm unravels the action of noise into measurements, further lowering entanglement and enabling efficient classical sampling up to larger circuit depths. We analyze a class of physically-relevant noise models (unital qubit channels) within a two-replica statistical mechanics treatment, finding weak measurements to be the optimal (i.e. most disentangling) unraveling. We then locate the noisy-SEBD complexity transition as a function of circuit depth and noise strength in realistic circuit models. As an illustrative example, we show that circuits on heavy-hexagon qubit arrays with noise rates of $\\approx 2\\%$ per CNOT, based on IBM Quantum processors, can be efficiently sampled up to a depth of 5 iSWAP (or 10 CNOT) gate layers. Our results help sharpen the requirements for practical hardness of simulation of noisy hardware.
Matrix product operator approach to nonequilibrium Floquet steady states Zihan Cheng, Andrew C. Potter Physical Review B, 2022 We present a numerical method to simulate non-equilibrium Floquet steady states of one-dimensional periodically-driven (Floquet) many-body systems coupled to a dissipative bath, called open-system Floquet DMRG (OFDMRG). This method is based on a matrix product operator ansatz for the Floquet density matrix in frequency-space, and enables access to large systems beyond the reach of exact master-equation or quantum trajectory simulations, while retaining information about the periodic micro-motion in Floquet steady states. An excited-state extension of this technique also allows computation of the dynamical approach to the steady state on asymptotically long timescales. We benchmark the OFDMRG approach with a driven-dissipative Ising model, and apply it to study the possibility of dissipatively stabilizing pre-thermal discrete time-crystalline order by coupling to a cold bath.
Direct comparison of auxiliary and itinerant coherent potential approximations for disordered lattice vibration: Phonon spectral and transport properties Jianxiong Zhai, Rui Xue, Zihan Cheng, Youqi Ke Physical Review B, 2021 The auxiliary and itinerant coherent potential approximations (ACPA and ICPA) have been proposed as effective methods for treating both mass and force-constant disorder in lattice vibration. In this work we make a direct comparison of ACPA and ICPA to identify the differences between these two methods for simulating vibrational properties of disordered materials and devices. We investigate the major approximations in the disorder self-energies of these two methods by using the diagrammatic method. The single-site ACPA neglects the crossing diagrams describing nonlocal correlations, while ICPA utilizes only the single-fluctuation states in the self-consistency and presents extra errors due to a change in the terms with nearest-neighbor fluctuation. To further demonstrate the important differences between the ACPA and ICPA in the phonon spectral and transport properties, we extend ICPA in combination with the Keldysh nonequilibrium Green's function technique to simulate quantum transport and introduce a Green's-function-based spectral unfolding technique to use with molecular ACPA and the supercell methods for comparison. By studying the disordered one- and three-dimensional alloys, we find that ACPA and ICPA agree very well in the weak scattering regime due to weak force-constant disorder or low phonon frequency. However, for the strong scattering of force-constant disorder, it is found that the two methods present important deviations in the linewidth (and height) of disorder-averaged phonon spectra. Compared to the ACPA and exact results, the problematic treatment of the nearest-neighbor fluctuation in ICPA can present unphysical scattering and induce large errors in the phonon transport, presenting important limitations of ICPA for transport simulation.
Simulation of bilayer Hamiltonians based on monitored quantum trajectories Y Xue, Z Cheng, M Ippoliti Physical Review B 113 (9), 094312 , 2026 2026 Citations: 1
Hardness of observing strong-to-weak symmetry breaking X Feng, Z Cheng, M Ippoliti Physical Review Letters 135 (20), 200402 , 2025 2025 Citations: 13
Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements Z Cheng, E Huang, V Khemani, MJ Gullans, M Ippoliti PRX Quantum 6 (3), 030333 , 2025 2025 Citations: 11
Pseudoentanglement from tensor networks Z Cheng, X Feng, M Ippoliti Physical Review Letters 135 (2), 020403 , 2025 2025 Citations: 12
Quantum systems with periodic driving, dissipation and measurements Z Cheng 2025
Universal structure of measurement-induced information in many-body ground states Z Cheng, R Wen, S Gopalakrishnan, R Vasseur, AC Potter Physical Review B 109 (19), 195128 , 2024 2024 Citations: 19
Generalized dynamical cluster theory for off-diagonal disorder J Zhai, Z Cheng, Y Zhang, Y Ke Physical Review B 109 (9), 094203 , 2024 2024 Citations: 2
Characterizing a non-equilibrium phase transition on a quantum computer E Chertkov, Z Cheng, AC Potter, S Gopalakrishnan, TM Gatterman, ... Nature Physics 19 (12), 1799-1804 , 2023 2023 Citations: 77
Efficient sampling of noisy shallow circuits via monitored unraveling Z Cheng, M Ippoliti PRX Quantum 4 (4), 040326 , 2023 2023 Citations: 24
Matrix product operator approach to nonequilibrium Floquet steady states Z Cheng, AC Potter Physical Review B 106 (22), L220307 , 2022 2022 Citations: 4
Direct comparison of auxiliary and itinerant coherent potential approximations for disordered lattice vibration: Phonon spectral and transport properties J Zhai, R Xue, Z Cheng, Y Ke Physical Review B 104 (2), 024205 , 2021 2021 Citations: 9
Fractal non-Fermi liquids from moiré Hofstadter phonons A Kumar, Z Cheng, AC Potter Physical Review B 102 (23), 235120 , 2020 2020 Citations: 4
Phonon dispersion of binary alloys with auxiliary coherent potential approximation Z Cheng, M Sang, J Zhai, Y Ke Physical Review B 100 (21), 214206 , 2019 2019 Citations: 8
Anomalous transparency induced by cooperative disorders in phonon transport J Zhai, Q Zhang, Z Cheng, J Ren, Y Ke, B Li Physical Review B 99 (19), 195429 , 2019 2019 Citations: 19
Auxiliary coherent medium theory for lattice vibrations in random binary alloys with mass and force-constant disorders Z Cheng, J Zhai, Q Zhang, Y Ke Physical Review B 99 (13), 134202 , 2019 2019 Citations: 15
MOST CITED SCHOLAR PUBLICATIONS
Characterizing a non-equilibrium phase transition on a quantum computer E Chertkov, Z Cheng, AC Potter, S Gopalakrishnan, TM Gatterman, ... Nature Physics 19 (12), 1799-1804 , 2023 2023 Citations: 77
Efficient sampling of noisy shallow circuits via monitored unraveling Z Cheng, M Ippoliti PRX Quantum 4 (4), 040326 , 2023 2023 Citations: 24
Universal structure of measurement-induced information in many-body ground states Z Cheng, R Wen, S Gopalakrishnan, R Vasseur, AC Potter Physical Review B 109 (19), 195128 , 2024 2024 Citations: 19
Anomalous transparency induced by cooperative disorders in phonon transport J Zhai, Q Zhang, Z Cheng, J Ren, Y Ke, B Li Physical Review B 99 (19), 195429 , 2019 2019 Citations: 19
Auxiliary coherent medium theory for lattice vibrations in random binary alloys with mass and force-constant disorders Z Cheng, J Zhai, Q Zhang, Y Ke Physical Review B 99 (13), 134202 , 2019 2019 Citations: 15
Hardness of observing strong-to-weak symmetry breaking X Feng, Z Cheng, M Ippoliti Physical Review Letters 135 (20), 200402 , 2025 2025 Citations: 13
Pseudoentanglement from tensor networks Z Cheng, X Feng, M Ippoliti Physical Review Letters 135 (2), 020403 , 2025 2025 Citations: 12
Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements Z Cheng, E Huang, V Khemani, MJ Gullans, M Ippoliti PRX Quantum 6 (3), 030333 , 2025 2025 Citations: 11
Direct comparison of auxiliary and itinerant coherent potential approximations for disordered lattice vibration: Phonon spectral and transport properties J Zhai, R Xue, Z Cheng, Y Ke Physical Review B 104 (2), 024205 , 2021 2021 Citations: 9
Phonon dispersion of binary alloys with auxiliary coherent potential approximation Z Cheng, M Sang, J Zhai, Y Ke Physical Review B 100 (21), 214206 , 2019 2019 Citations: 8
Matrix product operator approach to nonequilibrium Floquet steady states Z Cheng, AC Potter Physical Review B 106 (22), L220307 , 2022 2022 Citations: 4
Fractal non-Fermi liquids from moiré Hofstadter phonons A Kumar, Z Cheng, AC Potter Physical Review B 102 (23), 235120 , 2020 2020 Citations: 4
Generalized dynamical cluster theory for off-diagonal disorder J Zhai, Z Cheng, Y Zhang, Y Ke Physical Review B 109 (9), 094203 , 2024 2024 Citations: 2
Simulation of bilayer Hamiltonians based on monitored quantum trajectories Y Xue, Z Cheng, M Ippoliti Physical Review B 113 (9), 094312 , 2026 2026 Citations: 1
Quantum systems with periodic driving, dissipation and measurements Z Cheng 2025
