Quantum Isn’t Coming For Your Bitcoin

Now, you might be thinking, “but what about all the recent advancements?” There are two important things to keep in mind about recently published advancements. First, many of these advancements have been advancements in pure mathematics only. For example, the recent Google paper which had such an important result that they chose to redact the theoretical quantum circuit rather than risk it being used to break important cryptographic systems. This may seem like massive progress toward the future of CRQCs, but in fact it changed nothing. Unless (or until) the quantum hardware has its Falcon 9 moment, there simply is no device which comes anywhere near the stability and scale needed to run the redacted circuit. It’s pure theater to hide a circuit designed for a device which may never exist. Second, on the hardware side itself, we see many new results and bits of progress published in a given year, but how many of these relate to the same quantum computing candidate technology? How many represent merely a starting over after a prior result ended in a dead end? The reality is that these advancements do not represent some linear track toward eventual success. They represent the breadth-first search of an infinite possibility space within which quantum researchers are hoping to find a path along which they can proceed for even a modest distance without reaching yet another dead end.

When we look at the reality of the future of quantum computing, it’s hazy at best. There are promising technological developments. Especially, to my eye, in the area of neutral atom devices. But it’s far too early to tell if there’s a path open toward an eventual CRQC along any of the currently known branches or if more restarts are in our future. If, at some point, we see many iterations of the same candidate technology implementing progressively more capable devices, and computing meaningful results that a precocious child cannot also compute, we can revisit this discussion with different evidence.

In Theory

There are two possible explanations for the repeated failure of quantum research to develop a CRQC over many decades. It’s possible that it’s just a hard problem and we’re continuing to apply science and engineering to solve it and one day the ingenuity of the human species will prevail as it has in the development of the Internet, the smart phone, social media, and Bitcoin (left to the reader to decide which of these are positive developments). On the flip side, it may be that developing a CRQC is either impossible or will remain forever outside our grasp. Consider what it would mean for a CRQC to exist: the machine would have to represent within its superposition a field of possibilities the same size as the complexity of the cryptographic problem to be solved. I.e. to break the 128-bit security of the elliptic curve discrete log on Bitcoin’s secp256k1 curve, the quantum superposition would have to represent all possible values of a 128-bit number. In classical computing, representing all such values would require more computer storage (by many orders of magnitude) than humans have ever produced. If there is even the slightest granularity to the quantum superposition (i.e. the quantum superposition is not perfectly continuous across all possible values) then the quantum computer cannot ever become cryptographically relevant. If the energy required to hold a superposition scales with the complexity of the field being represented then a quantum computer cannot ever be cryptographically relevant. The contemporary understanding of quantum physics does not rule out either of these possibilities.

Conclusion: Bitcoin Cannot Rest

Despite all of the preceding, Bitcoin development toward new cryptographic algorithms must continue. While a quantum attack on Bitcoin’s cryptography is not imminent by any means, it’s entirely possible that another flaw could be found through other means. We know that certain elliptic curves have been found to have weaknesses, and secp256k1 could be next. Bitcoin has survived as long as it has because attacks on the system have strengthened it and that will continue to be true as the quantum FUD attack plays out. The development of P2MR or P2TRv2, of SHRINCS, SPHINCS, IBC, ML-DSA, and more post-quantum signature schemes will eventually lead to improvements to Bitcoin’s resilience in the face of future attacks even if an actual CRQC is never developed.