Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
arXiv:2310.06031 · doi:10.22331/q-2024-12-10-1557
Abstract
Quantum state preparation plays a crucial role in several areas of quantum information science, in applications such as quantum simulation, quantum metrology and quantum computing. However, typically state preparation requires resources that scale exponentially with the problem size, due to their probabilistic nature or otherwise, making studying such models challenging. In this article, we propose a method to prepare the ground state of the Affleck-Lieb-Kennedy-Tasaki (AKLT) model deterministically using a measurement-based imaginary time evolution (MITE) approach. By taking advantage of the special properties of the AKLT state, we show that it can be prepared efficiently using the MITE approach. Estimates based on the convergence of a sequence of local projections, as well as direct evolution of the MITE algorithm suggest a constant scaling with respect to the number of AKLT sites, which is an exponential improvement over the naive estimate for convergence. We show that the procedure is compatible with qubit-based simulators, and show that using a variational quantum algorithm for circuit recompilation, the measurement operator required for MITE can be well approximated by a circuit with a much shallower circuit depth compared with the one obtained using the default Qiskit method.
18 pages, 8 figures (published version for Quantum journal)
References in corpus (25)
- Many-Body Physics with Ultracold Gases
- Non-Abelian Anyons and Topological Quantum Computation
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- The density-matrix renormalization group in the age of matrix product states
- An atom-by-atom assembler of defect-free arbitrary 2d atomic arrays
- Quantum metrology from a quantum information science perspective
- Resource-efficient linear optical quantum computation
- Molecular Spin Qudits for Quantum Algorithms
- Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
- Native qudit entanglement in a trapped ion quantum processor
- Preparation of matrix product states with log-depth quantum circuits
- Optical one-way quantum computing with a simulated valence-bond solid
- Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements
- Simulation of interaction-induced chiral topological dynamics on a digital quantum computer
- Characterizing a non-equilibrium phase transition on a quantum computer
- Proposal for Observing Yang-Lee Criticality in Rydberg Atomic Arrays
- Full Bloch sphere teleportation of spinor Bose-Einstein condensates and spin ensembles
- High-fidelity realization of the AKLT state on a NISQ-era quantum processor
- Quantum simulator for the Hubbard model with long-range Coulomb interactions using surface acoustic waves
- Fully quantum scalable description of driven dissipative lattice models
- Dissipative preparation and stabilization of many-body quantum states in a superconducting qutrit array
- Observation of higher-order topological states on a quantum computer
- Preparing Valence-Bond-Solid states on noisy intermediate-scale quantum computers
- Imaginary time evolution with quantum nondemolition measurements: multi-qubit interactions via measurement nonlinearities
- Stack operation of tensor networks