Google's quantum supremacy announcement has received broad questions from academia and industry due to the debatable estimate of 10,000 years' running time for the classical simulation task on the Summit supercomputer. Has quantum supremacy already come? Or will it come in one or two decades later? To avoid hasty advertisements of quantum supremacy by tech giants or quantum startups and eliminate the cost of dedicating a team to the classical simulation task, we advocate an open-source approach to maintain a trustable benchmark performance. In this paper, we take a reinforcement learning approach for the classical simulation of quantum circuits and demonstrate its great potential by reporting an estimated simulation time of less than 4 days, a speedup of 5.40x over the state-of-the-art method. Specifically, we formulate the classical simulation task as a tensor network contraction ordering problem using the K-spin Ising model and employ a novel Hamiltonina-based reinforcement learning algorithm. Then, we establish standard criteria to evaluate the performance of classical simulation of quantum circuits. We develop a dozen of massively parallel environments to simulate quantum circuits.

Quantum machine learning (QML) is recognized as a promising approach to harness quantum computing for learning tasks [1-3]. As with all quantum algorithms, a central question is whether QML holds potential for quantum advantage [4-7] over classical computing. The counter-narrative to quantum advantage is dequantization, where upon close inspection certain quantum algorithms yield no benefit over classical counterparts, as one can classically solve the task at hand. Dequantization of quantum algorithms for machine learning, in particular, has seen a surge of interest in recent years, leaving few claims of quantum advantage unchallenged [8-12]. While QML models for classical data can be studied from several perspectives, significant theoretical developments have emerged from investigating the function families that parametrized quantum circuits (PQCs) can give rise to [8, 10, 13-16]. Characterizing the functional forms arising from PQCs allows us to delineate the boundaries of quantum learning and guide the search for advantage.

Measurement-induced entanglement (MIE) captures how local measurements generate long-range quantum correlations and drive dynamical phase transitions in many-body systems. Yet estimating MIE experimentally remains challenging: direct evaluation requires extensive post-selection over measurement outcomes, raising the question of whether MIE is accessible with only polynomial resources. We address this challenge by reframing MIE detection as a data-driven learning problem that assumes no prior knowledge of state preparation. Using measurement records alone, we train a neural network in a self-supervised manner to predict the uncertainty metric for MIE--the gap between upper and lower bounds of the average post-measurement bipartite entanglement. Applied to random circuits with one-dimensional all-to-all connectivity and two-dimensional nearest-neighbor coupling, our method reveals a learnability transition with increasing circuit depth: below a threshold, the uncertainty is small and decreases with polynomial measurement data and model parameters, while above it the uncertainty remains large despite increasing resources. We further verify this transition experimentally on current noisy quantum devices, demonstrating its robustness to realistic noise. These results highlight the power of data-driven approaches for learning MIE and delineate the practical limits of its classical learnability.

It should be needed to sample one million samples, achieving the required XEB. Figure 1 shows a corresponding circuit example. The sampling process using the quantum circuit is computed as follows, 1. Quantum circuits: There have been many quantum circuits proposed as follows, Sycamore quantum [3]: It consists of 53 qubits and 20 cycles. For the Boson sampling problem, it only needs 200 seconds to finish this task, while it needs 10, 000 years for classical simulation. For the Gaussian Boson Sampling problem, it can use 200 s to finish up to a million times compared with classical simulations.

Google's "quantum supremacy" announcement [3] has received broad questions from academia and industry due to the debatable estimate of 10, 000 years' running time for the classical simulation task on the Summit supercomputer. Has "quantum supremacy" already come? Or will it come in one or two decades later? To avoid hasty advertisements of "quantum supremacy" by tech giants or quantum startups and eliminate the cost of dedicating a team to the classical simulation task, we advocate an open-source approach to maintain a trustable benchmark performance. In this paper, we take a reinforcement learning approach for the classical simulation of quantum circuits and demonstrate its great potential by reporting an estimated simulation time of less than 4 days, a speedup of 5 .40

We implement a quantum generalization of a neural network on trapped-ion and IBM superconducting quantum computers to classify MNIST images, a common benchmark in computer vision. The network feedforward involves qubit rotations whose angles depend on the results of measurements in the previous layer. The network is trained via simulation, but inference is performed experimentally on quantum hardware. The classical-to-quantum correspondence is controlled by an interpolation parameter, $a$, which is zero in the classical limit. Increasing $a$ introduces quantum uncertainty into the measurements, which is shown to improve network performance at moderate values of the interpolation parameter. We then focus on particular images that fail to be classified by a classical neural network but are detected correctly in the quantum network. For such borderline cases, we observe strong deviations from the simulated behavior. We attribute this to physical noise, which causes the output to fluctuate between nearby minima of the classification energy landscape. Such strong sensitivity to physical noise is absent for clear images. We further benchmark physical noise by inserting additional single-qubit and two-qubit gate pairs into the neural network circuits. Our work provides a springboard toward more complex quantum neural networks on current devices: while the approach is rooted in standard classical machine learning, scaling up such networks may prove classically non-simulable and could offer a route to near-term quantum advantage.

Quantum computing is an exciting non-Von Neumann paradigm, offering provable speedups over classical computing for specific problems. However, the practical limits of classical simulatability for quantum circuits remain unclear, especially with current noisy quantum devices. In this work, we explore the potential of leveraging Large Language Models (LLMs) to simulate the output of a quantum Turing machine using Grover's quantum circuits, known to provide quadratic speedups over classical counterparts. To this end, we developed GroverGPT, a specialized model based on LLaMA's 8-billion-parameter architecture, trained on over 15 trillion tokens. Unlike brute-force state-vector simulations, which demand substantial computational resources, GroverGPT employs pattern recognition to approximate quantum search algorithms without explicitly representing quantum states. Analyzing 97K quantum search instances, GroverGPT consistently outperformed OpenAI's GPT-4o (45\% accuracy), achieving nearly 100\% accuracy on 6- and 10-qubit datasets when trained on 4-qubit or larger datasets. It also demonstrated strong generalization, surpassing 95\% accuracy for systems with over 20 qubits when trained on 3- to 6-qubit data. Analysis indicates GroverGPT captures quantum features of Grover's search rather than classical patterns, supported by novel prompting strategies to enhance performance. Although accuracy declines with increasing system size, these findings offer insights into the practical boundaries of classical simulatability. This work suggests task-specific LLMs can surpass general-purpose models like GPT-4o in quantum algorithm learning and serve as powerful tools for advancing quantum research.

The above citations are from SAO/NASA ADS (last updated successfully 2021-07-06 03:52:39). The list may be incomplete as not all publishers provide suitable and complete citation data. On Crossref's cited-by service no data on citing works was found (last attempt 2021-07-06 03:52:37). This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license.