Qumode Subspace Eigensolver Achieves Molecular Excited State Calculations with Bosonic Qumodes

Calculating the excited states of molecules presents a significant challenge for computational chemistry, yet understanding these states is crucial for predicting chemical reactions and designing new materials. Rishab Dutta, Cameron Cianci, and Alexander V. Soudackov, alongside colleagues from Yale University, the University of Connecticut, and the University of Chicago, now present a new method for tackling this problem, called the Qumode Subspace Eigensolver. This approach uniquely combines the strengths of both quantum bits and quantum harmonic oscillators, known as qumodes, to create a more efficient and expressive computational framework. By mapping molecular properties onto these qumode systems, the team demonstrates a potential pathway towards simulating complex molecular behaviour with fewer computational resources than currently possible, opening new avenues for designing molecules and understanding chemical processes.

Qubit-Qumode Systems for Molecular Excited States

Scientists are exploring a new approach to quantum simulation, combining qubits and qumodes to model molecular behavior and calculate excited state energies. This hybrid approach leverages the strengths of both types of quantum systems to overcome limitations encountered when simulating complex molecules. The research focuses on simulating conical intersections, crucial points in the energy landscape of nucleobases, the building blocks of DNA and RNA, which govern photochemical processes. Researchers control the qumodes using SNAP gates, efficiently manipulating quantum states of continuous variable systems, successfully simulating potential energy surfaces and energies at conical intersections in nucleobases. The results demonstrate that this hybrid approach, combined with CQE and SNAP gates, provides an efficient way to simulate molecular systems and accurately calculate energies, including those at conical intersections. Successfully characterizing these intersections in nucleobases provides insights into their photochemical behavior and shows promise for scaling to larger, more complex molecules. This research represents a significant step forward in quantum simulation, offering a new pathway to understanding photochemical processes in biology and chemistry, such as DNA damage and photosynthesis. This approach harnesses the unique capabilities of circuit quantum electrodynamics (cQED) devices, utilizing bosonic qumodes alongside qubits to construct highly expressive quantum states, potentially surpassing conventional qubit-based methods. The team maps the electronic structure problem into a qubit representation before embedding it within the Fock space of bosonic qumodes, simplifying state preparation and reducing quantum resources. The method employs a structure similar to the subspace-search variational quantum eigensolver, optimizing over multiple orthogonal states within a single framework, efficiently initializing input states as Fock states, discrete photon number levels readily accessible with established cQED techniques.

This architecture allows for the design of bosonic quantum states native to qubit-qumode devices, particularly well-suited for representing electronic excited states, offering a distinct advantage over qubit-only approaches. Experiments involve encoding multiple qubits into the Fock space of a single qumode, enabling the calculation of expectation values by measuring the qumode photon number distribution. Numerical benchmarks demonstrate that qumode-based circuits achieve comparable, and in some cases superior, accuracy to conventional qubit-based quantum states. This hybrid quantum-classical algorithm addresses the challenge of accurately modeling the behavior of electrons in molecules, a task that quickly becomes intractable for classical computers. The team successfully mapped the electronic structure problem onto a qubit-qumode system, enabling efficient state preparation and reducing quantum resources required for calculations, demonstrating performance through simulations of both dihydrogen and a conical intersection in cytosine. Researchers explored a bosonic model Hamiltonian to rigorously assess the expressivity of qumode gates, identifying specific scenarios where qumode-based implementations demonstrably outperform purely qubit-based approaches.

The results reveal instances where a simple qumode gate achieves comparable or superior accuracy to more complex qubit circuits in representing both ground and excited states. This breakthrough delivers a new paradigm for variational quantum algorithms, moving beyond traditional qubit-based systems to harness the advantages of bosonic degrees of freedom. The QSS-VQE algorithm is structured within a subspace-search framework, utilizing Fock states to efficiently initialize input states on the qumode platform. This approach utilises bosonic qumodes, the natural building blocks of circuit electrodynamics devices, to represent quantum information, offering a potentially more efficient alternative to traditional qubit-based methods. By mapping electronic structure problems onto the Hilbert space of these qumodes, the method simplifies state preparation and reduces the resources needed for computation, demonstrating performance through simulations of dihydrogen and a model system representing a conical intersection in cytosine. Results indicate that the qumode-based quantum state achieved comparable, or improved, energy accuracy compared to qubit-only approaches, particularly for complex systems with nearly degenerate excited states.

Furthermore, the researchers identified specific model bosonic Hamiltonians where qumode gates outperform their qubit-based counterparts, suggesting advantages in certain computational regimes. The authors acknowledge that their study focused on encoding qubits within a single qumode, and future work could explore scaling the method by incorporating multiple qumodes and more complex quantum states. This research represents a step towards harnessing the potential of bosonic quantum processors for simulating complex quantum systems, potentially exceeding the capabilities of purely qubit-based architectures.