Hybrid VQE-CVQE Algorithm with Diabatic State Preparation Achieves Chemical Accuracy on Quantum Systems

Quantum computing promises to revolutionise fields from materials science to drug discovery, but realising this potential requires overcoming significant challenges in algorithm design and hardware limitations. John P. T. Stenger, C. Stephen Hellberg, and Daniel Gunlycke, all from the U. S. Naval Research Laboratory, have developed a novel hybrid algorithm that combines the strengths of both Variational Eigensolver (VQE) and Cascaded VQE (CVQE) approaches. This new method utilises a unique diabatic state preparation technique to generate the necessary quantum circuits, and importantly, it performs effectively on both near-term, intermediate-scale quantum computers and future, long-term error-corrected machines. The team’s implementation on the IBM Brisbane system achieves remarkably accurate results, falling well within the stringent criteria for chemical accuracy, representing a significant step forward in the pursuit of practical quantum computation for complex chemical systems.

The team demonstrates the algorithm on a system of interacting electrons and shows how it can be used on both long-term error-corrected and short-term intermediate-scale quantum computers. Simulations performed on IBM Brisbane produced energies well within chemical accuracy. This approach leverages diabatic state preparation, beginning with a parameterized unitary operator to generate a guiding state from a model Hamiltonian with a known ground state. The team evolved this state using a discretized time evolution operator, carefully controlling time steps to approximate adiabatic state preparation even on near-term quantum computers. Researchers then defined a computational subspace by measuring the generated guiding state and expanding the resulting basis set with states coupled through the system’s Hamiltonian.

The team constructed an effective Hamiltonian, projected onto this subspace, allowing them to determine the lowest eigenvalue using classical computational methods. This method adapts to various stages of quantum computer development, functioning effectively with error-correcting quantum computers, high-coherence systems, near-term devices, and current hardware. The core of this work involves generating a guiding quantum state using diabatic state preparation, a method for evolving an initial state towards the ground state of a target Hamiltonian. This guiding state is then measured, and the resulting measurement outcomes form a basis set used to define a subspace for subsequent calculations. The team expands this initial basis set by including additional states derived from applying the Hamiltonian, creating a combined set spanning the computational subspace.

Experiments demonstrate that this approach can achieve energies within chemical accuracy, a crucial benchmark for quantum chemistry simulations. The algorithm’s adaptability is a key achievement, as it is applicable to both near-term, intermediate-scale quantum computers and future fault-tolerant machines. Specifically, the team utilized the IBM Brisbane quantum computer to perform simulations, showcasing the algorithm’s immediate practicality. The method utilizes diabatic state preparation to generate a quantum variational guiding state, then projects the system’s Hamiltonian onto a subspace defined by measurement results, allowing for efficient calculation of the lowest eigenvalue using a classical computer. Demonstrations on a model system of interacting electrons achieved energies within chemical accuracy when implemented on current quantum hardware. The team identified three distinct regimes governing optimal algorithm performance, dependent on the number of time steps and their duration.

Their findings reveal that, for present-day quantum computers, minimizing circuit complexity is paramount, with the best results obtained when the number of time steps is kept to a minimum. The algorithm’s flexibility allows for potential optimization through parameter updates in the near term and, ultimately, direct adiabatic state preparation with the advent of fault-tolerant quantum computers. The authors acknowledge a limitation in that the observed regimes were demonstrated using a specific model system, though they anticipate their presence in a broader range of physically relevant models. Future research may focus on exploring these regimes across diverse systems and further refining the algorithm to leverage increasingly powerful quantum hardware.