[Paper Review] Efficient quantum-enhanced classical simulation for patches of quantum landscapes

Sacha Lerch, Ricard Puig+6 more|arXiv (Cornell University)|Nov 29, 2024

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper introduces a quantum-enhanced classical simulation method that generates accurate classical surrogates for localized regions ('patches') of quantum expectation value landscapes produced by parameterized quantum circuits. By leveraging simple quantum measurements, the approach enables efficient classical simulation with provable time and sample complexity bounds, demonstrated on a 127-qubit heavy-hex lattice and variational quantum algorithms.

ABSTRACT

Understanding the capabilities of classical simulation methods is key to identifying where quantum computers are advantageous. Not only does this ensure that quantum computers are used only where necessary, but also one can potentially identify subroutines that can be offloaded onto a classical device. In this work, we show that it is always possible to generate a classical surrogate of a sub-region (dubbed a "patch") of an expectation landscape produced by a parameterized quantum circuit. That is, we provide a quantum-enhanced classical algorithm which, after simple measurements on a quantum device, allows one to classically simulate approximate expectation values of a subregion of a landscape. We provide time and sample complexity guarantees for a range of families of circuits of interest, and further numerically demonstrate our simulation algorithms on an exactly verifiable simulation of a Hamiltonian variational ansatz and long-time dynamics simulation on a 127-qubit heavy-hex topology.

Motivation & Objective

• To identify where classical simulation can effectively replace quantum computation in variational quantum algorithms.
• To develop a method that classically simulates localized subregions of quantum expectation landscapes without full quantum state tomography.
• To provide rigorous complexity guarantees (time and sample) for a range of physically relevant quantum circuit families.
• To enable offloading of computationally intensive subroutines to classical hardware while maintaining accuracy for specific parameter regions.
• To validate the method on large-scale quantum simulations, including a 127-qubit heavy-hex topology and variational quantum eigensolver instances.

Proposed method

• The method constructs a classical surrogate model for a local patch of a quantum expectation landscape using only a small number of parameterized quantum circuit evaluations.
• It leverages quantum device measurements to extract data points that are then used to train a classical model approximating the expectation value function in a local region.
• The classical model is built using a kernel-based regression approach, with the kernel derived from the quantum circuit's structure and measurement outcomes.
• The approach ensures that the classical simulation error is bounded within the patch, with complexity scaling polynomially in the number of parameters and system size.
• The method is applied to both variational quantum eigensolvers and long-time dynamics simulations, with validation on a 127-qubit heavy-hex architecture.
• Theoretical guarantees are derived for time and sample complexity across families of circuits, including those with local gates and specific entanglement structures.

Experimental results

Research questions

• RQ1 Can classical simulation accurately approximate localized regions of quantum expectation landscapes without full state reconstruction?
• RQ2 What is the minimal set of quantum measurements required to classically simulate a patch of a parameterized quantum circuit's output?
• RQ3 What are the time and sample complexity bounds for classical simulation of such patches across different circuit families?
• RQ4 Can this method be practically applied to large-scale quantum simulations, such as those on 127-qubit devices?
• RQ5 How does the accuracy of the classical surrogate compare to direct quantum simulation within the defined patch?

Key findings

• The method successfully generates classical surrogates for patches of quantum expectation landscapes with provable accuracy guarantees.
• The time and sample complexity of the classical simulation scale polynomially with the number of parameters and system size, enabling efficient computation.
• The approach was numerically validated on a 127-qubit heavy-hex lattice, demonstrating feasibility for large-scale quantum simulations.
• An exactly verifiable simulation of a Hamiltonian variational ansatz confirmed the correctness and accuracy of the classical surrogate model.
• The method enables offloading of quantum subroutines to classical hardware while maintaining fidelity within the patch, reducing reliance on quantum resources.
• The kernel-based regression model used in the classical surrogate achieves high accuracy with minimal quantum measurements, confirming the quantum-enhancement aspect of the method.