Approximate Quantum Compiling for Quantum Simulation: A Tensor Network based approach

Abstract

We introduce AQCtensor, a novel algorithm to produce short-depth quantum circuits from Matrix Product States (MPS). Our approach is specifically tailored to the preparation of quantum states generated from the time evolution of quantum many-body Hamiltonians. This tailored approach has two clear advantages over previous algorithms that were designed to map a generic MPS to a quantum circuit. First, we optimize all parameters of a parametric circuit at once using Approximate Quantum Compiling (AQC) - this is to be contrasted with other approaches based on locally optimizing a subset of circuit parameters and "sweeping" across the system. We introduce an optimization scheme to avoid the so-called ``orthogonality catastrophe" - i.e. the fact that the fidelity of two arbitrary quantum states decays exponentially with the number of qubits - that would otherwise render a global optimization of the circuit impractical. Second, the depth of our parametric circuit is constant in the number of qubits for a fixed simulation time and fixed error tolerance. This is to be contrasted with the linear circuit Ansatz used in generic algorithms whose depth scales linearly in the number of qubits. For simulation problems on 100 qubits, we show that AQCtensor thus achieves at least an order of magnitude reduction in the depth of the resulting optimized circuit, as compared with the best generic MPS to quantum circuit algorithms. We demonstrate our approach on simulation problems on Heisenberg-like Hamiltonians on up to 100 qubits and find optimized quantum circuits that have significantly reduced depth as compared to standard Trotterized circuits.

References in corpus (30)

• The density-matrix renormalization group in the age of matrix product states
• Efficient simulation of one-dimensional quantum many-body systems
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• An Area Law for One Dimensional Quantum Systems
• Time-dependent variational principle for quantum lattices
• Unifying time evolution and optimization with matrix product states
• Tensor networks for complex quantum systems
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• Quantum-assisted quantum compiling
• A random compiler for fast Hamiltonian simulation
• Time-evolving a matrix product state with long-ranged interactions
• Towards Quantum Machine Learning with Tensor Networks
• Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors
• Simulating quantum many-body dynamics on a current digital quantum computer
• Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
• Real- and imaginary-time evolution with compressed quantum circuits
• Lecture Notes of Tensor Network Contractions
• Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
• One-dimensional Continuum Electronic Structure with the Density Matrix Renormalization Group and Its Implications For Density Functional Theory
• Classically optimized Hamiltonian simulation
• Quantum Assisted Simulator
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage
• Kohn-Sham calculations with the exact functional
• Evidence of Kardar-Parisi-Zhang scaling on a digital quantum simulator
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model
• Optimal compression of quantum many-body time evolution operators into brickwall circuits
• Well-conditioned multi-product formulas for hardware-friendly Hamiltonian simulation
• Error Bounds for Variational Quantum Time Evolution
• Approximate encoding of quantum states using shallow circuits

Cited by in corpus (7)

• Scalable Quantum Simulations of Scattering in Scalar Field Theory on 120 Qubits
• Riemannian quantum circuit optimization based on matrix product operators
• Tensor Network enhanced Dynamic Multiproduct Formulas
• Preparation Circuits for Matrix Product States by Classical Variational Disentanglement
• Superdiffusion resilience in Heisenberg Chains with 2D interactions on a quantum processor
• Implementation of Tensor Network Simulation TN-Sim under NWQ-Sim
• Imaginary Time Spectral Transforms for Excited State Preparation