Quantum parallelism may be limited

TL;DR

This paper explores a limited quantum formalism constrained by classical computer memory, showing it preserves standard quantum mechanics but restricts the speed of quantum algorithms, especially affecting scalable quantum computing.

Contribution

It introduces a formalism that models quantum processes with limited classical memory, highlighting the impact on quantum algorithm speed and scalability.

Findings

Quantum evolutions slow down with increasing entangled state dimension

The formalism aligns with current experiments but limits quantum computational speed

Memory constraints of 10-20 qubits are sufficient for simulation purposes

Abstract

We consider quantum formalism limited by the classical simulating computer with the fixed memory. The memory is redistributed in the course of modeling by the variation of the set of classical states and the accuracy of the representation of amplitudes. This computational description completely preserves the conventional formalism and does not contradicts to experiments, but it makes impossible fast quantum algorithms. This description involves the slow down of quantum evolutions with the growth of the dimension of the minimal subspace containing entangled states, which arise in the evolution. This slow down is the single difference of the proposed formalism from the standard one; it is negligible for the systems from the usual experiments, including those in which many entangled particle participate, but grows rapidly in the attempt to realize the scalable quantum computations, which require the unlimited parallelism. The experimental verification of this version of quantum formalism is reduced to the fixation of this slow down. In all probability the memory of the abstract computer simulating quantum processes is limited by 10-20 qubits, so it iss possible to use the exiting computers for this aim.