New variational quantum algorithms developed at University of Kansas and Brookhaven National Laboratory achieved unprecedented precision in calculating ground and excited states within the Gross-Neveu model, reducing energy errors to one part per hundred thousand (specifically between 0.00001 and 0.0002). These calculations extended up to 400 qubits for certain scenarios through new methods for simulating quantum systems via accurate preparation of their lowest energy states.

These advancements utilise symmetry-preserving circuits which restrict computational searches to conserved charge sectors, essentially focusing on relevant solutions. This approach achieved tiny errors when calculating system energies, improving upon previously published results at comparable scales of complexity. At University of Kansas and Brookhaven National Laboratory, unprecedented accuracy, errors as low as one part per hundred thousand, was achieved when simulating quantum systems using these new variational algorithms.

The team focused on the Gross-Neveu model; building a miniature version of reality to study how particles interact. They successfully prepared both ground states, representing the lowest energy configuration of a system, and excited states up to scales of 400 qubits through circuits designed to preserve key symmetries within the simulation, restricting calculations to only relevant solutions.

These advancements surpass previously published results for similar complex scenarios, but rely upon comparison with established techniques like Density Matrix Renormalization Group, a benchmark akin to an extremely accurate yet slow calculator used to verify approximations. But can these methods be scaled further without sacrificing accuracy or introducing new computational challenges.

Variational algorithms unlock unprecedented accuracy in simulating large fermionic systems

Relative energy errors dropped to as low as 1 times 10^-5 using new variational quantum algorithms, a level of precision previously impossible due to limitations in algorithmic accuracy and needed computational resources for complex fermionic systems like the Gross-Neveu model. At University of Kansas and Brookhaven National Laboratory, scientists demonstrated that their fixed ansatzes and SC-ADAPT-VQE method accurately prepare ground states while preserving fermion number symmetries up to scales of 400 qubits with matrix product state evaluations.

This improvement allows physicists a pathway towards understanding strongly correlated materials and high-energy physics phenomena by exploring more intricate interactions within these models. Simulations revealed energy deviations between $0.35\% and 1.76\%$ when compared against density-matrix renormalization-group reference values at maximum bond dimension 256; imposing flavour number conservation, ensuring circuits respect individual fermion counts, improved achieved energies during tests with two flavours, showing how stricter symmetry constraints can enhance accuracy in quantum algorithms.

Scaling Quantum Simulations Presents Challenges Despite Significant Progress

The successful simulation of the Gross-Neveu model opens doors to exploration of both strongly correlated materials and high-energy physics, though this progress isn’t without caveats. SC-ADAPT-VQE shows promise by scaling simulations up to hundreds of qubits using classical methods like matrix product states, but consistent performance across all system sizes remains unproven. This limitation is acknowledged alongside difficulties comparing results directly with other techniques due to differing computational resources used during testing.

Refining performance across all system sizes will be a primary focus for further development; such improvements could unlock new insights into materials science and high-energy physics. Scalable circuits preserving either total or every flavor number represent an advance in preparing low-energy states important for complex quantum calculations, the team focused not simply on finding solutions, but physically realistic ones. Achieving energy errors as small as approximately 1 times 10^-5, 2 times 10^-4 demonstrates improved accuracy compared with previous methods when simulating models that simplify how particles interact, marking a step towards more reliable simulations of real physical systems. Evaluations extending to between 60 and 400 qubits yielded energy deviations of about 0.35%, 1.76% from reference values; this ability allows investigation into subtle effects arising from particle interactions without being overwhelmed by computational inaccuracies.

The researchers successfully simulated the Gross-Neveu model using scalable quantum circuits, preserving total or individual fermion numbers, and an adaptive variational quantum eigensolver (SC-ADAPT-VQE). Simulations were extended up to 400 qubits with deviations of approximately 0.35% -1.76% from reference values, indicating that enforcing flavor number conservation enhances results and allows for investigation into complex particle interactions. The authors plan further development to refine performance across all system sizes.

👉 More information
🗞 Symmetry-Preserving and Scalable Variational Circuits for the Lattice Gross-Neveu Model
✍️ Vivan Bhatt and Kyoungchul Kong (University of Kansas); Zhongtian Dong (Peking University); Kwangmin Yu (Brookhaven National Laboratory)
🧠 ArXiv: https://arxiv.org/abs/2610.30270

More like this