The Future of Quantum Computing: Streamlining Excited State Calculations with CPVQD Algorithm

Insider Brief:

• Researchers from NVIDIA, Stony Brook University, and Brookhaven National Laboratory have revolutionized the computation of excited states in quantum systems with the innovative charge-preserving algorithm (CPVQD).

• CPVQD harnesses symmetry and conserved charges to optimize calculations, reduce system dimensionality, and enhance computational efficiency in quantum chemistry and nuclear physics applications.

• Successful testing on systems with up to 24 qubits, utilizing NVIDIA’s CUDA-Q platform and the NERSC Perlmutter system, has showcased faster convergence and superior computational performance.

Calculating excited states in quantum systems has long been a significant challenge in the realm of quantum computing, especially in fields like quantum chemistry, high-energy physics, and nuclear physics. Traditional methods have proven to be computationally expensive and impractical on current quantum hardware due to their reliance on deep circuits and controlled unitaries. A recent arXiv preprint sheds light on a groundbreaking development by researchers from NVIDIA, Stony Brook University, and Brookhaven National Laboratory, introducing the charge-preserving VQD algorithm to revolutionize these computations using both quantum and classical processing units for enhanced efficiency.

VQD: Lesser-Known, But Not Of Lesser Value

The variational quantum deflation (VQD) algorithm, an extension of the widely studied variational quantum eigensolver, enables the computation of excited states—an essential element in applications spanning from quantum chemistry to condensed matter physics. While the standard VQD algorithm effectively determines excited states, its reliance on controlled unitaries poses limitations, making large-scale simulations challenging. This is particularly prevalent on existing quantum hardware with inherent error and noise vulnerabilities.

The introduction of the charge-preserving VQD (CPVQD) algorithm, as detailed in the paper, overcomes these inefficiencies by leveraging symmetry and conserved charges, leading to a reduction in system dimensionality for quicker and more reliable computations.

Streamlining Quantum Calculations with Charge-Preserving VQD

CPVQD operates within a specific charge sector, aligning with conserved physical quantities like electric charge to streamline computations within the system’s subset. By focusing calculations on this sector, unnecessary computations on irrelevant states are avoided, optimizing efficiency significantly.

The study outlines two key methods of dimensional reduction:

• Projection Method: Reduces system dimensionality by projecting the Hamiltonian onto the desired charge sector, discarding irrelevant states.

• Constraint Method: Constrains the Hamiltonian with additional terms to ensure charge preservation, maintaining the original qubit count while refining the optimization process for relevant state consideration.

Both methods prioritize computational efficiency while upholding result integrity. Testing of CPVQD on simulations of up to 24 qubits has demonstrated remarkable improvements in computational performance.

CPVQD Applications From Quantum Chemistry to Nuclear Physics

The application of CPVQD spans various domains, including quantum chemistry and nuclear physics. In quantum chemistry, the algorithm successfully computed excited states of molecules like hydrogen (H2) and helium hydride (HeH+) in different charge states, showcasing its versatility and accuracy.

For nuclear physics, CPVQD computed spectra and mass gaps of quantum field theories like the Schwinger model, offering insights into particle interactions and phase transitions within quantum systems.

CUDA-Q and Perlmutter Combine for Advanced Quantum Simulations

With a team primarily composed of NVIDIA scientists, the research uniquely leveraged CUDA-Q—an open-source platform facilitating hybrid quantum-classical computing—to integrate classical GPUs seamlessly with quantum processors. The utilization of NERSC’s Perlmutter system for large-scale simulations on a state vector simulator unveiled the potential of hybrid computing in advancing quantum research capabilities.

Integrating QPU and GPU offers accelerated convergence in optimizing parameters of quantum circuits employed in the VQD algorithm, aiding in circumventing current quantum hardware limitations by delegating certain computations to classical systems.

Not Without Limitations

Despite significant efficiency enhancements, the CPVQD algorithm presents challenges, notably the impact of noise and decoherence on quantum hardware, potentially compromising result accuracy. Real-world implementation on quantum devices may face constraints due to hardware imperfections.

Additionally, while projection and constraint methods excel in simplifying computations by concentrating on relevant charge sectors, heuristic determination of charge sector constraints could hinder the algorithm’s convergence in accurately computing certain excited states within intricate systems.

Scaling the algorithm to larger systems remains a concern, requiring further optimization beyond the tested 24-qubit limit to sustain efficiency.

Implications and Future Directions

Despite limitations, the CPVQD algorithm holds promise in overcoming existing method constraints and enabling large-scale simulations in high-energy physics, nuclear physics, and quantum chemistry. The team envisions extending CPVQD to other quantum algorithms, broadening its application scope to algorithms such as Subspace Search VQE (SSVQE) and ADAPT-VQE.

Key contributors to the study include Zohim Chandani, Kazuki Ikeda, Zhong-Bo Kang, Dmitri E. Kharzeev, Alexander McCaskey, Andrea Palermo, C.R. Ramakrishnan, Pooja Rao, Ranjani G. Sundaram, and Kwangmin Yu.