[Paper Review] Algorithmic approach to quantum physics

Yuri Ozhigov|ArXiv.org|Dec 26, 2004

Quantum Computing Algorithms and Architecture3 citations

TL;DR

This paper proposes an algorithmic approach to quantum physics, modeling quantum dynamics as a classical simulation using effective algorithms with polynomial resource costs. By introducing a minimal amplitude threshold (amplitude quantum), it derives Born's rule and decoherence naturally, unifying unitary evolution and measurement without observers, while ruling out scalable quantum computing as physically impossible under this framework.

ABSTRACT

Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the analysis, and a simulation gives a "film" which visualizes many particle quantum dynamics and is demonstrated to a user of the model. Restrictions following from the algorithm theory are considered on a level of fundamental physical laws. Born rule for the calculation of quantum probability as well as the decoherence is derived from the existence of a nonzero minimal value of amplitude module - a grain of amplitude. The limitation on the classical computational resources gives the unified description of quantum dynamics that is not divided to the unitary dynamics and measurements and does not depend on the existence of observer. It is proposed the description of states based on the nesting of particles in each other that permits to account the effects of all levels in the same model. Algorithmic approach admits the possibility of refutation, because it forbids the creation of a scalable quantum computer that is allowed in the conventional quantum formalism.

Motivation & Objective

• To develop a classical computational framework that simulates quantum dynamics of many-particle systems with polynomial time and memory costs.
• To unify unitary evolution and measurement into a single classical simulation process, independent of observers.
• To derive quantum probability (Born's rule) and decoherence from fundamental algorithmic constraints, particularly a minimal amplitude threshold.
• To challenge the feasibility of scalable quantum computers by showing they contradict the algorithmic approach's computational limits.
• To provide a practical, programmable model of quantum physics based on hierarchical particle nesting and amplitude reduction.

Proposed method

• Simulate quantum dynamics using a classical computer with effective algorithms requiring polynomial time and memory relative to system size.
• Represent quantum states hierarchically, where groups of particles at the same level form entangled states treated as single particles in the next level.
• Apply a reduction procedure that sets amplitudes below a fixed threshold (amplitude quantum) to zero, eliminating negligible superpositions.
• Use the amplitude reduction to simulate decoherence naturally, without explicit environmental modeling.
• Ensure probability conservation and approximate Born's rule by retaining only events with probability ≥ 1/T, where T is total simulation time.
• Represent the system evolution as a 'film' for visualization, with user-defined measurement points, avoiding observer interference.

Experimental results

Research questions

• RQ1 Can quantum dynamics of many-particle systems be fully simulated on a classical computer with polynomial resources?
• RQ2 Does the existence of a minimal amplitude (amplitude quantum) lead to the emergence of Born's rule and decoherence?
• RQ3 Can the distinction between unitary evolution and measurement be eliminated in a classical simulation framework?
• RQ4 Is the scalability of quantum computers compatible with the algorithmic approach's computational constraints?
• RQ5 How can quantum entanglement across all particle levels be accounted for within a resource-efficient simulation model?

Key findings

• The algorithmic approach derives Born's rule from the existence of a minimal amplitude module, eliminating the need for additional postulates.
• Decoherence emerges naturally from the amplitude reduction procedure, without requiring explicit environmental degrees of freedom.
• The simulation unifies unitary evolution and measurement into a single classical computational process, independent of observer presence.
• The model forbids the existence of a scalable quantum computer, contradicting conventional quantum formalism.
• The hierarchical nesting of particles allows efficient simulation of complex quantum systems by treating entangled groups as single entities.
• The approach provides a practical, programmable framework for simulating quantum dynamics with clear computational limits and visual output.