MATHEMATICIAN AND COMPUTER SCIENTIST SPECIALIZED IN LINEAR ALGEBRA AND THEORETICAL COMPUTING The theory of computing focuses on understanding the fundamental principles and limits of computation.
Beyond Shor's Algorithm: Why His Own Field Has Passed Him By Professor Shor, Your contribution to the field remains the paradigmatic demonstration of what a quantum computer could achieve. But precisely because of the weight your voice carries, I feel compelled to correct several points in your framing. You presented “quantum supremacy” as if it were reducible to the act of factoring large integers on a fault-tolerant machine, and further suggested that this goal remains “several decades away.” With due respect, this is a mischaracterization. Supremacy is not, and has never been, synonymous with cryptographic collapse. It is a complexity-theoretic notion: the existence of any problem in BQP demonstrably intractable for classical machines. By that definition, supremacy demonstrations already exist—random circuit sampling (Google’s Sycamore), boson sampling (Xanadu’s Borealis), Gaussian boson sampling with threshold detectors. These are not speculative curiosities; they are experimentally verified instantiations of separations between quantum and classical resources, unless one chooses to redefine supremacy post hoc as “breaking RSA or nothing.” Your suggestion that improved classical algorithms may refute these demonstrations is a valid caveat but ultimately bounded. Complexity theory (Aaronson–Arkhipov; Bremner–Montanaro–Shepherd) shows that efficient classical simulation of such distributions would collapse the polynomial hierarchy—an outcome more radical than accepting the reality of quantum advantage. Temporary algorithmic workarounds (tensor networks, Clifford+T stabilizer simulators) narrow but do not erase the separation. Moreover, the prediction that factoring is “decades away” rests on a linear extrapolation of today’s error rates. This ignores the non-linear trajectory of progress: bosonic encodings (GKP states), LDPC codes with constant overhead, modular ion-trap arrays, and photonic cluster states. Logical qubits with demonstrated break-even error suppression already exist. To dismiss these as incremental curiosities is to repeat, in 1946, the claim that stored-program digital machines were “obviously” incapable of scaling. What matters here is conceptual clarity. Supremacy is not utility. Factoring will indeed be the cryptographically dramatic instantiation, but it is not the definitional gatekeeper. To equate supremacy with factoring is to erase the very progress that your own algorithm inspired. Supremacy has already been achieved in restricted but complexity-theoretically rigorous models. To suggest otherwise risks turning a scientific milestone into a rhetorical mirage. Few individuals have shaped quantum computation as deeply as you have. For that reason, when you speak, the community listens—and sometimes uncritically. With admiration for your foundational work, but with equal commitment to correcting what must not remain unchallenged, Marcos Eduardo Elias Founder, Holosystems Quantum Algorithms / EquiVerse AI
Peter Shor states the obvious that there are no existing examples of quantum algorithms available on any quantum hardware that currently show quantum supremacy and while factoring could potentially be an example of such a case Shor predicts that practical factoring is decades away. What’s needed are new algorithms. Cosmos Club, PSW seminar series, Washington DC 9/19/2025 Talk: https://lnkd.in/e6M36hE9
Entendi duas coisas do cartaz: que a definição atual de supremacia quântica é mais comercial que prática , e que ele não sugere uma definição alternativa, apenas um marco : assim a afirmação a ser refutada seria : Estamos a várias décadas de manter cerca de 2.000 qbits lógicos coerentes por tempo suficiente para quebrar RSA!
MATHEMATICIAN AND COMPUTER SCIENTIST SPECIALIZED IN LINEAR ALGEBRA AND THEORETICAL COMPUTING The theory of computing focuses on understanding the fundamental principles and limits of computation.
5dWendell Damato Luciano Lampi Lawrence Chung Koo Massachusetts Institute of Technology Peter Shor Marco Tulli Douglas Guedes de Castro José Antonio Comegno Filho Tiago Amaro Guilherme Pedriali Guilherme Meirelles