Quantum time dynamics of 1D-Heisenberg models employing the Yang-Baxter equation for circuit compression

Abstract

Quantum time dynamics (QTD) is considered a promising problem for quantum supremacy on near-term quantum computers. However, QTD quantum circuits grow with increasing time simulations. This study focuses on simulating the time dynamics of 1-D integrable spin chains with nearest neighbor interactions. We show how the quantum Yang-Baxter equation can be exploited to compress and produce a shallow quantum circuit. With this compression scheme, the depth of the quantum circuit becomes independent of step size and only depends on the number of spins. We show that the compressed circuit scales quadratically with system size, which allows for the simulations of time dynamics of very large 1-D spin chains. We derive the compressed circuit representations for different special cases of the Heisenberg Hamiltonian. We compare and demonstrate the effectiveness of this approach by performing simulations on quantum computers.

References in corpus (12)

• Non-Abelian Anyons and Topological Quantum Computation
• Quantum Quench in the Transverse Field Ising Chain
• Generalized Thermalization in an Integrable Lattice System
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation
• Quantum circuits for strongly correlated quantum systems
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Is efficiency of classical simulations of quantum dynamics related to integrability?
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution
• Constant-Depth Circuits for Dynamic Simulations of Materials on Quantum Computers
• Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression
• Entropy of XY Spin Chain and Block Toeplitz Determinants

Cited by in corpus (14)

• Low-depth simulations of fermionic systems on square-grid quantum hardware
• The Floquet Baxterisation
• Time Evolution of Uniform Sequential Circuits
• Operator dynamics and entanglement in space-time dual Hadamard lattices
• Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation
• Riemannian quantum circuit optimization for Hamiltonian simulation
• Optimal realization of Yang-Baxter gate on quantum computers
• Two-dimensional coherent spectrum of high-spin models via a quantum computing approach
• QuYBE -- An Algebraic Compiler for Quantum Circuit Compression
• The Yang-Baxter equation, Quantum computing and Quantum entanglement
• Digital Quantum Simulation of Scalar Yukawa Coupling
• The Parity Flow Formalism: Tracking Quantum Information Throughout Computation
• Symmetric channel verification for purifying noisy quantum channels
• Quantum Algorithms for State Preparation and Data Classification based on Stabilizer Codes