Classical Computers Simulate Quantum Systems with up to 2000 Qubits

Researchers have developed a novel phase-space approach for emulating the continuous-time evolution of large qubit registers, addressing a significant challenge in quantum computing. Christian de Correc from Universit e Paris-Saclay, CNRS/IN2P3, IJCLab and Eviden Quantum Lab, Denis Lacroix from Universit e Paris-Saclay, CNRS/IN2P3, IJCLab, and Corentin Bertrand from Eviden Quantum Lab, detail a method based on statistical ensembles of mean-field trajectories, effectively replacing quantum fluctuations with classical ones. This technique scales favourably with system size, enabling simulations of up to several thousand qubits on conventional computers, and provides a valuable benchmark for comparison with methods restricted to smaller qubit numbers. The study, benchmarked on the -local transverse-field Ising model with up to 2000 qubits and extended to 2D and 3D Ising models, demonstrates the versatility and potential of this approach for exploring complex quantum systems.

Researchers have developed a new computational technique to simulate how to verify the accuracy of quantum simulations as the number of qubits increases and quantum processors become more powerful. The study introduces a phase-space approach, a method for approximating quantum dynamics using classical computations, and demonstrates its ability to model systems containing up to 2000 qubits. While existing classical emulation methods often struggle with increasing qubit numbers or complex interactions, this technique offers a scalable alternative with a computational cost that grows at a manageable rate, scaling with a quadratic cost relative to system size. The core of this advancement lies in a method that replaces the complex quantum behaviour of qubits with a statistical ensemble of classical trajectories. This ‘Phase-Space Approximation’ (PSA) effectively substitutes quantum fluctuations with classical ones, allowing for simulations on conventional computers and shares conceptual similarities with the discrete truncated Wigner approximation (dTWA), though it originates from a distinct theoretical framework and formulation. The formulation adopted here emphasizes the role of the density matrix, aiming to provide a more accessible presentation for researchers within the quantum computing community, building upon earlier work applying the PSA to fermionic many-body problems and adapting it to qubits with varying interaction topologies. The approach has been rigorously tested on the k-local transverse-field Ising model (TFIM), a standard benchmark in quantum information science, exploring systems with varying degrees of connectivity, from qubits interacting only with their nearest neighbours to those with all-to-all interactions. The researchers systematically varied the strength of the interactions and the number of qubits, up to 2000, to assess the method’s accuracy and limitations. A key parameter, η, is defined as J/h multiplied by k − k(k+1)/2L, where L represents the number of qubits, and serves as a measure of connectivity. Simulations were also performed on two- and three-dimensional Ising models, extending the technique beyond one-dimensional systems. The results indicate that the PSA accurately predicts the evolution of individual qubit properties, providing a valuable reference point for comparison with actual quantum computations. However, the method’s predictive power is less reliable when analysing properties that depend on the interactions between multiple qubits. Detailed analysis of the mean-field dynamics reveals how the approach approximates the evolution of Pauli matrices, showing reasonable agreement in tracking the time-dependent expectation values of X, Y, and Z operators for a 20-qubit system, particularly for lower values of η, such as 0.2 and 1. For instance, at η = 0.2 and k = 1, the mean-field approximation closely follows the exact evolution of the Pauli matrices over a time period of 10 units of h−1, while increasing k to 19 maintains qualitative accuracy but introduces deviations from the exact solution. This research provides a new tool for validating quantum simulations and understanding the limits of classical emulation as quantum computers continue to advance. The ability to simulate large qubit registers, even with approximations, is a critical step towards ensuring the reliability of future quantum technologies. Scientists pursuing scalable quantum computation face a persistent bottleneck in simulation, as verifying behaviour and developing algorithms demands computational power that rapidly exceeds the capacity of even the most advanced supercomputers. By employing a phase-space approach, researchers have demonstrated the ability to simulate the behaviour of qubit registers containing thousands of qubits, a substantial leap beyond the reach of many existing techniques. This access to larger, classically-simulated quantum systems allows for more rigorous testing of quantum algorithms and error correction schemes, accelerating the development cycle and providing a valuable benchmark against which to assess the performance of actual quantum hardware. Crucially, this method isn’t about replacing quantum computers, but rather augmenting the toolkit available to those building them. However, the modelling excels at predicting the behaviour of individual qubits but loses accuracy when examining correlations between qubits, a critical distinction as entanglement is the essence of quantum computation. Looking ahead, the challenge lies in refining these classical simulations to better capture multi-qubit interactions, potentially combining this phase-space approach with techniques like tensor networks to yield even more powerful and accurate models, ultimately guiding the development of genuinely scalable quantum technologies.