Determinism vs. Amplification Computation by Admissibility as an Alternative to Quantum Randomness

Stefano Pironio

Michael Aksman

Modern quantum information theory assumes that absolute security and computational advantage must emerge from the controlled amplification of microscopic uncertainty. This assumption has culminated in the recent ETH Zurich randomness amplification experiment, where cryptographic security is obtained through Bell certified randomness generated by cryogenic superconducting qubits. We argue that this approach represents the final and most refined expression of a deeper legacy paradigm: Computation by Exploration. In this paradigm, a machine explores an enormous state space and relies on probability or filtering to locate useful states. In this manuscript, we present a fundamental alternative: Computation by Admissibility. In this paradigm, the physical state space itself is constrained so that inadmissible states simply cannot exist. By utilizing the deterministic topological projections of the DSM-861 architecture, we demonstrate that security, error correction, memory, and computation are not distinct algorithmic tasks,

Detlef Dürr, Sheldon Goldstein, Nino Zanghı̀

Michael Aksman

This work introduces "Computation by Admissibility" as a deterministic, physical alternative to quantum computing's reliance on combinatorial state exploration and randomness amplification. Rather than expending massive overhead to maintain fragile superpositions and perform active error correction, this framework establishes rigid topological and geometric boundary conditions where the desired solution emerges as the only admissible physical state. The computational substrate is grounded in three-dimensional solenoidal vortex dynamics. Convective vortex stretching accelerates system trajectories toward localized reconnection events, where anomalous inviscid dissipation acts as an irreversible thermodynamic trapdoor, permanently expelling environmental perturbations. In the Deterministic Spectral Manifold (DSM-861) processor architecture, stability is enforced through a dual-layer mechanism: out-of-plane noise is instantaneously annihilated by geometric boundary projection, while in-plane fluctuations are exponentially suppressed by a massive discrete spectral gap. Computation is thus transformed from probabilistic exploration into autonomous physical relaxation down a Lyapunov free-energy landscape, achieving hardware-level fault tolerance without algorithmic overhead or quantum randomness.

Nikolay V. Vitanov

Abstract In quantum computation the target fidelity of the qubit gates is very high, with the admissible error being in the range from 10−3 to 10−4 and even less, depending on the protocol. The direct experimental determination of such a tiny error is very challenging by standard quantum-process tomography. Instead, the method of randomized benchmarking, which uses a random sequence of Clifford gates, has become a standard tool for determination of the average gate error as the decay constant in the exponentially decaying fidelity. In this paper, the task for determining a tiny error is addressed by sequentially repeating the same gate multiple times, which leads to the coherent amplification of the error, until it reaches large enough values to be measured reliably. If the transition probability is p = 1 − ϵ with ϵ ≪ 1 in the single process, then classical intuition dictates that the probability after N passes should be P N ≈ 1 − N ϵ . However, this classical expectation is misleading because it neglects interference effects. This paper presents a rigorous theoretical analysis based on the SU(2) symmetry of the qubit propagator, resulting in explicit analytic relations that link the N-pass propagator to the single-pass one in terms of Chebyshev polynomials. In particular, the relations suggest that in some special cases the N-pass transition probability degrades as P N = 1 − N 2 ϵ , i.e. dramatically faster than the classical probability estimate. In the general case, however, the relation between the single-pass and N-pass propagators is much more involved. Recipes are proposed for unambiguous determination of the gate errors in the general case for both Clifford and non-Clifford gates.