Sequential Quantum Circuits as Maps between Gapped Phases

Abstract

Finite-depth quantum circuits preserve the long-range entanglement structure in quantum states and map between states within a gapped phase. To map between states of different gapped phases, we can use Sequential Quantum Circuits which apply unitary transformations to local patches, strips, or other sub-regions of a system in a sequential way. The sequential structure of the circuit on the one hand preserves entanglement area law and hence the gapped-ness of the quantum states. On the other hand, the circuit has generically a linear depth, hence it is capable of changing the long-range correlation and entanglement of quantum states and the phase they belong to. In this paper, we discuss systematically the definition, basic properties, and prototypical examples of sequential quantum circuits that map product states to GHZ states, symmetry-protected topological states, intrinsic topological states, and fracton states. We discuss the physical interpretation of the power of the circuits through connection to condensation, Kramers-Wannier duality, and the notion of foliation for fracton phases.

22 pages, 14 figures

References in corpus (10)

• A class of quantum many-body states that can be efficiently simulated
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Explicit tensor network representation for the ground states of string-net models
• Chiral Floquet Phases of Many-body Localized Bosons
• Sequential Generation of Matrix-Product States in Cavity QED
• Generalized string-nets for unitary fusion categories without tetrahedral symmetry
• Sequentially generated states for the study of two dimensional systems
• Sequential Implementation of Global Quantum Operations
• Renormalization of Ising cage-net model and generalized foliation
• Non-local finite-depth circuits for constructing SPT states and quantum cellular automata

Cited by in corpus (36)

• Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
• Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
• Constant-depth preparation of matrix product states with adaptive quantum circuits
• Absence of barren plateaus in finite local-depth circuits with long-range entanglement
• Quantum Phases and Transitions in Spin Chains with Non-Invertible Symmetries
• Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension
• Realizing triality and $p$-ality by lattice twisted gauging in (1+1)d quantum spin systems
• Observation of a non-Hermitian supersonic mode on a trapped-ion quantum computer
• Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
• Higher Berry Curvature from the Wave function II: Locally Parameterized States Beyond One Dimension
• String operators for Cheshire strings in topological phases
• Duality via Sequential Quantum Circuit in the Topological Holography Formalism
• Additivity, Haag duality, and non-invertible symmetries
• Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement
• Protocols for Creating Anyons and Defects via Gauging
• Global symmetries of quantum lattice models under non-invertible dualities
• Fusion of one-dimensional gapped phases and their domain walls
• Self-$G$-ality in 1+1 dimensions
• Duality-preserving deformation of 3+1d lattice ${\mathbb{Z}}_2$ gauge theory with exact gapped ground states
• Quantum Phase Transitions between Symmetry-Enriched Fracton Phases
• Projective Representations, Bogomolov Multiplier, and Their Applications in Physics
• Many-body quantum catalysts for transforming between phases of matter
• Sequential Adiabatic Generation of Chiral Topological States
• Dualities between 2+1d fusion surface models from braided fusion categories
• Frobenius light cone and the shift unitary
• Fusion of Low-Entanglement Excitations in 2D Toric Code
• Reconfigurable dissipative entanglement between many spin ensembles: from robust quantum sensing to many-body state engineering
• Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes
• General many-body entanglement swapping protocol: opportunities for distributed quantum computing
• Quantum Circuits for Matrix-Product Unitaries
• Quantum many-body scarring from Kramers-Wannier duality
• Higher-order topological phases protected by noninvertible and subsystem symmetries
• Short remarks on shallow unitary circuits
• Holographic duality between bulk topological order and boundary mixed-state order