[Paper Review] Comment on "Quantum supremacy using a programmable superconducting processor"

Karl Svozil|arXiv (Cornell University)|Nov 1, 2019

Quantum chaos and dynamical systems2 references4 citations

TL;DR

This paper challenges the claim of quantum supremacy by arguing that Google's Sycamore processor, while efficient for its specific task of sampling random quantum circuits, does not achieve universal computational capability. It contends that classical chaotic systems with transverse homoclinic orbits can outperform both classical and quantum architectures on certain tasks, and that quantum random number generators already violate the original Church-Turing thesis by providing true randomness beyond what any classical or quantum pseudorandom algorithm can achieve.

ABSTRACT

Even if Google AI's Sycamore processor is efficient for the particular task it has been designed for it fails to deliver universal computational capacity. Furthermore, even classical devices implementing transverse homoclinic orbits realize exponential speedups with respect to universal classical as well as quantum computations. Moreover, relative to the validity of quantum mechanics, there already exist quantum oracles which violate the Church-Turing thesis.

Motivation & Objective

• To question whether Google's Sycamore processor truly demonstrates quantum supremacy beyond a narrow computational task.
• To examine whether classical chaotic systems, such as those with transverse homoclinic orbits, can achieve exponential speedups over universal classical and quantum architectures.
• To assess whether quantum random number generators already provide a fundamental advantage by violating the original Church-Turing thesis.
• To clarify the distinction between computational efficiency for specific tasks and universal computational capability.

Proposed method

• Analyzes the computational limitations of the Sycamore processor, emphasizing its lack of universal computation capability despite being programmable.
• Reviews classical chaotic systems, particularly those exhibiting transverse homoclinic orbits, as physical systems capable of exponential speedup on specific tasks.
• Examines quantum random number generators as physical realizations that produce irreducibly random outcomes, violating the Church-Turing thesis.
• Compares the computational power of quantum oracles, classical chaotic systems, and universal Turing machines in terms of computational speed and theoretical limits.
• Uses the extended Church-Turing thesis as a benchmark to evaluate claims of quantum advantage.
• Argues that if quantum mechanics is valid, then quantum oracles already provide an absolute advantage over all classical and quantum pseudorandom algorithms.

Experimental results

Research questions

• RQ1 Can classical chaotic systems with transverse homoclinic orbits outperform universal classical and quantum computers on specific computational tasks?
• RQ2 Does the Sycamore processor’s performance constitute a robust form of quantum supremacy, or is it limited to a narrow class of problems?
• RQ3 Do quantum random number generators already violate the original Church-Turing thesis by providing true randomness unattainable by any classical or quantum pseudorandom algorithm?
• RQ4 Is the claim of 'fully programmable' universal computation justified for the Sycamore processor under standard theoretical computer science definitions?
• RQ5 Can systems that are not universal computers still demonstrate exponential speedups relative to universal architectures?

Key findings

• The Sycamore processor, despite its efficiency in sampling random quantum circuits, fails to support universal computation or solve NP-complete problems efficiently.
• Classical chaotic systems, such as those with transverse homoclinic orbits, can achieve exponential speedups over both classical and quantum universal architectures on specific tasks.
• Such classical chaotic systems do not qualify as universal computers but still present a computational advantage that violates the extended Church-Turing thesis.
• Quantum random number generators, based on quantum mechanics' complementarity and contextuality, already provide a true randomness advantage that cannot be replicated by any classical or quantum pseudorandom algorithm.
• The existence of such quantum oracles constitutes a violation of the original Church-Turing thesis, not just the extended version.
• The paper concludes that claims of quantum supremacy are overstated, as similar or greater advantages already exist in classical chaotic systems and in commercially available quantum random number generators.