Fundamental charges for dual-unitary circuits
arXiv:2312.14148 · doi:10.22331/q-2025-01-30-1615
Abstract
Dual-unitary quantum circuits have recently attracted attention as an analytically tractable model of many-body quantum dynamics. Consisting of a 1+1D lattice of 2-qudit gates arranged in a 'brickwork' pattern, these models are defined by the constraint that each gate must remain unitary under swapping the roles of space and time. This dual-unitarity restricts the dynamics of local operators in these circuits: the support of any such operator must grow at the effective speed of light of the system, along one or both of the edges of a causal light cone set by the geometry of the circuit. Using this property, it is shown here that for 1+1D dual-unitary circuits the set of width- conserved densities (constructed from operators supported over consecutive sites) is in one-to-one correspondence with the set of width- solitons - operators which, up to a multiplicative phase, are simply spatially translated at the effective speed of light by the dual-unitary dynamics. A number of ways to construct these many-body solitons (explicitly in the case where the local Hilbert space dimension ) are then demonstrated: firstly, via a simple construction involving products of smaller, constituent solitons; and secondly, via a construction which cannot be understood as simply in terms of products of smaller solitons, but which does have a neat interpretation in terms of products of fermions under a Jordan-Wigner transformation. This provides partial progress towards a characterisation of the microscopic structure of complex many-body solitons (in dual-unitary circuits on qubits), whilst also establishing a link between fermionic models and dual-unitary circuits, advancing our understanding of what kinds of physics can be explored in this framework.
38 pages, 3 figures. Section on connections between integrable dual-unitary circuits and matchgates added. Two appendices added: 1) on non-maximal velocity solitons 2) on numerical evaluation of dynamical constraints on operator space imposed by dual-unitarity. Previous discussion of dynamical constraints on operator space in appendices moved to main body of the text and expanded upon
References in corpus (71)
- Decoherence Free Subspaces for Quantum Computation
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- Operator Spreading in Random Unitary Circuits
- Quantum Entanglement Growth Under Random Unitary Dynamics
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
- Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
- Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
- Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
- Solution of a minimal model for many-body quantum chaos
- Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
- Remarks on the notion of quantum integrability
- String order and symmetries in quantum spin lattices
- One-Dimensional Symmetry Protected Topological Phases and their Transitions
- Exact dynamics in dual-unitary quantum circuits
- Conformal field theory out of equilibrium: a review
- Matchgates and classical simulation of quantum circuits
- Postselection-free entanglement dynamics via spacetime duality
- Entanglement spreading in a minimal model of maximal many-body quantum chaos
- Strategies for solving the Fermi-Hubbard model on near-term quantum computers
- Unitary circuits of finite depth and infinite width from quantum channels
- Chiral Floquet Phases of Many-body Localized Bosons
- The entanglement membrane in chaotic many-body systems
- Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension
- Integrable Trotterization: Local Conservation Laws and Boundary Driving
- Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
- Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
- Exact Ising model simulation on a quantum computer
- Scrambling in Random Unitary Circuits: Exact Results
- Ballistic spin transport in a periodically driven integrable quantum system
- Spacetime duality between localization transitions and measurement-induced transitions
- Exact emergent quantum state designs from quantum chaotic dynamics
- Maximum velocity quantum circuits
- Radical chiral Floquet phases in a periodically driven Kitaev model and beyond
- Dynamical purification and the emergence of quantum state designs from the projected ensemble
- Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
- Creating ensembles of dual unitary and maximally entangling quantum evolutions
- Random Matrix Spectral Form Factor of Dual-Unitary Quantum Circuits
- Operator Entanglement in Local Quantum Circuits II: Solitons in Chains of Qubits
- Computational power of one- and two-dimensional dual-unitary quantum circuits
- Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
- Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions
- Entanglement Barriers in Dual-Unitary Circuits
- Maximal entanglement velocity implies dual unitarity
- Time Asymptotics and Entanglement Generation of Clifford Quantum Cellular Automata
- Classification of Quantum Cellular Automata
- Chaos and Ergodicity in Extended Quantum Systems with Noisy Driving
- Correlations and commuting transfer matrices in integrable unitary circuits
- Clifford Quantum Cellular Automata: Trivial group in 2D and Witt group in 3D
- Hilbert Space Fragmentation in Open Quantum Systems
- Exact dynamics in dual-unitary quantum circuits with projective measurements
- Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond
- Many Body Quantum Chaos and Dual Unitarity Round-a-Face
- Growth of entanglement of generic states under dual-unitary dynamics
- Relationship between Symmetry Protected Topological Phases and Boundary Conformal Field Theories via the Entanglement Spectrum
- From Dual Unitarity to Generic Quantum Operator Spreading
- Construction and local equivalence of dual-unitary operators: from dynamical maps to quantum combinatorial designs
- Hierarchical generalization of dual unitarity
- Crystalline Quantum Circuits
- Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
- Circuits of space and time quantum channels
- Ternary unitary quantum lattice models and circuits in dimensions
- Quantum information spreading in generalised dual-unitary circuits
- Quantum Many-Body Scars in Dual-Unitary Circuits
- The entanglement membrane in exactly solvable lattice models
- Operator dynamics and entanglement in space-time dual Hadamard lattices
- Solvable entanglement dynamics in quantum circuits with generalized space-time duality
- Discrete holography in dual-unitary circuits
- Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics
- On two non-ergodic reversible cellular automata, one classical, the other quantum
- Extending Matchgate Simulation Methods to Universal Quantum Circuits
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- Exactly solvable many-body dynamics from space-time duality
- Entanglement of Disjoint Intervals in Dual-Unitary Circuits: Exact Results
- Entanglement in dual unitary quantum circuits with impurities
- Probes of Full Eigenstate Thermalization in Ergodicity-Breaking Quantum Circuits
- Geometric constructions of generalized dual-unitary circuits from biunitarity
- Dual-unitary shadow tomography