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Random Quantum Circuits
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Quantum circuits -- built from local unitary gates and local measurements -- are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far-from-equilibrium. These models have shed light on longstanding questions about thermalization and chaos, and on the underlying universal dynamics of quantum information and entanglement. In addition, such models generate new sets of questions and give rise to phenomena with no traditional analog, such as new dynamical phases in quantum systems that are monitored by an external observer. Quantum circuit dynamics is also topical in view of experimental progress in building digital quantum simulators that allow control of precisely these ingredients. Randomness in the circuit elements allows a high level of theoretical control, with a key theme being mappings between real-time quantum dynamics and effective classical lattice models or dynamical processes. Many of the universal phenomena that can be identified in this tractable setting apply to much wider classes of more structured many-body dynamics.
Forward citations
Cited by 7 Pith papers
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Quantum Simulation of Random Unitaries from Clebsch-Gordan Transforms
Clebsch-Gordan transforms give exact compressed oracles for Haar-random unitary group actions, with efficient circuits for U(d).
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Measurement induced scrambling and emergent symmetries in random circuits
Random measurement-only circuits with q'-body measurements scramble entanglement only when the qudit dimension exceeds q'/(q'-2), and two measurement models map to U(1) and SU(2) spin models with critical purification.
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Streamlined Krylov construction and classification of ergodic Floquet systems
A Szegő/CMV Krylov construction maps Floquet unitary dynamics to a five-diagonal chain, with a conjectured classification of chaos and integrability by Verblunsky coefficient asymptotics.
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Universal crossovers in weakly-monitored quantum critical states
Weak measurements drive the critical Ising ground state directly to a projective, area-law fixed point, but the tricritical Ising ground state flows to a weak-measurement fixed point with logarithmic entanglement and ...
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Quantum random walks on d-regular graphs with Haar-random coin operators
Haar-random coin quantum walks on d-regular graphs yield a non-ergodic averaged channel that depolarizes the coin while preserving forever-measurable initial-state information in the vertex subspace for Cayley graphs ...
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Coherent error induced phase transition
The paper shows that in stabilizer codes a change in the logical stabilizer group after a coherent Clifford error and syndrome measurement exactly determines the MAP recovery probability, and that above a critical err...
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Emergence of Krylov complexity through quantum walks: An exploration of the quantum origins of complexity
Reducing a graph walk to distance-layers reproduces Krylov/spread complexity, yielding analytic finite-q SYK Lanczos coefficients and hypercube complexity D sin²(t/D), with faster saturation than classical-walk circuits.
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