Quantum Computing Accurately Models Benzene, Reveals Hardware Limitations for Chemistry.

Variational quantum eigensolver performance was assessed using benzene as a model system. Optimisations to the algorithm and classical optimisation routines reduced computational cost, but current hardware noise limits accurate molecular energy calculations. Future hardware improvements are essential for scalable quantum chemistry applications utilising this approach.

Determining the energy levels of molecules is fundamental to understanding chemical behaviour and designing new materials. Quantum computers offer a potential pathway to accurately model these systems, surpassing the limitations of classical methods. However, current quantum hardware presents significant challenges to realising this potential. Researchers at the Donostia International Physics Center (DIPC) and Multiverse Computing, led by Abel Carreras, Román Orús, and David Casanova, have systematically investigated these limitations using the variational eigensolver (VQE) algorithm – a hybrid quantum-classical approach suited to near-term devices. Their work, detailed in a study titled ‘Limitations of Quantum Hardware for Molecular Energy Estimation Using VQE’, assesses the performance of VQE, specifically the adaptive derivative-assembled pseudo-Trotter ansatz (ADAPT-VQE) method, on existing hardware, identifying key bottlenecks and outlining the specifications required for future devices to enable practical molecular simulations.

Advancing Variational Quantum Eigensolvers for Molecular Simulations on Noisy Intermediate-Scale Quantum Hardware

Variational quantum eigensolvers (VQE) currently represent a leading computational approach for determining molecular ground-state energies within the constraints of Noisy Intermediate-Scale Quantum (NISQ) technology. Researchers actively pursue strategies to simplify molecular Hamiltonians, optimise quantum circuit ansatze – the specific arrangement of quantum gates used to prepare a trial wave function – and refine classical optimisation routines. This study investigates the capabilities and limitations of the adaptive derivative-assembled pseudo-Trotter ansatz VQE (ADAPT-VQE) when implemented on current quantum hardware, demonstrating algorithmic and computational improvements that push the boundaries of molecular simulation.

The investigation details the ADAPT algorithm, an iterative process that constructs a quantum circuit by sequentially adding operators that most effectively reduce the system’s energy. Analysis reveals that circuit depth – the number of quantum gates – significantly impacts performance. Researchers compared standard, reverse, and optimised CNOT (Controlled-NOT) orientations, finding the latter yields the shallowest circuits.

The study quantified the impact of hardware limitations, demonstrating a constraint on the maximum number of two-qubit gates and Pauli observables – fundamental quantum operators representing measurable physical quantities – that can be processed, restricting the size and complexity of tractable problems. Data indicates that the IBM Brussels computer, tested multiple times, exhibits similar limitations to other IBM processors, highlighting a systemic constraint across the platform.

The investigation details specific gate timings used in simulations and experiments on the IBM Torino processor, establishing a clear understanding of the time costs associated with different quantum operations. U1, U2, and U3 single-qubit gates require 0, 50, and 100 nanoseconds respectively, while CNOT gates take 300 nanoseconds, and reset and measurement operations each require 1000 nanoseconds.

Despite these algorithmic and computational improvements, the results highlight the substantial impact of noise on state preparation and energy measurement, preventing the attainment of sufficient accuracy for reliable chemical insights. Calculations using the ADAPT ansatz on the IBM Torino computer achieve energies approaching the Hartree-Fock (HF) and Full Configuration Interaction (FCI) values, with the difference between the two representing the correlation energy – in this case, 53.9 mHa for a system with 4 active orbitals and 4 electrons. However, current noise levels prevent accurate evaluations of molecular Hamiltonians, hindering the extraction of reliable chemical insights, and necessitating further advancements in both hardware and error mitigation techniques.

This work provides a detailed assessment of the interplay between algorithmic optimisation, hardware limitations, and noise, charting a course for future advancements in both algorithms and hardware to enable practical and scalable molecular modelling using VQE. Using benzene as a benchmark, the study reveals critical bottlenecks in current implementations. Researchers implemented several strategies to mitigate the computational demands of molecular Hamiltonians, including Hamiltonian simplification and ansatz optimisation, alongside modifications to the COBYLA classical optimisation algorithm, to achieve more efficient and accurate calculations.