Researchers at Indiana University and Virginia Tech have developed a new algorithm that dramatically accelerates classical simulation of complex quantum systems. The variational double bracket flow (vDBF) algorithm, using a technique called Pauli Propagation, achieves sub-1% relative errors for Heisenberg and Hubbard lattices of up to 128 qubits. vDBF accurately simulates a 10×10 Heisenberg lattice, containing 100 qubits, in approximately 2 minutes on a single CPU thread, a task that previously required over 50 hours using 64 threads with DMRG. These results demonstrate that classical simulation techniques can provide practical tools for many-body physics.

Pauli Propagation Accelerates Correlated Quantum System Simulation

This advance uses Pauli Propagation, a technique initially created for benchmarking quantum hardware, and combines it with greedy operator selection, coefficient-based fluctuation truncation and energy-variance extrapolation to improve accuracy. The resulting efficiency addresses a longstanding challenge in computational physics and chemistry: accurately modeling strongly correlated quantum systems. Classical methods rapidly evolved to match or exceed the quantum results, with algorithms like Sparse Pauli Dynamics and Pauli Propagation proving effective at simulating deep.

This competitive dynamic demonstrates how attempts to build quantum computers are simultaneously driving innovation in classical computational techniques. The vDBF algorithm’s performance is particularly notable when contrasted with DMRG, a tensor network method efficient for one-dimensional systems but struggling with higher dimensions. “Pauli propagation enables fast classical simulation of strongly correlated quantum systems,” the authors state, highlighting the core benefit of their approach. On the maximally frustrated 8×8 $J_{1} - J_{2}$ lattice and the hole-doped 8×8 Hubbard model, the tightest thresholds extrapolate to within a few tenths of a percent of the best published variational estimates.

Future work will focus on expanding the algorithm’s capabilities to calculate properties beyond just ground state energy, potentially unlocking even more detailed insights into the behavior of complex quantum materials.

Greedy Selection and Truncation Enhance vDBF Accuracy

Rather than exhaustively exploring all potential operators, vDBF employs a greedy selection strategy, prioritizing those with the most significant impact on refining the ground state energy estimate. This focused approach, combined with coefficient-based fluctuation truncation, manages the exponential growth in computational complexity that typically plagues simulations of strongly correlated quantum systems.

The algorithm’s design allows it to accumulate terms strategically, building a flow generator for each iteration without requiring excessive computational resources. The algorithm’s ability to deliver accurate results with significantly reduced computational resources positions it as a valuable tool for exploring complex quantum systems, offering a compact operator-based route to ground-state energy estimation without explicitly storing a many-body wavefunction.

The vDBF calculations were performed using custom software, DBF.jl and PauliOperators.jl, designed for efficient binary manipulations with standard symplectic Pauli representations. Detailed analysis of the Heisenberg model reveals a progression of accuracy as thresholds are tightened.

vDBF Performance: 2 Minutes vs. 50 Hours for 10×10 Heisenberg Lattice

This performance leap stems from vDBF’s combination of Pauli propagation with gradient-based selection of Pauli generators, coefficient-based fluctuation truncation and energy-variance extrapolation, creating a compact operator-based route that bypasses the need to explicitly store a many-body wavefunction. The efficiency extends beyond simpler bipartite lattices, demonstrating the algorithm’s versatility in tackling more complex quantum systems. These systems, prone to sign problems that hinder traditional simulation techniques, still yielded results within 0.3% of the best published variational estimates after threshold extrapolation.

The 8×8 Hubbard model at half-filling (128 qubits) required more than 80 hours on 64 threads for DMRG calculations to reach a comparable energy, while vDBF achieved approximately 0.4% accuracy in 40 minutes. The ability of vDBF to achieve these results with significantly reduced computational resources highlights its potential as a practical tool for studying strongly correlated systems. The work demonstrates that the same core ideas can serve as efficient computational kernels for estimating ground-state energies, offering a promising alternative to existing methods.

For the hole-doped 8×8 Hubbard model at U/t = 4, the tightest vDBF thresholds extrapolate to within 0.625% of the best published variational estimates.

vDBF Validation on 84-Qubit Hexabenzocoronene π-Valence Active Space

Calculations on the full π-valence space of hexabenzocoronene, a system requiring 84 qubits, demonstrate the algorithm’s applicability to molecular systems beyond lattice models. The most reliable extrapolated correlation energies agree with DMRG to within 1%. These results demonstrate that classical simulation techniques developed in the context of quantum advantage benchmarking can provide practical tools for many-body physics.

Classical Simulation Tools Inspired by Quantum Advantage Benchmarking

The development of algorithms inspired by the pursuit of quantum advantage is now yielding practical tools for classical simulation, with a new method demonstrating a significant speedup for complex quantum systems. This accuracy, coupled with the algorithm’s efficiency, suggests a broadening utility beyond the initial goal of benchmarking quantum computers. This speed advantage stems from a combination of techniques, including greedy operator selection and coefficient-based fluctuation truncation, which allow for efficient approximation of ground state energies without explicitly storing a many-body wavefunction.

The team’s approach also incorporates energy-variance extrapolation, capitalizing on the expected linear relationship between energy and variance as convergence is approached. Beyond speed, the algorithm demonstrates accuracy on systems that pose challenges for other computational methods. This level of precision is notable, as these systems are often difficult to simulate using quantum Monte Carlo techniques.

👉 More information
🗞 Pauli Propagation Enables Fast Classical Simulation of Strongly Correlated Quantum Systems
✍️ Chinmay Shrikhande, Arnab Bachhar, José Aarón Rodríguez-Jiménez, Edward F. Valeev and Nicholas J. Mayhall
🧠 DOI: http://link.aps.org/doi/10.1103/kq3v-whcq

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