[Paper Review] Reliable AI: Does the Next Generation Require Quantum Computing?

Aras Bacho, Holger Boche+1 more|arXiv (Cornell University)|Jul 3, 2023

Quantum Computing Algorithms and ArchitectureComputer Science3 citations

TL;DR

This paper investigates whether the next generation of reliable artificial intelligence necessitates quantum or analog computing, arguing that digital computers—based on the Turing machine model—face fundamental computability limits in solving continuous problems like optimization, differential equations, and inverse problems. While quantum computing offers speedups, it cannot overcome non-computability issues rooted in discrete models; analog computing models such as the BSS machine, however, can theoretically solve these problems exactly, suggesting that future AI reliability may depend on post-Turing computing paradigms beyond classical and quantum digital models.

ABSTRACT

In this survey, we aim to explore the fundamental question of whether the next generation of artificial intelligence requires quantum computing. Artificial intelligence is increasingly playing a crucial role in many aspects of our daily lives and is central to the fourth industrial revolution. It is therefore imperative that artificial intelligence is reliable and trustworthy. However, there are still many issues with reliability of artificial intelligence, such as privacy, responsibility, safety, and security, in areas such as autonomous driving, healthcare, robotics, and others. These problems can have various causes, including insufficient data, biases, and robustness problems, as well as fundamental issues such as computability problems on digital hardware. The cause of these computability problems is rooted in the fact that digital hardware is based on the computing model of the Turing machine, which is inherently discrete. Notably, our findings demonstrate that digital hardware is inherently constrained in solving problems about optimization, deep learning, or differential equations. Therefore, these limitations carry substantial implications for the field of artificial intelligence, in particular for machine learning. Furthermore, although it is well known that the quantum computer shows a quantum advantage for certain classes of problems, our findings establish that some of these limitations persist when employing quantum computing models based on the quantum circuit or the quantum Turing machine paradigm. In contrast, analog computing models, such as the Blum-Shub-Smale machine, exhibit the potential to surmount these limitations.

Motivation & Objective

• To investigate the fundamental limitations of digital computing—rooted in the Turing machine model—for solving continuous problems critical to AI, such as optimization, differential equations, and inverse problems.
• To assess whether quantum computing, despite its speed advantages, can overcome the same computability limitations inherent in digital hardware.
• To evaluate the theoretical potential of analog computing models, particularly the Blum-Shub-Smale (BSS) machine, in solving non-computable problems on digital systems.
• To examine the implications of these computational constraints for the reliability, fairness, and trustworthiness of AI in high-stakes domains like healthcare, autonomous systems, and robotics.
• To argue that the future of reliable AI may require post-Turing computing models, including analog and quantum analog systems, to transcend the theoretical limits of classical and quantum digital computation.

Proposed method

• Theoretical analysis of the Turing machine and quantum Turing machine models to identify inherent limitations in computing continuous mathematical objects such as real numbers and solutions to partial differential equations.
• Comparison of algorithmic complexity and solvability between digital hardware, quantum computers (based on quantum circuit and quantum Turing machine models), and analog computing models like the BSS machine.
• Formalization of the concept of non-computability in the context of inverse problems and optimization, showing that exact solutions are unattainable on digital systems due to discrete representation.
• Use of the BSS machine model to demonstrate theoretical solvability of any inverse problem of a given dimension, in contrast to the algorithmic restrictions on digital hardware.
• Analysis of quantum algorithms such as Shor’s and Grover’s to assess their performance relative to classical counterparts and their inability to resolve non-computability issues.
• Synthesis of results from computational complexity theory, real computation, and quantum information theory to evaluate the feasibility of reliable AI under different computing paradigms.

Experimental results

Research questions

• RQ1 Can digital computers, based on the Turing machine model, reliably solve continuous mathematical problems such as partial differential equations and inverse problems?
• RQ2 To what extent do quantum computers—despite their speed advantages—overcome the fundamental computability limitations of digital hardware?
• RQ3 Can analog computing models like the BSS machine solve problems that are non-computable on digital or quantum digital systems?
• RQ4 What are the theoretical and practical implications of non-computability in AI applications such as autonomous driving, healthcare, and robotics?
• RQ5 Is the development of post-Turing computing—specifically analog or quantum analog systems—necessary for the next generation of reliable artificial intelligence?

Key findings

• Digital hardware based on the Turing machine model cannot exactly represent or compute with continuous quantities like real numbers, leading to inherent non-computability in problems such as solving partial differential equations and inverse problems.
• Even quantum computers based on the quantum Turing machine model do not resolve the issue of non-computability, as they remain bound by discrete computation and cannot exactly compute with real numbers.
• The Blum-Shub-Smale (BSS) machine, as an analog computing model, can theoretically solve any inverse problem of a given dimension, demonstrating exact solvability where digital and quantum digital systems fail.
• While quantum computers offer exponential speedups for specific problems (e.g., Shor’s algorithm), they provide only quadratic speedups for search problems (Grover’s algorithm), and neither case resolves the underlying non-computability issue.
• Theoretical results show that exact solutions to continuous problems are unattainable on digital systems, and this limitation directly undermines the reliability, fairness, and safety of AI in critical applications.
• The study concludes that future AI reliability may require post-Turing computing models—particularly analog or analog quantum systems—beyond classical and quantum digital computation.