Quantum

The Classical Boundary of Quantum Computation: History-Resolved Causal Stochastic Machines and the Cost of Classicalization

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Briefings

This article proposes a precise classical boundary for quantum computation using history-resolved causal stochastic machines (HCSMs). It establishes that HCSM history laws coincide exactly with the fixed-basis, prefix-preserving diagonal sector of ideal quantum processes, denoted as PTM_proc. This boundary is identified as the limit where reversible quantum processes can be simulated stochastically, while coherent quantum processes extend strictly beyond it. The paper argues that universal quantum continuations require retaining predictive information absent from visible probabilities, leading to quantum-state dimension lower bounds under full-state encoding assumptions.

Key points

• HCSM history laws coincide exactly with the fixed-basis, prefix-preserving diagonal sector of ideal quantum processes, denoted as PTM_proc.
• The boundary between quantum and classical computation is defined by the requirement to retain predictive information absent from visible probabilities in stochastic simulations.

Context

The study addresses the fundamental question of what separates quantum computation from classical computation when a classical model may retain every branch history and arbitrary causal memory. This research provides a precise classical boundary and a no-free-classicalization principle, refining the familiar slogan PTM subset QTM into a specific structural constraint on quantum processes.

Limitations

The evidence is limited to a single preprint (arXiv:2610.22750v1) from October 2026, which may not reflect final peer-reviewed conclusions. The study relies on theoretical proofs and abstract definitions rather than experimental data or empirical validation. Key parameters like specific dimension lower bounds are derived under continuous full-state encoding assumptions without detailed numerical constraints or known exceptions.

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