Quantum Algorithm Efficiently Calculates Excited States in Complex Systems.

Understanding the excited states of complex quantum systems presents a persistent challenge in fields ranging from nuclear physics to molecular chemistry. These states, representing higher energy levels within a system, dictate its response to external stimuli and govern crucial processes like chemical reactions and radioactive decay. Researchers now present a novel computational approach to efficiently determine these excited states, building upon the adaptive derivative-assembled pseudo-Trotter Ansatz variational eigensolver (ADAPT-VQE) method, a technique used to approximate solutions to the Schrödinger equation for many-body systems. Jing Zhang, Denis Lacroix, and colleagues at Université Paris-Saclay and the CNRS/IN2P3’s IJCLab detail their algorithm in a recent publication titled “Excited States from ADAPT-VQE convergence path in Many-Body Problems: application to nuclear pairing problem and molecule dissociation”, demonstrating its efficacy in modelling both atomic nuclei and molecular behaviour with minimal computational cost.

The relentless pursuit of understanding complex quantum systems continually drives innovation in computational techniques, particularly in excited state calculations. Researchers actively investigate diverse methodologies, ranging from refined quantum algorithms to hybrid quantum-classical approaches, to accurately determine the energetic landscape of these systems and unlock deeper insights into their behaviour.

Parella-Dilm´e et al. explore methods for reducing entanglement, a key quantum mechanical phenomenon where particles become correlated, through optimised fermion-to-qubit mappings, a crucial step in translating quantum mechanical problems into a form suitable for quantum computers. Tang et al. concentrate on hardware-efficient ansatz construction, where an ansatz represents a trial wave function used in variational quantum algorithms, using adaptive algorithms, acknowledging the limitations of current quantum hardware and striving to maximise performance within those constraints. Barison et al. present quantum-centric computation of molecular excited states using extended sample-based quantum diagonalization, offering a novel approach that leverages the unique capabilities of quantum computation. Ding et al. investigate ensemble variational principles for excited states, providing a theoretical framework for improving the accuracy and efficiency of excited state calculations.

Researchers actively apply these computational methods to a variety of systems, with a significant trend centering on leveraging quantum computing for computational chemistry. Multiple reviews, including those by Bausch, Cereja et al., Veis et al., and Whitfield et al., highlight the growing application of Variational Quantum Eigensolver (VQE) and related algorithms to molecular systems, frequently targeting excited states as a key objective. VQE is a hybrid quantum-classical algorithm used to find the ground state energy of a molecule.

Yordanov et al. introduce an adaptive VQE method specifically designed to target excited states through qubit excitations, offering a direct quantum approach to calculating excited state energies. Researchers consistently explore alternative strategies beyond purely quantum approaches, expanding the toolkit for tackling complex quantum systems. Rebentrost et al. explore quantum subspace expansion, a technique that reduces the computational cost of simulating quantum systems by focusing on the most important degrees of freedom. Bauman et al. investigate variational quantum simulation, a method that uses a variational principle to approximate the ground state of a quantum system, offering a flexible and efficient approach to quantum simulation.

Arute et al. demonstrate quantum supremacy, showcasing the potential of quantum computers to outperform classical computers on specific tasks.

A novel algorithm for determining low-lying excited states within many-body interacting systems builds upon the established framework of the adaptive derivative-assembled pseudo-Trotter Ansatz variational eigensolver (ADAPT-VQE). This method employs a space diagonalization technique operating within a subspace of states identified along the convergence pathway of ADAPT-VQE as it seeks the ground state solution. The algorithm effectively leverages information gathered during ground state optimisation to efficiently calculate excited states, demonstrating accuracy with a minimal increase in computational resources. The core innovation lies in the selection of the subspace for diagonalization, utilising the states encountered during the ADAPT-VQE convergence process rather than arbitrarily defining this space. This adaptive approach ensures that the selected subspace contains states most relevant to both the ground and excited states, improving the efficiency and accuracy of the calculation.

Researchers demonstrate that this method not only accurately determines excited state energies but also potentially accelerates the convergence of the ADAPT-VQE algorithm itself, creating a synergistic effect. Validation of the algorithm occurs through application to model systems, including like-particle pairing and neutron-proton pairing, confirming the method’s ability to accurately reproduce known results. Furthermore, the algorithm successfully models molecular dissociation, a more complex scenario that highlights its versatility and robustness, and demonstrates its potential for tackling realistic quantum chemistry problems.