Computational supremacy in quantum simulation (2403.00910v1)

Abstract: Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. Establishing this capability, especially for impactful and meaningful problems, remains a central challenge. One such problem is the simulation of nonequilibrium dynamics of a magnetic spin system quenched through a quantum phase transition. State-of-the-art classical simulations demand resources that grow exponentially with system size. Here we show that superconducting quantum annealing processors can rapidly generate samples in close agreement with solutions of the Schr\"odinger equation. We demonstrate area-law scaling of entanglement in the model quench in two-, three- and infinite-dimensional spin glasses, supporting the observed stretched-exponential scaling of effort for classical approaches. We assess approximate methods based on tensor networks and neural networks and conclude that no known approach can achieve the same accuracy as the quantum annealer within a reasonable timeframe. Thus quantum annealers can answer questions of practical importance that classical computers cannot.

• The paper shows that superconducting quantum annealers achieve computational supremacy by efficiently simulating quantum phase transitions in TFIMs.
• The study employs QA processors across various lattice dimensions, outperforming classical tensor network methods in speed and scalability.
• Extensive numerical evidence confirms that QA processors can simulate systems with thousands of qubits, highlighting potential in material science and AI.

Analysis of Computational Supremacy in Quantum Simulation

The paper, titled "Computational Supremacy in Quantum Simulation," presents an evaluation of quantum anealing (QA) processors as an alternative computational paradigm for simulating non-equilibrium quantum dynamics. The core assertion is their superior capability in tackling problems that are currently unmanageable for classical computational frameworks. This evaluation focuses on simulating quantum phase transitions in transverse-field Ising models (TFIMs). The paper's applicability spans condensed matter physics and optimization domains, marking the problems as relevant to practical interests.

Design and Methodology

The research employs superconducting QA processors to simulate quantum annealing processes through multiple system structures such as 2D, 3D, and infinite-dimensional lattices. It is crucial to highlight that the systems' dynamics are gauged by transitioning through quantum phase changes—a zone traditionally plagued by exponential difficulty in classical computational approaches. The QA processors generate solutions that align closely with the Schrödinger equation for these systems, demonstrating a significant efficiency in performance when compared to known classical simulation capabilities.

Comparative Analysis with Classical Methods

The paper contrasts QA processors' efficiency to classical methodologies, employing tensor networks and neural networks. Notably, it deploys matrix product states (MPS) and projected entangled-pair states (PEPS) as representatives of the classical approaches. Among these, MPS demonstrates scalability limitations due to area-law constraints, particularly in high-dimension simulations where entanglement entropy grows significantly. Conclusively, the MPS methods meet substantial computational barriers in this domain, appended by polynomial scaling demands in resource allocation like memory and time requirements.

The practical constraints highlight the QA's advantage in this context: the measured performance of the QA processors, in terms of speed and scalability, reflects both short-term superiority and potential untapped capacity for larger system sizes.

Findings and Numerical Evidence

The paper supports these claims with substantive numerical evidence. It demonstrates that QA processors outperform even the finest classical approaches when simulations go beyond minor scales. The quantum simulation resolves complex states at significant sizes (spanning several thousand qubits), which is presently impractical using classical simulation to both time and resource intensiveness. For instance, computational requirements extrapolated for classical systems indicated runtime scales extending to millions of years on existing supercomputing platforms—even with optimistic scaling assumptions.

Furthermore, the paper emphasizes the scaling of critical dynamic exponents under these QA simulations, which remain consistent with theoretical expectations across various lattice topologies.

Practical Implications and Future Prospects

The implications extend toward promising advancements in material sciences and AI, leveraging QA's potential beyond experimental scales in optimization-related scenarios. On a broader spectrum, the work encourages the growth of quantum computation in practical domains where classical methods scale infeasibly.

Conclusions

In conclusion, the paper delineates clear strides QA processors have taken over classic computational methods in quantum simulations. This work underscores QA systems as a viable avenue, particularly as computations explore scenarios traditionally beyond classical reach. Therefore, QA presents not only a robust alternative but also catalyzes the advent of novel computational frameworks for solving extensive, high-dimensional quantum dynamical systems.