Crystalline Quantum Circuits

Abstract

Random quantum circuits continue to inspire a wide range of applications in quantum information science and many-body quantum physics, while remaining analytically tractable through probabilistic methods. Motivated by an interest in deterministic circuits with similar applications, we construct classes of \textit{nonrandom} unitary Clifford circuits by imposing translation invariance in both time and space. Further imposing dual-unitarity, our circuits effectively become crystalline spacetime lattices whose vertices are SWAP or iSWAP two-qubit gates and whose edges may contain one-qubit gates. One can then require invariance under (subgroups of) the crystal's point group. Working on the square and kagome lattices, we use the formalism of Clifford quantum cellular automata to describe operator spreading, entanglement generation, and recurrence times of these circuits. A full classification on the square lattice reveals, of particular interest, a "nonfractal good scrambling class" with dense operator spreading that generates codes with linear contiguous code distance and high performance under erasure errors at the end of the circuit. We also break unitarity by adding spacetime-translation-invariant measurements and find a class of such circuits with fractal dynamics.

28 pages, 23 figures + 6 pages, 5 figures in 3 appendices. v2: Added two appendices, revised and added references. v3: Improved presentation based on referee comments, close to published version. See also https://errorcorrectionzoo.org/c/crystalline_dynamic_gen

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Cited by in corpus (16)

• Majorana Loop Models for Measurement-Only Quantum Circuits
• Bell sampling from quantum circuits
• From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
• Zero-temperature entanglement membranes in quantum circuits
• Operator dynamics and entanglement in space-time dual Hadamard lattices
• Exactly solvable many-body dynamics from space-time duality
• Structured volume-law entanglement in an interacting, monitored Majorana spin liquid
• Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
• Tensor network decompositions for absolutely maximally entangled states
• Fundamental charges for dual-unitary circuits
• Exact Correlation Functions for Dual-Unitary Quantum circuits with exceptional points
• Geometric constructions of generalized dual-unitary circuits from biunitarity
• Kicked-Ising Quantum Battery
• Multiple topological corner states in the continuum of extended kagome lattice
• Probes of Full Eigenstate Thermalization in Ergodicity-Breaking Quantum Circuits
• Roughening Transition in Quantum Circuits