Efficient Verification of Ground States of Frustration-Free Hamiltonians

Abstract

Ground states of local Hamiltonians are of key interest in many-body physics and also in quantum information processing. Efficient verification of these states are crucial to many applications, but very challenging. Here we propose a simple, but powerful recipe for verifying the ground states of general frustration-free Hamiltonians based on local measurements. Moreover, we derive rigorous bounds on the sample complexity by virtue of the quantum detectability lemma (with improvement) and quantum union bound. Notably, the number of samples required does not increase with the system size when the underlying Hamiltonian is local and gapped, which is the case of most interest. As an application, we propose a general approach for verifying Affleck-Kennedy-Lieb-Tasaki (AKLT) states on arbitrary graphs based on local spin measurements, which requires only a constant number of samples for AKLT states defined on various lattices. Our work is of interest not only to many tasks in quantum information processing, but also to the study of many-body physics.

arXiv comment17+5 pages and 2 figures; accepted by Quantum

References in corpus (64)

• Classification of topological quantum matter with symmetries
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Adiabatic Quantum Computing
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Efficient quantum state tomography
• Symmetry Protected Topological phases of Quantum Matter
• Quantum certification and benchmarking
• Efficient tomography of a quantum many-body system
• Verifiable measurement-only blind quantum computing with stabilizer testing
• Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource
• Computational advantage of quantum random sampling
• Theory of quantum system certification: a tutorial
• Optimal verification of entangled states with local measurements
• Reliable quantum certification for photonic quantum technologies
• Quantum computational capability of a 2D valence bond solid phase
• Architectures for quantum simulation showing a quantum speedup
• Efficient Verification of Pure Quantum States in the Adversarial Scenario
• A computationally universal phase of quantum matter
• Theoretical and Experimental Perspectives of Quantum Verification
• Computational Power of Symmetry-Protected Topological Phases
• Verification of Many-Qubit States
• Optical one-way quantum computing with a simulated valence-bond solid
• Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
• A study of LOCC-detection of a maximally entangled state using hypothesis testing
• Rapid adiabatic preparation of injective PEPS and Gibbs states
• Efficient Verification of Hypergraph States
• General framework for verifying pure quantum states in the adversarial scenario
• Three-dimensional entanglement on a silicon chip
• Direct certification of a class of quantum simulations
• Statistical Methods for Quantum State Verification and Fidelity Estimation
• Optimal Verification of Two-Qubit Pure States
• Optimal verification and fidelity estimation of maximally entangled states
• Self-guaranteed measurement-based quantum computation
• Efficient verification of bipartite pure states
• Optimal verification of general bipartite pure states
• Verifiable fault-tolerance in measurement-based quantum computation
• Efficient verification of Dicke states
• Fidelity witnesses for fermionic quantum simulations
• Experimental Optimal Verification of Entangled States using Local Measurements
• The 2D AKLT state on the honeycomb lattice is a universal resource for quantum computation
• Quantum union bounds for sequential projective measurements
• Optimal Verification of Greenberger-Horne-Zeilinger States
• Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing
• Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices
• Demonstrating the AKLT spectral gap on 2D degree-3 lattices
• Spectral gaps of AKLT Hamiltonians using Tensor Network methods
• Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice
• Towards the standardization of quantum state verification using optimal strategies
• Verification of phased Dicke states
• Sample-efficient device-independent quantum state verification and certification
• A simple proof of the detectability lemma and spectral gap amplification
• Quantum spin systems for measurement-based quantum computation
• Verifying commuting quantum computations via fidelity estimation of weighted graph states
• Robust and efficient verification of graph states in blind measurement-based quantum computation
• A class of two-dimensional AKLT models with a gap
• Entanglement in Valence-Bond-Solid States
• Quantum verification and estimation with few copies
• AKLT models on decorated square lattices are gapped
• Universally Optimal Verification of Entangled States with Nondemolition Measurements
• Efficient verification of continuous-variable quantum states and devices without assuming identical and independent operations
• Preparation and verification of tensor network states
• Efficient verification of Affleck-Kennedy-Lieb-Tasaki states
• Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation
• Harnessing symmetry-protected topological order for quantum memories

Cited by in corpus (7)

• Models of interacting bosons with exact ground states: a unified approach
• Quantum subspace verification for error correction codes
• Experimental Verification of Entangled States in the Adversarial Scenario
• Relative-belief inference in quantum information theory
• Universal and Efficient Quantum State Verification via Schmidt Decomposition and Mutually Unbiased Bases
• Prescriptive preparation and verification of nonstabilizer states
• Beating the Optimal Verification of Entangled States via Collective Strategies