Solvable Quantum Circuits in Tree+1 Dimensions
arXiv:2503.20927 · doi:10.1103/fbgh-rq3l
Abstract
We devise tractable models of unitary quantum many-body dynamics on tree graphs, as a first step towards a deeper understanding of dynamics in non-Euclidean spaces. To this end, we first demonstrate how to construct strictly local quantum circuits that preserve the symmetries of trees, such that their dynamical light cones grow isotropically. For trees with coordination number z, such circuits can be built from z-site gates. We then introduce a family of gates for which the dynamics is exactly solvable; these satisfy a set of constraints that we term 'tree-unitarity'. Notably, tree-unitarity reduces to the previously-established notion of dual-unitarity for z = 2, when the tree reduces to a line. Among the unexpected features of tree-unitarity is a trade-off between 'maximum butterfly velocity' dynamics of out-of-time-order correlators and the existence of non-vanishing correlation functions in multiple directions, a tension absent in one-dimensional dual-unitary models and their Euclidean generalizations. We connect the existence of (a wide class of) solvable dynamics with non-maximal butterfly velocity directly to a property of the underlying circuit geometry called -hyperbolicity, and argue that such dynamics can only arise in non-Euclidean geometries. We give various examples of tree-unitary gates, discuss dynamical correlations, out-of-time-order correlators, and entanglement growth, and show that the kicked Ising model on a tree is a physically-motivated example of maximum-velocity tree-unitary dynamics.
Added new section connecting results to hyperbolicity. 23+11 pages, 13+4 figures
References in corpus (83)
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Improved Simulation of Stabilizer Circuits
- Logical quantum processor based on reconfigurable atom arrays
- Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- Operator Spreading in Random Unitary Circuits
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement
- Quantum Zeno Effect and the Many-body Entanglement Transition
- Quantum Entanglement Growth Under Random Unitary Dynamics
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- Measurement-induced criticality in random quantum circuits
- Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
- Random Quantum Circuits
- Unitary-projective entanglement dynamics
- Tools for quantum simulation with ultracold atoms in optical lattices
- Dynamical purification phase transitions induced by quantum measurements
- Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
- Quantum Low-Density Parity-Check Codes
- Information Scrambling in Computationally Complex Quantum Circuits
- Hyperbolic Lattices in Circuit Quantum Electrodynamics
- Solution of a minimal model for many-body quantum chaos
- Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
- Spectral statistics in spatially extended chaotic quantum many-body systems
- Exact dynamics in dual-unitary quantum circuits
- Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
- Matchgates and classical simulation of quantum circuits
- Entanglement spreading in a minimal model of maximal many-body quantum chaos
- Programmable Interactions and Emergent Geometry in an Atomic Array
- Unitary circuits of finite depth and infinite width from quantum channels
- Efficient tensor network simulation of IBM's Eagle kicked Ising experiment
- The entanglement membrane in chaotic many-body systems
- Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension
- Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
- Scrambling in Random Unitary Circuits: Exact Results
- Constructions and Noise Threshold of Hyperbolic Surface Codes
- Exact emergent quantum state designs from quantum chaotic dynamics
- Particle-Time Duality in the Kicked Ising Chain II: Applications to the Spectrum
- Particle-Time Duality in the Kicked Ising Chain I: The Dual Operator
- Hadamard-free circuits expose the structure of the Clifford group
- Maximum velocity quantum circuits
- Hyperbolic and Semi-Hyperbolic Surface Codes for Quantum Storage
- Dynamical purification and the emergence of quantum state designs from the projected ensemble
- Creating ensembles of dual unitary and maximally entangling quantum evolutions
- Cavity method for quantum spin glasses on the Bethe lattice
- The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States
- Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
- Computational power of one- and two-dimensional dual-unitary quantum circuits
- Hyper-invariant tensor networks and holography
- Clustering of non-ergodic eigenstates in quantum spin glasses
- Maximal entanglement velocity implies dual unitarity
- Exact local correlations in kicked chains at light cone edges
- Exact dynamics in dual-unitary quantum circuits with projective measurements
- Many Body Quantum Chaos and Dual Unitarity Round-a-Face
- Measurement-induced phase transitions on dynamical quantum trees
- Transport and entanglement growth in long-range random Clifford circuits
- Tensor Networks contraction and the Belief Propagation algorithm
- Non-equilibrium dynamics of charged dual-unitary circuits
- Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes
- From Dual Unitarity to Generic Quantum Operator Spreading
- Hierarchical generalization of dual unitarity
- Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
- There are no Goldstone bosons on the Bethe lattice
- Quantum information spreading in generalised dual-unitary circuits
- Ternary unitary quantum lattice models and circuits in dimensions
- AKLT Models with Quantum Spin Glass Ground States
- Fock-space delocalization and the emergence of the Porter-Thomas distribution from dual-unitary dynamics
- The entanglement membrane in exactly solvable lattice models
- Zero-temperature entanglement membranes in quantum circuits
- From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
- Colloquium: Synthetic quantum matter in non-standard geometries
- Eigenstate localization in a many-body quantum system
- Quantum memory at nonzero temperature in a thermodynamically trivial system
- Low-density parity-check codes as stable phases of quantum matter
- Operator dynamics and entanglement in space-time dual Hadamard lattices
- LDPC stabilizer codes as gapped quantum phases: stability under graph-local perturbations
- Perturbative stability and error correction thresholds of quantum codes
- Fault-tolerant hyperbolic Floquet quantum error correcting codes
- Solvable entanglement dynamics in quantum circuits with generalized space-time duality
- Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
- Bulk-boundary correspondence from hyper-invariant tensor networks
- Charge and Spin Sharpening Transitions on Dynamical Quantum Trees
- Entanglement spectrum of matchgate circuits with universal and non-universal resources