Quantum Algorithms Map Molecular Excited States

Srivathsan Poyyapakkam Sundar and colleagues at University of North present a new approach combining advanced quantum algorithms, ADAPT-VQE/LUCJ and q-sc-EOM, to calculate excited state potential energy surfaces in demanding chemical scenarios. The work sharply reduces the computational scaling of these calculations from O(N$^{12}$) to O(N$^{5}$) through the Davidson algorithm and basis rotation grouping. Importantly, the team implements the q-sc-EOM algorithm on real quantum hardware. By incorporating error mitigation strategies targeting gate and measurement errors, they achieve reasonably accurate excited-state energies, identifying gate noise as the key limitation and charting a path towards scalable, generally applicable quantum excited-state methods.

Davidson algorithm and basis rotation enable scalable quantum excited-state simulations

A novel method reduces the computational scaling of excited-state calculations from O(N$^{12}$) to O(N$^{5}$), a five-fold improvement that enables simulations previously impossible for all but the smallest molecules. This scaling reduction is crucial because traditional quantum chemical methods, such as coupled cluster theory, exhibit a steep computational cost that limits their applicability to larger systems. The O(N$^{12}$) scaling arises from the need to consider all possible electron excitations within the molecular system, a combinatorial explosion as the number of electrons (N) increases. By employing the Davidson algorithm, a technique originally developed for solving the Schrödinger equation in nuclear physics, the researchers efficiently diagonalise the large matrices associated with excited-state calculations. This algorithm iteratively refines an initial guess for the excited state, converging towards the true solution with significantly reduced computational effort. Furthermore, basis rotation grouping, a technique used to optimise the selection of basis functions, further contributes to the computational efficiency. This combination allows for the investigation of complex chemical scenarios, such as bond dissociation, which are particularly challenging for conventional methods due to the multi-configurational nature of the electronic wavefunction.

Implementing this algorithm on quantum hardware, coupled with error mitigation strategies like M3 readout error mitigation and symmetry projection, delivers reasonably accurate excited-state energies despite the limitations of current quantum processors. M3 readout error mitigation is a post-processing technique that estimates and corrects for errors arising from the measurement process on the quantum computer. Symmetry projection enforces the known symmetries of the molecular system, reducing the noise and improving the accuracy of the results. These error mitigation techniques are essential for extracting meaningful information from noisy quantum computations. The team’s successful implementation of q-sc-EOM on actual hardware represents a significant step towards realising the potential of quantum computers for tackling complex chemical problems.

Gate noise proved to be the primary source of error, highlighting a clear path for future hardware development and algorithm refinement. Quantum gates, the fundamental building blocks of quantum circuits, are susceptible to various sources of noise, including control errors and decoherence. These errors accumulate during the computation, degrading the accuracy of the results. Identifying gate noise as the dominant error source allows researchers to focus their efforts on developing more robust quantum gates and error correction techniques. The computational advance was validated by comparing results with the established classical EOM-CCSD method for molecules undergoing bond dissociation, specifically ammonia and water. Employing an active space of six electrons in six spatial orbitals for ammonia resulted in a 12-qubit system with 117 potential excitations; however, the ADAPT-VQE algorithm deliberately selected and optimised only 25 of these, demonstrating efficient resource allocation. The active space is a reduced set of orbitals and electrons used to approximate the full electronic structure, reducing the computational cost. ADAPT-VQE, a variant of the variational quantum eigensolver, adaptively selects the most important excitations to include in the calculation, further optimising resource usage.

Efficient resource allocation, combined with the excited-state calculation, successfully reproduced the full configuration interaction (FCI) energies, indicating a high degree of accuracy in capturing molecular correlation and providing insight into the algorithm’s performance. FCI is a highly accurate, but computationally expensive, method that serves as a benchmark for evaluating the performance of other quantum chemical methods. Achieving FCI-level accuracy with a reduced number of qubits demonstrates the efficiency and potential of the proposed algorithm. Assessing the impact of sampling errors, inherent to quantum hardware, provided a realistic evaluation of potential quantum utility. Quantum computations rely on sampling the output of a quantum circuit, and the number of samples required to achieve a desired level of accuracy is limited by the coherence time of the qubits. Understanding the impact of sampling errors is crucial for determining the feasibility of using quantum computers for practical applications. While the algorithm demonstrates promising accuracy, achieving excited-state properties suitable for spectroscopic analysis and practical applications still requires significant improvements in both quantum hardware and error mitigation techniques, particularly in reducing gate noise.

Demonstrating a functional quantum workflow for molecular excited state calculations

Accurately modelling molecular excited states remains a central goal in the pursuit of quantum utility, promising breakthroughs in fields ranging from materials science to drug design. Understanding the behaviour of molecules in excited states is crucial for predicting their optical properties, chemical reactivity, and biological activity. A viable path towards calculating these states on quantum hardware has been shown, but a fundamental tension exists regarding the practical advantage over established classical methods. The team, Irvine, acknowledge that their quantum approach does not definitively outperform the classical EOM-CCSD technique in terms of absolute accuracy currently; instead, it proves the possibility of obtaining reasonably accurate results and establishes a key benchmark for future development. EOM-CCSD is a widely used classical method for calculating excited states, but its computational cost limits its applicability to larger systems.

The significance of this work lies in demonstrating a functional quantum workflow, utilising algorithms such as q-sc-EOM and ADAPT-VQE/LUCJ on actual quantum hardware. Reducing the computational scaling to O(N$^{5}$) through algorithmic optimisation is particularly significant, enabling simulations of larger molecules previously inaccessible to all but the most powerful computers, and opening avenues for exploring more complex chemical systems. This scalability is essential for tackling real-world problems in chemistry and materials science. The team’s work identified gate noise as the primary limitation to achieving higher accuracy, directing future hardware development efforts towards noise reduction strategies. Addressing this limitation is crucial for realising the full potential of quantum computers for chemical simulations.

This work establishes a functional quantum workflow for calculating excited-state energies, a vital step towards realising practical applications of quantum computers in chemistry. By successfully implementing the algorithm on quantum hardware and combining it with error mitigation techniques, scientists have demonstrated a pathway beyond theoretical modelling. This workflow provides a template for future research in quantum chemistry, allowing researchers to explore more complex molecular systems and chemical processes. Paving the way for future investigations into more complex molecular systems and chemical processes, this research represents a significant step forward in the field of quantum chemistry and computational physics. The development of robust and scalable quantum algorithms for excited-state calculations will ultimately enable the design of new materials with tailored properties and the discovery of novel drugs with improved efficacy.

The researchers successfully demonstrated a quantum workflow for calculating excited-state energies, achieving reasonably accurate results on quantum hardware. This is important because calculating these energies is computationally demanding for classical computers, limiting the size of molecules that can be studied. By optimising the q-sc-EOM algorithm to reduce computational scaling to O(N$^{5}$), scientists were able to perform simulations previously inaccessible, and identified gate noise as the main source of error. The authors suggest this work establishes a benchmark for future development and paves the way for more complex molecular investigations.