[Paper Review] Hardware-efficient Quantum Optimizer for Small Molecules and Quantum Magnets

Abhinav Kandala, Antonio Mezzacapo+4 more|arXiv (Cornell University)|Apr 17, 2017

Quantum Computing Algorithms and Architecture11 citations

TL;DR

This paper presents a hardware-efficient variational quantum eigensolver (VQE) tailored to native interactions in superconducting quantum processors, enabling experimental ground state energy optimization for molecules like BeH2 and quantum magnets using up to six qubits and over 100 Pauli terms. The method achieves strong agreement with noisy simulations, demonstrating scalability potential for classically intractable fermionic problems.

ABSTRACT

Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to these interacting fermion problems has exponential cost, while Monte Carlo methods are plagued by the fermionic sign problem. These limitations of classical computational methods have made even few-atom molecular structures problems of practical interest for medium-sized quantum computers. Yet, thus far experimental implementations have been restricted to molecules involving only Period I elements. Here, we demonstrate the experimental optimization of up to six-qubit Hamiltonian problems with over a hundred Pauli terms, determining the ground state energy for molecules of increasing size, up to BeH2. This is enabled by a hardware-efficient variational quantum eigensolver with trial states specifically tailored to the available interactions in our quantum processor, combined with a compact encoding of fermionic Hamiltonians and a robust stochastic optimization routine. We further demonstrate the flexibility of our approach by applying the technique to a problem of quantum magnetism. Across all studied problems, we find agreement between experiment and numerical simulations with a noisy model of the device. These results help elucidate the requirements for scaling the method to larger systems, and aim at bridging the gap between problems at the forefront of high-performance computing and their implementation on quantum hardware.

Motivation & Objective

• Address classically intractable quantum chemistry and condensed matter problems beyond the reach of classical high-performance computing.
• Overcome the fermionic sign problem in Monte Carlo methods and exponential scaling in exact diagonalization by leveraging near-term quantum hardware.
• Enable experimental implementation of quantum algorithms for molecules beyond Period I elements, extending beyond prior demonstrations limited to Period I.
• Demonstrate robust ground state energy optimization on real quantum hardware using a compact fermionic encoding and stochastic optimization.
• Extend the method to quantum magnetism problems to validate its generality and flexibility across different quantum many-body systems.

Proposed method

• Design a hardware-efficient VQE with ansatz states constructed from native two-qubit entangling gates available on the superconducting processor, minimizing circuit depth and gate count.
• Implement a compact fermionic-to-qubit encoding that reduces the number of qubits and Pauli terms required to represent molecular and spin Hamiltonians.
• Utilize a stochastic optimization routine robust to noise and gate errors, enabling convergence despite noisy intermediate-scale quantum (NISQ) device limitations.
• Tailor the variational form to the specific entangling interactions available in the quantum processor, enhancing fidelity and reducing error propagation.
• Integrate a noisy device model in simulations to validate experimental results and guide error mitigation strategies.
• Apply the framework to both molecular Hamiltonians (e.g., BeH2) and spin Hamiltonians modeling quantum magnets, demonstrating cross-domain applicability.

Experimental results

Research questions

• RQ1 Can a hardware-efficient VQE with processor-native entangling gates achieve accurate ground state energy estimation for small molecules beyond Period I?
• RQ2 How does the compact fermionic encoding reduce the resource overhead in terms of qubits and Pauli terms for quantum simulation?
• RQ3 To what extent does stochastic optimization enable convergence on noisy quantum hardware despite gate and measurement errors?
• RQ4 Can the same VQE framework be effectively applied to quantum magnetism problems, indicating generality beyond quantum chemistry?
• RQ5 How well do experimental results align with simulations using a noisy model of the quantum device?

Key findings

• The method successfully optimized the ground state energy of BeH2, a six-qubit system with over 100 Pauli terms, marking a significant step beyond previous demonstrations limited to Period I molecules.
• Experimental results showed strong agreement with numerical simulations using a noisy device model, validating the robustness of the optimization and encoding approach.
• The hardware-efficient ansatz, built from native two-qubit gates, enabled high-fidelity state preparation and energy estimation on a real superconducting quantum processor.
• The compact fermionic encoding significantly reduced the number of required Pauli terms, improving resource efficiency and reducing error-prone operations.
• The stochastic optimization routine achieved convergence despite noise, demonstrating resilience in near-term quantum hardware conditions.
• The framework was successfully extended to a quantum magnetism problem, confirming its flexibility and potential for broader applications in quantum many-body physics.