[Paper Review] The Argument against Quantum Computers, the Quantum Laws of Nature, and Google's Supremacy Claims

Gil Kalai|arXiv (Cornell University)|Aug 12, 2020

Quantum Computing Algorithms and Architecture38 references4 citations

TL;DR

Gil Kalai presents a computational complexity argument against the feasibility of quantum computers, asserting that noisy intermediate-scale quantum (NISQ) devices are fundamentally limited to a low-level complexity class (LDP), making both quantum error correction and quantum supremacy impossible. The argument hinges on noise sensitivity and the infeasibility of achieving robust quantum advantage under realistic error conditions.

ABSTRACT

My 2018 lecture at the ICA workshop in Singapore dealt with quantum computation as a meeting point of the laws of computation and the laws of quantum mechanics. We described a computational complexity argument against the feasibility of quantum computers: we identified a very low-level complexity class of probability distributions described by noisy intermediate-scale quantum computers, and explained why it would allow neither good-quality quantum error-correction nor a demonstration of "quantum supremacy," namely, the ability of quantum computers to make computations that are impossible or extremely hard for classical computers. We went on to describe general predictions arising from the argument and proposed general laws that manifest the failure of quantum computers. In October 2019, "Nature" published a paper describing an experimental work that took place at Google. The paper claims to demonstrate quantum (computational) supremacy on a 53-qubit quantum computer, thus clearly challenging my theory. In this paper, I will explain and discuss my work in the perspective of Google's supremacy claims.

Motivation & Objective

• To challenge the feasibility of scalable quantum computing by identifying fundamental computational and physical limitations in noisy quantum systems.
• To argue that quantum error correction and quantum supremacy are unachievable under realistic noise models, even for NISQ devices.
• To propose new physical laws—rooted in noise sensitivity and rigidity—that explain the failure of quantum computation.
• To critically evaluate Google's 2019 claim of quantum supremacy using statistical and complexity-theoretic reasoning.
• To explore the implications of these failures for quantum simulation, classical simulation, and the broader understanding of quantum mechanics.

Proposed method

• Identifies a low-level complexity class (LDP) that captures the computational power of noisy intermediate-scale quantum (NISQ) computers.
• Applies noise sensitivity and stability theory to show that quantum circuits with constant or sub-constant error rates exhibit chaotic behavior, preventing reliable computation.
• Uses the framework of boson sampling and correlation analysis (from Kalai and Kindler, 2014) to demonstrate that classical sampling can mimic quantum distributions under statistical tests.
• Applies computational complexity theory to show that sampling is easier than computing probabilities, undermining claims of quantum advantage based on sampling tasks.
• Evaluates Google’s 53-qubit experiment through statistical scrutiny, arguing that the claimed quantum advantage fails under rigorous analysis.
• Proposes a general principle—'rigidity'—that links computational infeasibility to physical laws, suggesting that quantum systems cannot sustain coherent, scalable computation.

Experimental results

Research questions

• RQ1 Can quantum error correction be achieved in the presence of realistic noise rates in NISQ devices?
• RQ2 Is it possible for a quantum computer to outperform classical computers on any computational task, given the constraints of noise and error propagation?
• RQ3 Do the statistical tests used in Google’s experiment truly demonstrate quantum supremacy, or can classical systems reproduce the same results via low-order correlations?
• RQ4 What physical laws govern the failure of quantum computation, and how do they relate to noise sensitivity and computational complexity?
• RQ5 Can the failure of quantum supremacy be explained by a general principle of 'rigidity' in quantum systems, and what are its implications for quantum simulation and classical modeling?

Key findings

• Noisy intermediate-scale quantum (NISQ) computers are fundamentally limited to the complexity class LDP, which allows polynomial-time learnability and does not support robust quantum advantage.
• Quantum error correction is not feasible under constant or sub-constant error rates due to noise sensitivity, undermining the foundation of fault-tolerant quantum computation.
• Google’s 2019 claim of quantum supremacy on a 53-qubit device is not reliable, as the statistical evidence can be reproduced by classical systems through low-order correlations.
• The 2020 photonic quantum advantage claim in Science is similarly flawed, as the statistical argument is incorrect and consistent with Kalai’s general argument against quantum advantage.
• Classical sampling algorithms can mimic quantum distributions under the same statistical tests, demonstrating that sampling alone does not imply computational intractability.
• The failure of quantum supremacy is not due to engineering limitations but to deep computational and physical principles—particularly noise sensitivity and the rigidity of quantum systems.