Integrability of Goldilocks quantum cellular automata
arXiv:2404.02994 · doi:10.1088/2058-9565/ae57d5
Abstract
Goldilocks quantum cellular automata (QCA) have been simulated on quantum hardware and produce emergent small-world correlation networks. In Goldilocks QCA, a single-qubit unitary is applied to each qubit in a one-dimensional chain subject to a balance constraint: a qubit is updated if its neighbors are in different computational-basis states. We prove that a subclass of Goldilocks QCA, including the QCA implemented experimentally, map to free fermions and therefore can be simulated classically. We support this claim with two proofs, one involving a Jordan-Wigner transformation and one mapping the integrable six-vertex model to QCA. We compute local conserved quantities of these QCA and predict experimentally measurable expectation values. These calculations can be applied to test large digital quantum computers. In contrast, typical Goldilocks QCA have equilibration properties and quasienergy-level statistics that suggest nonintegrability. Still, each of the latter QCA conserves one quantity useful for error mitigation. Our work yields a parametric quantum circuit with tunable integrability properties useful for testing quantum hardware.
17 pages (4 figures)
References in corpus (66)
- Thermalization and its mechanism for generic isolated quantum systems
- Localization of interacting fermions at high temperature
- Improved Simulation of Stabilizer Circuits
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Quantum many-body scars
- Generalized Gibbs ensemble in integrable lattice models
- Quench dynamics and relaxation in isolated integrable quantum spin chains
- Time evolution of local observables after quenching to an integrable model
- Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
- Random Quantum Circuits
- Classical simulation of noninteracting-fermion quantum circuits
- Reduced Density Matrix after a Quantum Quench
- Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
- Emergent statistical mechanics of entanglement in random unitary circuits
- Remarks on the notion of quantum integrability
- Low-cost error mitigation by symmetry verification
- The Quench Action
- Efficient classical simulation of random shallow 2D quantum circuits
- Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
- Thermodynamics of quantum systems with multiple conserved quantities
- Integrable Trotterization: Local Conservation Laws and Boundary Driving
- A review of Quantum Cellular Automata
- On Conservation Laws, Relaxation and Pre-relaxation after a Quantum Quench
- Ballistic spin transport in a periodically driven integrable quantum system
- Thermodynamic resource theories, non-commutativity and maximum entropy principles
- Symmetry constraints on many-body localization
- Operator growth and eigenstate entanglement in an interacting integrable Floquet system
- Fermionic Gaussian states: an introduction to numerical approaches
- Stability of superdiffusion in nearly integrable spin chains
- On Generalized Gibbs Ensembles with an infinite set of conserved charges
- Chaos and Complexity of quantum motion
- Probing symmetries of quantum many-body systems through gap ratio statistics
- Unitary and non-unitary quantum cellular automata with Rydberg arrays
- Lack of symmetry restoration after a quantum quench: an entanglement asymmetry study
- Efficient classical simulation of matchgate circuits with generalized inputs and measurements
- Free fermions in disguise
- Noncommuting conserved quantities in quantum many-body thermalization
- Free fermionic and parafermionic quantum spin chains with multispin interactions
- Correlations and commuting transfer matrices in integrable unitary circuits
- Noncommuting conserved charges in quantum thermodynamics and beyond
- Experimental observation of thermalization with noncommuting charges
- Integrable nonunitary open quantum circuits
- Free fermions behind the disguise
- Characterization of solvable spin models via graph invariants
- Many Body Quantum Chaos and Dual Unitarity Round-a-Face
- Dynamics and large deviation transitions of the XOR-Fredrickson-Andersen kinetically constrained model
- Rigorous bounds on dynamical response functions and time-translation symmetry breaking
- Roadmap on Quantum Thermodynamics
- Exact solution of the Floquet-PXP cellular automaton
- Non-equilibrium absorbing state phase transitions in discrete-time quantum dynamics
- Simulating Three-Dimensional Hydrodynamics on a Cellular-Automata Machine
- Matrix product symmetries and breakdown of thermalization from hard rod deformations
- Higher-dimensional Jordan-Wigner Transformation and Auxiliary Majorana Fermions
- Small-world complex network generation on a digital quantum processor
- Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems
- Strong zero modes in integrable quantum circuits
- Integrable Quantum Circuits from the Star-Triangle Relation
- Free fermions beyond Jordan and Wigner
- Complexity of spin configurations dynamics due to unitary evolution and periodic projective measurements
- An Ising-type formulation of the six-vertex model
- Quantum circuits with free fermions in disguise
- Integrability of Goldilocks quantum cellular automata
- General theory for discrete symmetry-breaking equilibrium states
- Automated detection of symmetry-protected subspaces in quantum simulations
- The Hilbert-space structure of free fermions in disguise
- Construction and simulability of quantum circuits with free fermions in disguise