A brief history of quantum vs classical computational advantage (2412.14703v1)

Abstract: In this review article we summarize all experiments claiming quantum computational advantage to date. Our review highlights challenges, loopholes, and refutations appearing in subsequent work to provide a complete picture of the current statuses of these experiments. In addition, we also discuss theoretical computational advantage in example problems such as approximate optimization and recommendation systems. Finally, we review recent experiments in quantum error correction -- the biggest frontier to reach experimental quantum advantage in Shor's algorithm.

• The paper surveys the history of experiments claiming quantum computational advantage, theoretical advantage scenarios, and advancements in quantum error correction.
• Recent quantum advantage experiments, such as Google's Sycamore and USTC's Gaussian boson sampling, face ongoing challenges and counter-simulation efforts from classical computing.
• Theoretical quantum advantages are explored, but realizing fault-tolerant quantum computing requires significant progress in quantum error correction, which is an active research area.

A Comprehensive Review of Quantum vs Classical Computational Advantage

The paper "A Brief History of Quantum vs Classical Computational Advantage" provides an exhaustive survey of the evolution, challenges, and current state of experiments claiming quantum computational advantage. The review meticulously compiles the experiments to date, investigates theoretical advantage scenarios, and accentuates ongoing developments in quantum error correction crucial for achieving practical quantum supremacy. The paper is authored by Ryan LaRose from the Center for Quantum Computing, Science, and Engineering at Michigan State University. This research encapsulates a comprehensive history and an insightful discourse on quantum vs classical computational advantage, with detailed dissemination across three pivotal fronts: empirical quantum advantage experiments, theoretical propositions of quantum superiority, and advancements in quantum error correction.

Quantum Advantage Experiments

The paper succinctly catalogs experiments that claim quantum computational advantage, commencing with the landmark 2019 demonstration by Google’s Sycamore processor executing random circuit sampling. This experiment, quantified to outperform the world’s best classical computers, was a foundational demonstration of potential quantum supremacy. The authors trace subsequent experiments, including notable efforts in Gaussian boson sampling by the USTC team, which extended complexity and affirmed superiority claims with increasingly sophisticated experiments.

Each experiment is meticulously reviewed with an exposition of methodical advancements, experimental parameters, performance benchmarks, and fidelity assessments. Notably, Google’s 2023 experiments, showcasing significant parameter enhancements, underscore relentless progress in scaling quantum systems. However, the review acknowledges that none of these experiments remain unchallenged, with classical emulation efforts consistently narrowing the quantum advantage horizon. Zhao et al. (2024)'s simulation fundamentally debunked Google's 2019 claims, accentuating the rapid evolution of classical computing strategies to bridge the performance gap.

Implications and Challenges

A significant strength of this review is its candid acknowledgment of the dynamic competitive landscape where quantum and classical computations vie for supremacy. The paper clarifies how classical simulation techniques have iteratively undermined various claims, showcasing a captivating record of quantum-classical interplay. Methods like tensor network contractions and matrix product states have iteratively eroded the perceived advantage of quantum computers by exploiting operational noise and leveraging classical computational prowess.

Moreover, LaRose focuses on the pivotal role of verification in asserting claims to quantum advantage. Approaches like the Linear Cross Entropy Benchmarking (XEB) are critically appraised for their vulnerabilities, inviting discourse on robust evaluation frameworks that can confidently adjudicate quantum and classical performances.

Theoretical Quantum Advantage

The paper extends its discourse into theoretical domains, exploring scenarios where quantum algorithms promise superiority, notably in optimization (QAOA) and quantum chemistry simulations. Historical theoretical advantage insights, such as speedups offered by Shor's algorithm for integer factorization, are rigorously revisited. However, known classical improvement paradigms like Tang's dequantized classical algorithms expose vulnerabilities in presumed quantum advantages, revealing a complex landscape where claimed quantum ascendancy can be contingent on specific assumptions.

Quantum Error Correction: A Crucial Frontier

Lastly, the paper addresses developments in quantum error correction, vital for harnessing theoretical advantages into feasible experimental demonstrations. LaRose systematically addresses the evolution of error correction schemes from prototype demonstrations to recent constructions showing gains through surface code enhancements. The paper underscores that achieving scalable, fault-tolerant quantum computing is a marathon rather than a sprint, inviting continued innovation and scaling in error correction methodologies.

Conclusion and Future Outlook

In conclusion, this paper serves as an in-depth resource, detailing the shifting sands of computational advantage between quantum and classical paradigms. It candidly captures the empirical, theoretical, and applied spectrums, arguing that while notable progress has been made, significant strides are required to realize fault-tolerant quantum computing. Looking forward, the trajectory of quantum computing remains exciting. The interplay with classical computational improvements continues to spur breakthroughs, positioning quantum computation as an evolving frontier in the computational sciences. The paper calls for ongoing collaborative exploration across quantum algorithms, hardware advancements, and error correction to forge the next era of computation.