Abstract Cavity-modified chemistry uses strong light-matter interactions to modify the electronic properties of molecules in order to enable new physical phenomena such as novel reaction pathways. As cavity chemistry often involves critical regions where configurations become nearly degenerate, the ability to treat multireference problems is crucial to understanding polaritonic systems. In this Letter, we show through the use of a unitary ansatz derived from the anti-Hermitian contracted Schrödinger equation that cavity-modified systems with strong correlation, such as the deformation of rectangular H4 coupled to a cavity mode, can be solved efficiently and accurately on a quantum device. In contrast, while our quantum algorithm can be made formally exact, classical-computing methods as well as other quantum-computing algorithms often yield answers that are both quantitatively and qualitatively incorrect. Additionally, we demonstrate the current feasibility of the algorithm on near intermediate-scale quantum hardware by computing the dissociation curve of H2 strongly coupled to a bosonic bath.
Abstract Cavity-modified chemistry uses strong light-matter interactions to modify the electronic properties of molecules in order to enable new physical phenomena such as novel reaction pathways. As cavity chemistry often involves critical regions where configurations become nearly degenerate, the ability to treat multireference problems is crucial to understanding polaritonic systems. In this Letter, we show through the use of a unitary ansatz derived from the anti-Hermitian contracted Schrödinger equation that cavity-modified systems with strong correlation, such as the deformation of rectangular H4 coupled to a cavity mode, can be solved efficiently and accurately on a quantum device. In contrast, while our quantum algorithm can be made formally exact, classical-computing methods as well as other quantum-computing algorithms often yield answers that are both quantitatively and qualitatively incorrect. Additionally, we demonstrate the current feasibility of the algorithm on near intermediate-scale quantum hardware by computing the dissociation curve of H2 strongly coupled to a bosonic bath.
In the field of polaritonic chemistry, strong light-matter interactions are used to alter chemical reactions inside optical cavities. To understand these processes, the development of reliable theoretical models is essential. While traditional methods have to balance accuracy and system size, new developments in quantum computing offer a path for accurate calculations on currently available quantum devices. Here, we introduce the quantum electrodynamics unitary coupled cluster (QED-UCC) method combined with the Variational Quantum Eigensolver algorithm, as well as the quantum electrodynamics equation-of-motion (QED-EOM) method formulated in the qubit basis that allow accurate calculations of ground-state and excited-state properties of strongly coupled light-matter systems suitable for quantum computers. These methods show excellent agreement with the exact reference results and can outperform their traditional counterparts when strong electronic correlations become significant. This work sets the stage for future developments of polaritonic quantum chemistry methods suitable for both classical and quantum computers.
Computer simulation is central to understanding the behaviour of matter. Yet, more than a century after the development of quantum theory, first-principles simulation of chemistry remains a daunting challenge, owing to the exponential growth in memory required to represent interacting quantum particles such as electrons in molecules. Quantum computing offers, in principle, a fundamentally more efficient paradigm for simulating quantum systems, with quantum chemistry often cited as a flagship application. However, many quantum algorithms face intrinsic limitations, and any genuine quantum advantage must surpass the strong baseline set by decades of progress in classical algorithms and hardware. While classical methods often suffice for simulating weakly correlated systems, systems with many strongly correlated electrons remain a challenge for both classical and quantum approaches. In this thesis, we develop quantum algorithms for solving the time-independent Schrödinger equation, with a focus on molecular systems with strongly correlated electrons. We introduce a framework for identifying a compact set of states that parametrise the many-body wavefunction by capturing the correlation due to spin coupling between localised electrons. This representation requires very few variational parameters but incurs a very high memory cost on classical computers. To overcome this, we design quantum circuits that efficiently prepare such states by exploiting their symmetry, encoding the dominant entanglement structure of electronic wavefunctions into the initial qubit states. Through theoretical analysis and classical simulations of quantum computers, we show that this substantially reduces the quantum resources required to accurately compute ground- and excitedstate properties. Finally, we develop an approach for approximating the optimal ansatz within the variational quantum eigensolver, an algorithm designed for near-term quantum devices. Our method constructs wavefunctions from products of symmetrypreserving unitary operators and couples discrete and continuous optimisation to yield highly compact representations of strongly correlated electrons using shallow quantum circuits. Together, these results establish complementary directions for embedding problemspecific structure into quantum simulation algorithms, advancing the practical simulation of strongly correlated electrons.
Efficient simulation of strongly correlated electrons has become a routine tool in molecular electronic structure theory due to recent advances in approximate configuration interaction (CI) techniques. Nonetheless, the quantitative and predictive description of molecular electronic states remains a significant challenge due to the difficulty of computing all-electron correlation beyond CI. Here, we describe a new open-source implementation of the anti-Hermitian contracted Schrödinger equation (ACSE) for use in accurate simulation of all-electron correlation in molecules. In contrast to standard approaches via multireference perturbation theory, the scaling of the ACSE does not depend on the complexity of the strongly correlated reference wavefunction. Furthermore, the ACSE employs the exact electronic Hamiltonian, rather than an approximate perturbative Hamiltonian. Our benchmark results demonstrate good accuracy for main group and transition metal systems, in weakly and strongly correlated regimes, with various basis sets, and for ground and excited states. The results suggest that the ACSE has potential as a scalable and robust technique for simulating all-electron correlation in molecular ground and excited states.
In the field of ab initio polaritonic chemistry, the use of quantum computers may offer, in the long term, a promising computational pathway for simulating and exploring novel cavity-induced light-matter phenomena. Addressing such problems on emerging platforms, however, already presents significant challenges that need to be considered for near-term applications. Within the framework of the variational quantum eigensolver (VQE), a key question concerns the development of quantum circuit Ans\"atze capable of encoding strongly correlated electron-photon states at a reasonable resource cost. Motivated by this question, in this work we develop different Ansatz strategies covering not only conventional qubit-based approaches but also higher-dimensional information units. Specifically, we introduce a set of circuits tailored to three different quantum computing architectures: (i) qubits, (ii) qudits, and (iii) hybrid qubit-qumode units of information. All circuits are designed to be both compact and physically motivated, with a central element being the development of spin-adapted electron-photon entangling fragment circuits tailored to the native capabilities of each platform. Integrating the different Ans\"atze within the state-averaged VQE, we numerically benchmark the three strategies on a cavity-embedded H2 molecule using state-vector simulations. Our results show that each proposed Ansatz achieves high accuracy in encoding the ground, first, and second polaritonic eigenstates of the system, even reproducing characteristic light-matter phenomena such as light-induced avoided crossings and conical intersections. This prospective work, beyond introducing multiple computational strategies adapted to different platforms, also highlights the potential of higher-dimensional quantum architectures to address hybrid fermion-boson systems.
Recent years have witnessed a surge of experimental and theoretical interest in controlling the properties of matter, such as its chemical reactivity, by confining it in optical cavities, where the enhancement of the light-matter coupling strength leads to the creation of hybrid light-matter states known as polaritons. However, ab initio calculations that account for the quantum nature of both the electromagnetic field and matter are challenging and have only started to be developed in recent years. We introduce a deep learning variational quantum Monte Carlo method to solve the electronic and photonic Schrödinger equations of molecules trapped in optical cavities. We extend typical electronic neural network wave function ansätze to describe joint fermionic and bosonic systems, i.e., electron-photon systems, in a quantum Monte Carlo framework. We apply our method to hydrogen molecules in a cavity, computing both ground and excited states. We assess their energy, dipole moment, charge density shift due to the cavity, the state of the photonic field, and the entanglement developed between the electrons and photons. Where possible, we compare our results with more conventional quantum chemistry methods proposed in the literature, finding good qualitative agreement, thus extending the range of scientific problems that can be tackled using machine learning techniques.
The recent advent of quantum algorithms for noisy quantum devices offers a new route toward simulating strong light–matter interactions of molecules in optical cavities for polaritonic chemistry. In this work, we introduce a general framework for simulating electron–photon-coupled systems on small, noisy quantum devices. This method is based on the variational quantum eigensolver (VQE) with the polaritonic unitary coupled cluster (PUCC) ansatz. To achieve chemical accuracy, we exploit various symmetries in qubit reduction methods, such as electron–photon parity, and use recently developed error mitigation schemes, such as the reference zero-noise extrapolation method. We explore the robustness of the VQE-PUCC approach across a diverse set of regimes for the bond length, cavity frequency, and coupling strength of the H 2 molecule in an optical cavity. To quantify the performance, we measure two properties: ground-state energy, fundamentally relevant to chemical reactivity, and photon number, an experimentally accessible general indicator of electron–photon correlation.