Variational Quantum Simulation of Valence-Bond Solids
arXiv:2201.02545 · doi:10.22331/q-2022-12-13-874
Abstract
We introduce a hybrid quantum-classical variational algorithm to simulate ground-state phase diagrams of frustrated quantum spin models in the thermodynamic limit. The method is based on a cluster-Gutzwiller ansatz where the wave function of the cluster is provided by a parameterized quantum circuit whose key ingredient is a two-qubit real XY gate allowing to efficiently generate valence-bonds on nearest-neighbor qubits. Additional tunable single-qubit Z- and two-qubit ZZ-rotation gates allow the description of magnetically ordered and paramagnetic phases while restricting the variational optimization to the U(1) subspace. We benchmark the method against the J1-J2 Heisenberg model on the square lattice and uncover its phase diagram, which hosts long-range ordered Neel and columnar anti-ferromagnetic phases, as well as an intermediate valence-bond solid phase characterized by a periodic pattern of 2x2 strongly-correlated plaquettes. Our results show that the convergence of the algorithm is guided by the onset of long-range order, opening a promising route to synthetically realize frustrated quantum magnets and their quantum phase transition to paramagnetic valence-bond solids with currently developed superconducting circuit devices.
arXiv comment7+3 pages, 4+3 figures
References in corpus (72)
- Quantum Computing in the NISQ era and beyond
- Fault-tolerant quantum computation by anyons
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Anyons in an exactly solved model and beyond
- A variational eigenvalue solver on a quantum processor
- Variational Quantum Algorithms
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- Barren plateaus in quantum neural network training landscapes
- The theory of variational hybrid quantum-classical algorithms
- Noisy intermediate-scale quantum (NISQ) algorithms
- Quantum Spin Liquid States
- Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
- Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
- Programmable Quantum Simulations of Spin Systems with Trapped Ions
- Noise-Induced Barren Plateaus in Variational Quantum Algorithms
- Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
- Towards Practical Quantum Variational Algorithms
- Realizing Repeated Quantum Error Correction in a Distance-Three Surface Code
- Connecting ansatz expressibility to gradient magnitudes and barren plateaus
- Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
- Herbertsmithite and the Search for the Quantum Spin Liquid
- Simulating quantum computation by contracting tensor networks
- Variational Quantum Computation of Excited States
- Training variational quantum algorithms is NP-hard
- Simulating Physical Phenomena by Quantum Networks
- Spin Liquid Ground State of the Spin-1/2 Square - Heisenberg Model
- Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices
- Sequential generation of entangled multi-qubit states
- Quantum Algorithms for Fermionic Simulations
- Valence Bond Solids for Quantum Computation
- Demonstrating a Continuous Set of Two-qubit Gates for Near-term Quantum Algorithms
- Solving strongly correlated electron models on a quantum computer
- Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
- Digital quantum simulation of spin models with circuit quantum electrodynamics
- Effect of barren plateaus on gradient-free optimization
- Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
- Direct evidence for a gapless spin liquid by frustrating Néel antiferromagnetism
- Spontaneous plaquette dimerization in the Heisenberg model
- Critical level crossings and gapless spin liquid in the square-lattice spin- - Heisenberg antiferromagnet
- Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
- Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource
- The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
- Quantum algorithms to simulate many-body physics of correlated fermions
- Variational Quantum Eigensolver with Fewer Qubits
- Observation of a 4-spin Plaquette Singlet State in the Shastry-Sutherland compound SrCu2(BO3)2
- 64-Qubit Quantum Circuit Simulation
- Constructing gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice
- Algebraic Approach to Interacting Quantum Systems
- Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design
- Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
- Error Mitigation by Symmetry Verification on a Variational Quantum Eigensolver
- Massively parallel quantum computer simulator, eleven years later
- Parallel Quantum Simulation of Large Systems on Small Quantum Computers
- Diabatic gates for frequency-tunable superconducting qubits
- Implementation of the XY interaction family with calibration of a single pulse
- Quantum computational capability of a 2D valence bond solid phase
- A tensor product state approach to spin-1/2 square - antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality
- Hierarchical mean-field approach to the - Heisenberg model on a square lattice
- Holographic quantum algorithms for simulating correlated spin systems
- The Variational Power of Quantum Circuit Tensor Networks
- Improving the Performance of Deep Quantum Optimization Algorithms with Continuous Gate Sets
- Spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice: a plaquette renormalized tensor network study
- Universal quantum circuits for quantum chemistry
- Scaling of variational quantum circuit depth for condensed matter systems
- On the Computational Complexity of Curing the Sign Problem
- Composite Boson Mapping for Lattice Boson Systems
- Chiral phases of two-dimensional hard-core bosons with frustrated ring-exchange
- Local physics of magnetization plateaux in the Shastry-Sutherland model
- Staircase of crystal phases of hard-core bosons on the Kagome lattice
- Phase diagram of the Heisenberg antiferromagnet with four-spin interactions
- Translation-Invariant Parent Hamiltonians of Valence Bond Crystals
- Parent Hamiltonian as a benchmark problem for variational quantum eigensolvers