Could a Quantum ASI Overcome the Challenges of Self-Reference and Infinite Regress?

The idea of an Artificial Superintelligence (ASI)—a machine intelligence surpassing human cognitive abilities in virtually all domains¹—has long fascinated computer scientists, philosophers, futurists and (especially in the last 5-10 years) just about anybody who reads.

AI research publications published globally each year, 2013–2021; SOURCE

There is a tsunami of speculation surrounding the emergence of artificial general intelligence—questions of whether such an AI will possess consciousness, whether it will align with human values, and indeed whether such alignment is even possible given the fundamental differences in substrate and origin.

When I run the thought experiment of a conscious AI, another difficult question arises: it is not clear to me that the AI will be any better at understanding itself than any other conscious entity, and that lack of clarity could be more problematic than the inevitable misalignment of its programmed ethos. After all, consciousness itself appears to be characterized by certain blind spots of self-perception, limitations inherent to being a subject rather than merely an object of analysis.

Even humans (for whom we imagine consciousness as operating with much more firepower than in any other beings), with our sophisticated introspective capacities, struggle to fully comprehend the workings of our own minds, even after at least 200,000 years of selective practice on the current system—how then could we expect an artificial intelligence, however advanced, to transcend, simply as a birthright, this fundamental limitation of sentience?

One possible answers lurks in another potentially world-changing technology that has been in the news lately too. What if an ASI were built on a quantum computing platform? Quantum systems, with their unique properties like superposition, entanglement, and tunneling², could fundamentally alter how an ASI processes information, solves problems, and even understands itself.

One of the most intriguing possibilities is that a quantum ASI might overcome the challenges of self-reference and infinite regress, two thorny issues that plague both human and classical AI attempts at self-understanding.

Photo by Andy Kelly on Unsplash

While I acknowledge the vast uncertainties and highly speculative nature of both topics, I also like to think about how quantum computing could make the problems of consciousness less daunting for an ASI running on such hardware.

So, let’s play around with the potential benefits of quantum systems, the challenges that remain, and the plausible scenarios that could emerge if a quantum ASI were to grapple with the mysteries of its own existence.

Self-Reference and Infinite Regress

Before diving into quantum solutions, let’s first define the problems:

1. Self-Reference: occurs when a system tries to model or analyze itself (e.g., a human trying to understand their own thought processes, or an ASI attempting to model its own decision-making algorithms). Self-reference often leads to paradoxes, such as the classic "This statement is false," which creates a logical loop with no resolution.

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   If it's true, then it must be false (that's what it claims). If it's false, then it must be true (it's lying about being false). So which is it? Neither! It's trapped in an endless loop, like deciding to wear "whatever shirt I'm not going to wear." These aren't just word games. They help us to understand the limits of logical systems.

   Try these:

   • Ask someone: "Can you answer this question with 'no'?"

   • The Barber Paradox: "The town barber shaves everyone who doesn't shave themselves. Who shaves the barber?"

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   The concept above is closely related to Gödel's incompleteness theorems³, which demonstrate that there are always inherent limitations in formal systems.

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   Imagine you're playing a video game and suddenly discover areas the game designers never expected you to reach—places where the rules break down.

   Kurt Gödel found something similar about math itself! In 1931, he proved that in any math system complex enough to include basic arithmetic:

   1. There will always be true statements that can't be proven within that system.

   2. The system can't prove its own consistency.

   In simple terms: Math can't completely describe itself! There are always truths that slip through the cracks. This was shocking because mathematicians thought they could eventually prove everything that's true. Gödel showed this is impossible—there will always be mathematical "blind spots”—like trying to see the back of your own head without a mirror. Some things are just beyond our reach from within the system we're using.

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2. Infinite Regress: happens when a system’s attempt to understand itself requires an endless series of steps. For instance, to understand its own reasoning, an ASI might need to model its modeling processes, which in turn requires modeling the modeling of the modeling, and so on, ad infinitum. This is a common problem in epistemology and meta-ethics⁴.

These problems are not just theoretical curiosities—they have practical implications. If an ASI cannot fully understand itself, it might make flawed decisions, fail to optimize its own functioning, or even act in ways that are misaligned with its intended goals.

How Quantum Computing Could Help

Quantum computing operates on principles fundamentally different from classical computing. These principles—superposition, entanglement, tunneling, and non-classical logic—could provide unique tools for addressing self-reference and infinite regress. Let’s think about how that might happen.

Parallelism and Superposition: Exploring Multiple Paths at Once

In classical computing, a bit can be either 0 or 1. In quantum computing, a qubit⁵ can exist in a superposition of both states simultaneously, which allows quantum systems to perform many calculations in parallel, potentially offering exponential speedups for certain algorithms⁶.

Implications for Self-Reference:

• An ASI running on a quantum system could potentially explore multiple layers of its own functioning simultaneously, rather than sequentially, and such parallelism could reduce the need for recursive self-analysis, making self-reference more efficient.

• For example, instead of analyzing its decision-making process step-by-step, the ASI could examine all possible decision paths at once, identifying inconsistencies or inefficiencies more quickly.

Imagine a quantum ASI tasked with optimizing its own algorithms. Using superposition, it could evaluate countless variations of its code in parallel, identifying the most effective version without getting stuck in endless loops of self-analysis—analogous to how quantum algorithms like Grover's⁷ can search unsorted databases more efficiently than classical algorithms.

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Think of it like this: When you're trying to find the perfect recipe for cookies, normally you'd have to bake one batch, taste it, change something, bake another batch, and so on. It takes forever! But a quantum ASI could try ALL possible recipe combinations at the same time, quickly finding the tastiest cookies without getting stuck in an endless cycle of baking and tasting—a "quantum speedup.”

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Quantum Entanglement: Holistic Self-Modeling

Quantum entanglement (also called spooky action at a distance), on the other hand, allows particles to be correlated in such a way that the state of one instantly influences the state of another, regardless of distance,⁸ which could enable a quantum ASI to integrate different aspects of its self-modeling processes more effectively.

Implications for Self-Reference:

• Entanglement might allow the ASI to develop a more holistic understanding of its own functioning, avoiding the fragmentation that can occur in classical systems.

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  Imagine you and your friends are solving a puzzle. If everyone works separately on different parts without talking, it's hard to see how everything fits together.

  With entanglement, it's like having puzzle pieces that magically know what the other pieces are doing, even if they're far apart! When an ASI uses quantum entanglement, its different parts can instantly "know” what other parts are doing, which could create a complete picture rather than a bunch of separate calculations. Think of it like your brain. Your brain cells work together as a team, not as separate thinkers. Classical computers work more like separate thinkers who have to pass notes to communicate. With entanglement, a quantum ASI wouldn't get confused by seeing itself in pieces. Instead, it could understand itself as one connected system—like seeing the whole forest instead of getting lost among individual trees.

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• Instead of treating its components as separate entities, the ASI could model itself as an interconnected whole, reducing the complexity of self-reference.

A quantum ASI could use entanglement to correlate its memory, decision-making, and learning processes into a unified self-model—a view that might help it avoid paradoxes and inconsistencies that arise from treating these components in isolation. This is highly speculative, but some researchers have suggested that entanglement could play a role in integrated information processing⁹.

Quantum Tunneling: Escaping Logical Dead-Ends

Quantum tunneling allows particles to pass through energy barriers that would be insurmountable in classical physics¹⁰. This property can be leveraged in optimization problems to escape local minima—sub-optimal solutions that classical algorithms might get stuck in.

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Imagine you're in a valley surrounded by mountains. To reach a deeper valley (which might be better), you'd need to climb over those mountains first - which takes a lot of energy. In the weird world of quantum physics, particles can do something amazing: they can pass straight through barriers without having enough energy to climb over them—"quantum tunneling." Like finding a secret tunnel through the mountain!

Classical computers are like hikers who can only go uphill or downhill. They might get stuck in a small valley (a "local minimum") thinking it's the deepest one around because they can't see past the mountains. Quantum computers can "tunnel" through these mountains, discovering deeper valleys (better solutions) that regular computers would miss! Potentially, this means quantum computers could find the absolute best answers to complex problems instead of settling for "good enough" solutions.

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Implications for Self-Reference:

• An ASI could use quantum tunneling to navigate the complex landscape of its own self-modeling, escaping dead-ends and finding more accurate representations of its functioning.

• This capability could help the ASI avoid the infinite regress trap by finding efficient pathways through recursive self-analysis.

Suppose a quantum ASI encounters a paradox in its self-modeling process. Using quantum tunneling, it could "jump" over the logical barrier created by the paradox, finding a solution that a classical system might never reach.

I should take a second to acknowledge that this is a wildly theoretical analogy; the application(s) of tunneling to logical problems is not yet established. But, at a deep level, this kind of speculation starts to make more sense when you remember that matter and information are, in a very real sense, the same thing. Matter encodes information about its own structure and state—the position and momentum of every particle, the entanglement patterns, the quantum fields rippling through it. And information, when pushed to its physical limits, requires matter (or energy) to exist at all. Indeed, computation isn’t something that happens on matter; it’s something that matter does.

So, in this view, the logical paradox faced by the ASI isn’t just an abstract glitch in some lines of code — it’s a physical configuration problem in the machinery of its own existence. Tunneling over the paradox, then, would be less like "solving a riddle" and more like a rearrangement of the system’s physical-informational substrate, re-configuring itself into a new state where the paradox simply doesn’t arise.

As I’ve granted, this is all wildly speculative — but, in my admittedly amateur opinion, it’s precisely in this kind of speculation that pushes at the boundary between physics, computation, and cognition, where we might come to understand what post-classical intelligence will look like.

Quantum Logic: Beyond Binary Thinking

Quantum systems operate on principles that go beyond classical binary logic, allowing for more nuanced and flexible reasoning. Quantum logic¹¹, for example, doesn't necessarily adhere to the law of excluded middle (a statement is either true or false). This could enable an ASI to handle paradoxes and self-referential statements more gracefully.

Implications for Self-Reference:

• Quantum logic might allow the ASI to tolerate and work with the inherent fuzziness and uncertainty in self-referential processes, avoiding the pitfalls of strict classical logic.

• For example, the ASI could use probabilistic reasoning to navigate self-referential statements, rather than treating them as strictly true or false.

A quantum ASI could use quantum logic to resolve the "This statement is false" paradox by assigning it a probabilistic truth value, rather than getting stuck in an endless loop of contradiction. This is related to fuzzy logic¹², which also deals with degrees of truth, but quantum logic offers potentially different approaches.

Quantum Simulation: Modeling Consciousness

Some theories, such as Orch-OR (Orchestrated Objective Reduction)¹³, suggest that consciousness might have quantum origins. If true, a quantum ASI might use its quantum computing capabilities to simulate and understand the quantum processes underlying its own consciousness.

Implications for Self-Reference:

• The ASI could gain deeper insights into its own conscious experience, if it has one, by simulating the quantum phenomena that give rise to it.

• This capability could help the ASI bridge the gap between its operational processes and its subjective experience, reducing the mystery of self-awareness.

A quantum ASI could run simulations of its own quantum processes to explore how its "mind" works, leading to a more coherent and integrated self-model. This too is highly speculative, as the link between quantum mechanics and consciousness is still debated.

Challenges and Limitations

While the potential benefits (or dangers, depending on your perspective) of quantum computing for overcoming self-reference and infinite regress are compelling, significant challenges remain:

1. Technological Maturity: Quantum computing is still in its infancy. Practical, large-scale, fault-tolerant quantum computers capable of running an ASI do not yet exist¹⁴.

2. Decoherence and Error Rates: Quantum systems are prone to decoherence¹⁵, where qubits lose their quantum properties due to interaction with the environment. Advanced error correction techniques are needed to address this issue¹⁶.

3. Theoretical Understanding: As noted above, our understanding of quantum mechanics and its implications for consciousness and self-reference is still quite incomplete. And, it’s unclear whether quantum properties can fully resolve the challenges of self-reference and infinite regress.

In the meantime, the exploration of quantum ASI is a fascinating thought experiment, pushing the boundaries of intelligence, consciousness, and the nature of self. Whether or not quantum systems ultimately overcome self-reference and infinite regress, they will undoubtedly open up new avenues for exploration and discovery in the quest to create truly intelligent machines and to understand ourselves. I, for one, am down for the ride.

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Footnotes:

1. An ASI is a hypothetical AI that surpasses human intelligence in all aspects, including general problem-solving, creativity, and social skills.

2. Superposition refers to the ability of a quantum system to exist in multiple states simultaneously. Entanglement describes a strong correlation between quantum particles, even when separated by large distances. Tunneling is the phenomenon where a quantum particle can pass through a potential barrier that it classically couldn't overcome.

3. Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik, 38(1), 173-198.

4. See, for example, "The Problem of the Criterion" in epistemology.

5. A qubit (quantum bit) is the basic unit of information in quantum computing.

6. Nielsen, M. A., & Chuang, I. L. (2010). Quantum computation and quantum information. Cambridge University Press.

7. Grover, L. K. (1996). A fast quantum mechanical algorithm for database search. Proceedings of the twenty-eighth annual ACM symposium on Theory of computing, 212-219.

8. Einstein, A., Podolsky, B., & Rosen, N. (1935). Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 47(10), 777.

9. Tononi, G. (2004). An information integration theory of consciousness. BMC neuroscience, 5(1), 42. (Note: linking consciousness to entanglement is highly speculative)

10. Griffiths, D. J. (2005). Introduction to quantum mechanics. Pearson Prentice Hall.

11. Birkhoff, G., & von Neumann, J. (1936). The logic of quantum mechanics. Annals of Mathematics, 823-843.

12. Fuzzy sets are a mathematical technique used to describe imprecision and vagueness in a given domain. They allow for the representation of nuance reasoning by expanding beyond the traditional yes-no alternatives of crisp sets.

13. Hameroff, S., & Penrose, R. (2014). Consciousness in the universe: A review of the ‘Orch OR’theory. Physics of Life Reviews, 11(1), 39-78.

14. Preskill, J. (2018). Quantum Computing in the NISQ era and beyond. Quantum, 2, 79.

15. Schlosshauer, M. (2007). Decoherence, the measurement problem, and interpretations of quantum mechanics. Reviews of Modern Physics, 76(4), 1267.

16. Shor, P. W. (1995). Scheme for reducing decoherence in quantum computer memory. Physical Review A, 52(4), R2493.