To cheer you up in difficult times 29: Free will, predictability and quantum computers

I wrote a paper, in Hebrew, entitled “Free will, predictability and quantum computers.” Click for the pdf file (Version of Nov. 25, 2021; orig. version). As you probably know, the free will problem is the apparent contradiction between the fact that the laws of nature are deterministic on the one hand, and the notion that people are making free choices that affect their future on the other hand. Here on my blog, I mentioned the free will problem twice: once, briefly, in connection with a lecture by Menachem Yaari (2008), and once in TYI 33 (2017) while conducting the “great free will poll” (see picture below for the outcomes). As for the paper, I hesitated whether to write it in Hebrew or in English; I finally chose Hebrew and I plan to prepare also an English version sometime in the fall.

Here is the abstract of my new paper.

תקציר: המאמר עוסק בקשר בין השאלות הנוגעות להיתכנות מחשבים קוונטיים, הפרדיקטביליות של מערכות קוונטיות מורכבות בטבע, והסתירה הקיימת לכאורה בין חוקי הטבע לבין רצון חופשי. נדון במקביל במחשב הקוונטי “סיקמור” בעל 12 יחידות חישוב (קיוביטים), ובאליס, שעל רצונה החופשי ננסה לתהות. התאוריה של המחבר העוסקת באי האפשרות של חישוב קוונטי, מצביעה באופן ישיר על אי האפשרות לנבא במדויק את מחשב הסיקמור, כמו גם את מוחה של אליס.  בניתוח מורכב יותר נראה, שאי האפשרות של חישוב קוונטי תומכת בגישה לפיה חוקי הטבע אינם שוללים בחירה חופשית. בבסיס הטיעון הזה עומדת עמימות בדרך שבה העתיד נקבע מהעבר ואשר איננה נעוצה באופי המתמטי של חוקי הפיסיקה (שהם לגמרי דטרמיניסטים), אלא בתיאור הפיסיקלי של העצמים שאנו דנים בהם. אנו דנים גם בהפרדה בין טענות לגבי העתיד שטמונות במארג הסיבתי הקיים בין העבר והעתיד, לבין טענות הנוגעות לעתיד ואשר אינן נמצאות במארג זה

Abstract: We study the connection between the possibility of quantum computers, the predictability of complex quantum systems in nature, and the free will problem. We consider in parallel two examples: the Sycamore quantum computer with 12 qubits (computing elements) and Alice, whose decisions and free will we try to question. The author’s theory that quantum computation is impossible (in principle) directly indicates that the future of both Alice’s brain and the Sycamore quantum computer cannot be predicted. A more involved analysis shows that failure of quantum computation supports the view that the laws of nature do not contradict free will. At the center of the argument is ambiguity in the way the future is determined by the past, not in terms of the mathematical laws of physics (which are fully deterministic) but in terms of the physical description of the objects we discuss. In addition, we discuss the separation between claims about the future that belong to the causal fabric of the past and the future, and claims that don’t belong to this fabric.

Two examples that we consider in parallel throughout the paper are “Alice”, whose free will we try to explore, and Google’s “Sycamore” quantum computer with 12 qubits. So, even if Google’s Sycamore does not lead to “quantum supremacy” (and I suspect it does not!) it could still be used in the pursuit of human free will 🙂 . Aram Harrow’s hypothetical quantum computer from our 2012 quantum debate (post 4) also plays a role in my paper.

My interest in the problem was provoked by Avishai Margalit in the mid 90s. Later I was engaged in a long email debate with Ron Aharoni following his 2009 (Hebrew) book on philosophy about this problem and related philosophical questions.  Since then, I have been following with interest writings on the problem by Scott Aaronson, Sabine Hossenfelder, Tzahi Gilboa, and others, and had brief discussions about free will with Bernard Chazelle and a few other friends. Writing the paper provided me an
immensely enjoyable opportunity to discuss the problem once again with
philosophers, friends and colleagues.

One question that I initially discussed but later left out is the following:

From the point of view of people in the mid 20th century, did quantum mechanics offer an opportunity for understanding the apparent contradiction between free will and the deterministic laws of nature? (Schrödinger himself wrote a paper where he was skeptical about this.)

My a priori intuition about the free will problem is in analogy with Zeno’s famous motions paradoxes. Zeno’s paradoxes offered an opportunity to re-examine the mathematics and physics of motion while not shaking the common sense understanding of motion. (In fact, the ancient Greeks knew enough about the mathematics and physics of motion to conclude that motion is possible and that Achilles will overtake the tortoise, and they could compute precisely when.)  Similarly, the question of free will is an opportunity to explore determinism and related issues, but probably not to challenge our basic understanding of human choice. 

Here are a few relevant links. Papers by Schrödinger (1936), Bohr (1937), and an essay by Einstein on free will (see picture below). Ron Aharoni’s paper (Hebrew) on Newcomb’s paradox published in “Iyun” from 1984 (Ron kindly agreed to explain his view on the FW problem in some future post.); A post by Scott Aaronson about his paper on the matter (related posts on SO (2021), (2012); Posts by Sabine Hossenfelder (2016), (2014), (2020), (2013), (2019), (2011), (2012) (and her paper on the matter); A post by Sean Carrol (2011); Itzhak Gilboa’s take; A paper by Neven, Read and Rees with a proposed engineering of conscious quantum animat that possesses agency and feelings; The World Without Quantum Computation with emphasis on Predictability and Free Will (click for the Power Point presentation). A lecture I gave on Aug 26, 2021 at the ML4Q Students’ & Postdocs’ Retreat 2021.

This post can be seen as my response to TTY33 for which Ori was eagerly waiting. The paper could be seen as a FW booster for Hebrew-speaking audience, and, as I said, I hope to produce a similar FW booster for English-speaking audience in the upcoming fall.


(Clockwise) The cover of Jennan Ismael’s 2016 book, Alice, the Sycamore computer, and a cartoon about free will.


Three figures from the paper


Einstein’s Essay on free will (left) and the outcomes of our 2017 great free will poll. (Einstein’s opening statement about the moon was inspired by Spinoza.)

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6 Responses to To cheer you up in difficult times 29: Free will, predictability and quantum computers

  1. David says:

    I dont believe the natural law can ever be completely deterministic because of entropy and chaos factor

  2. There’s something fundamental I don’t understand in this article. On page 8 you appear to claim that the underlying laws of physics are deterministic to the extent that if we had a complete physical description of the current state of the Sycamore device (say) as well as its future interaction with the rest of the universe (“Sycamore-2”) or, instead, know the “wave function of the universe” (“Sycamore-1”), then we’d be able to predict the future exactly (in the deterministic sense of classical mechanics).

    That is not a reasonable description of QM. While in statistical mechanics the probabilistic description captures our ignorance about the state of the system (which could be in one of a large multitude of states which are equivalent from the point of view of macroscopic quantities), the probabilistic nature of quantum measurements is inherent: it does not reflect our ignorance about some underlying state variables of the system. Specifically, the EPR paradox (verified experimentally as well) shows that there are no missing local degrees of freedom (so-called “hidden variables”). Conceivably there are hidden global degrees of freedom, but those can’t allow for the kind of determinism that you want, especially consistently with relativity (there need not be a consistent notion of “present”, “past”, or “future” across the universe, just for one example).

    It is true that the time evolution of linear QM is deterministic. But the coupling to a classical system (“measurement”) is not, and this is not due to the noise in the classical system, our lack of knowledge of the quantum system, or anything like that. So a complete description of the state (i.e. quantum state) of the Sycamore computer today will predict its quantum state tomorrow, but not the precise samples it will produce, and there is no way to know the specific samples even in principle (though knowing the quantum state will tell us the distribution of the samples).

    What have I missed?

    Aside: on page 6 I think נסיוניים was supposed to be נסיונאים.

    • Gil Kalai says:

      Hi Lior,

      Not only that you do not miss anything but your comment is related to huge discussions on the interpretation of quantum mechanics that I ignore in the paper. You are absolutely correct that thinking about the outcome of Sycamore (and simpler experiments in quantum mechanics) as deterministic is not a reasonable description of QM.

      Note however, that when you talk about the wave function of the entire universe what you mention as “the coupling to a classical system” could, in principle, be replaced with a statement with no mention of “classical systems”. See, for example, point 5 in Scott’s where the classical system you refer to is described as

      “a particular kind of quantum system that interacts with other quantum systems, becomes entangled with them, and thereby records information about them—reversibly in principle but irreversibly in practice.”

      I agree with you that Sycamore – 1 has no physical meaning and, unlike Scott, I agree that the recorded information is irreversible in principle. Moreover, what my argument against QC asserts is that even the “precise probability distribution described by Sycamore – 3” has no physical meaning since the samples are inherently chaotic – not just probabilistic. (You can regard it as the inherent shadow of Sycamore 1 on Sycamore 3.)

      In other words, you are correct in saying that the coupling to a classical system (“measurement”) is inherently non deterministic. The way to reconcile your statement with the fact that time evolution of linear QM is deterministic (and all the classical systems are part of our quantum world) is that there is some ambiguity – not in the evolution, but in the definition of the physical description of the objects we discuss.

  3. Gil Kalai says:

    Here is a very nice comment by Or Sattath on Facebook with much food for thought

    “I have to say that I find it surprising that (most) people commonly discuss only computational tasks and do not take a slightly broader perspective: For example, an exponential advantage in the number of queries for a certain task in query complexity? Similarly, in communication complexity? What about distributed computing? And what about cryptographic tasks?
    Specifically for cryptographic tasks, quantum key distribution was extensively studied, and *does* work in a noisy environment, and has been demonstrated experimentally, and even commercially (though that’s probably not the point). Similarly, quantum money (and specifically quantum money) is known to be noise-tolerant (see ). If you’re interested in other examples, I’m pretty sure I can think of several more. The main drawback of quantum money is that it requires quantum memory, but if you’re not interested in the application but the fundamental properties, it has been demonstrated experimentally (in other words, it is unforgeable, but you can’t really store the “money” for more than a few milliseconds), e.g.,
    Perhaps from your perspective, this is problematic because the security of these protocols relies on the correctness of quantum mechanics. But still, the security is falsifiable: if you argue that there’s no “quantum advantage” you would have to somehow break the QKD scheme/forge the money.”

  4. Kredilog says:

    Thanks for sharing!

  5. Pingback: Face to face talks and recorded videotaped introductions | Combinatorics and more

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