Optimal compression of quantum many-body time evolution operators into brickwall circuits

Abstract

Near term quantum computers suffer from a degree of decoherence which is prohibitive for high fidelity simulations with deep circuits. An economical use of circuit depth is therefore paramount. For digital quantum simulation of quantum many-body systems, real time evolution is typically achieved by a Trotter decomposition of the time evolution operator into circuits consisting only of two qubit gates. To match the geometry of the physical system and the CNOT connectivity of the quantum processor, additional SWAP gates are needed. We show that optimal fidelity, beyond what is achievable by simple Trotter decompositions for a fixed gate count, can be obtained by compiling the evolution operator into optimal brickwall circuits for the $S=1/2$ quantum Heisenberg model on chains and ladders, when mapped to one dimensional quantum processors without the need of additional SWAP gates.

References in corpus (7)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Probing many-body dynamics on a 51-atom quantum simulator
• Simulated Quantum Computation of Molecular Energies
• Digital quantum simulation of spin models with circuit quantum electrodynamics
• Operator space entanglement entropy in transverse Ising chain
• Operator entanglement entropy of the time evolution operator in chaotic systems
• Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression

Cited by in corpus (23)

• Classically optimized Hamiltonian simulation
• Towards adiabatic quantum computing using compressed quantum circuits
• Optimised Trotter Decompositions for Classical and Quantum Computing
• Nonlinear dynamics as a ground-state solution on quantum computers
• Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer
• Approximate encoding of quantum states using shallow circuits
• Combining Matrix Product States and Noisy Quantum Computers for Quantum Simulation
• Scalable Quantum Simulations of Scattering in Scalar Field Theory on 120 Qubits
• Problem specific classical optimization of Hamiltonian simulation
• Adaptive Trotterization for time-dependent Hamiltonian quantum dynamics using piecewise conservation laws
• Trotter error with commutator scaling for the Fermi-Hubbard model
• Riemannian quantum circuit optimization for Hamiltonian simulation
• Efficient and practical Hamiltonian simulation from time-dependent product formulas
• Approximate Quantum Compiling for Quantum Simulation: A Tensor Network based approach
• Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits
• Riemannian quantum circuit optimization based on matrix product operators
• Dynamical chaos in the integrable Toda chain induced by time discretization
• Compressed quantum error mitigation
• Deep Circuit Compression for Quantum Dynamics via Tensor Networks
• Optimal compression of constrained quantum time evolution
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Phase Estimation with Compressed Controlled Time Evolution
• Trotter transition in BCS pairing dynamics