Preparing matrix product states via fusion: constraints and extensions
arXiv:2404.16360 · doi:10.1103/cv3q-5l8w
Abstract
In the era of noisy, intermediate-scale quantum (NISQ) devices, the efficient preparation of many-body resource states is a task of paramount importance. In this paper we focus on the deterministic preparation of matrix-product states (MPS) in constant depth by utilizing measurements and classical communication to fuse smaller states into larger ones. We place strong constraints on the MPS that can be prepared using this method, which we refer to as MPS fusion. Namely, we establish that it is necessary for the MPS to have a flat entanglement spectrum. Using the recently introduced split-index MPS (SIMPS) representation, we then introduce a family of states that belong to interesting phases of matter protected by non-onsite symmetries, including anomalous and non-invertible symmetries, and also serve as resources for long-range quantum teleportation, but which lie beyond the scope of ordinary MPS fusion. It is shown constructively that these states can be prepared in constant depth using a broader class of measurement-assisted protocols, which we dub SIMPS fusion. Even in cases when MPS fusion is possible, using SIMPS fusion can give rise to significantly reduced resource overhead. We also discuss constraints on SIMPS fusion and propose a general framework for fusion that encompasses the MPS and SIMPS protocols. Our results therefore simultaneously establish the boundaries of conventional MPS fusion and push the envelope of which states can be prepared using measurement-assisted protocols.
V3: Published version containing new sections IV A, IV B, and V A. V2: Updated references
References in corpus (38)
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- String order and symmetries in quantum spin lattices
- Localizable Entanglement
- Real- and imaginary-time evolution with compressed quantum circuits
- Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
- Measurement-induced entanglement and teleportation on a noisy quantum processor
- Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
- Preparing random states and benchmarking with many-body quantum chaos
- Measurement as a shortcut to long-range entangled quantum matter
- Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
- Quantum Circuits assisted by LOCC: Transformations and Phases of Matter
- Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
- Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements
- Long-range entanglement from measuring symmetry-protected topological phases
- Efficient Long-Range Entanglement using Dynamic Circuits
- Preparation of matrix product states with log-depth quantum circuits
- Matrix Product States: Symmetries and Two-Body Hamiltonians
- Shortest Route to Non-Abelian Topological Order on a Quantum Processor
- Measurements conspire nonlocally to restructure critical quantum states
- Dynamical purification and the emergence of quantum state designs from the projected ensemble
- Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer
- Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
- Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements
- Speed limits and locality in many-body quantum dynamics
- Mixed-state long-range order and criticality from measurement and feedback
- Constant-depth preparation of matrix product states with adaptive quantum circuits
- Classifying phases protected by matrix product operator symmetries using matrix product states
- Approximating many-body quantum states with quantum circuits and measurements
- Quantum spin systems for measurement-based quantum computation
- Matrix Product State Representations
- Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension
- Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
- Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements
- Playing nonlocal games across a topological phase transition on a quantum computer
- Classification of measurement-based quantum wire in stabilizer PEPS
- Phases of Matrix Product States with Symmetric Quantum Circuits and Symmetric Measurements with Feedforward
- Non-onsite symmetries and quantum teleportation in split-index matrix product states