Extensively Not P-Bi-Immune promiseBQP-Complete Languages

TL;DR

This paper explores the classical simulability of quantum circuits, establishing the existence of infinitely many such instances under various restrictions, and introduces a language to which all BQP problems reduce, with implications for P-bi-immunity.

Contribution

It demonstrates the existence of infinitely many classically simulable quantum circuit instances beyond Gottesman-Knill, and constructs a language to which all BQP problems reduce, challenging assumptions about P-bi-immunity.

Findings

Existence of infinite classically simulable quantum circuit instances.

Many restrictions still allow infinite simulable instances.

A universal language reducible from all BQP problems, not P-bi-immune.

Abstract

In this paper, I first establish -- via methods other than the Gottesman-Knill theorem -- the existence of an infinite set of instances of simulating a quantum circuit to decide a decision problem that can be simulated classically. I then examine under what restrictions on quantum circuits the existence of infinitely many classically simulable instances persists. There turns out to be a vast number of such restrictions, and any combination of those found can be applied at the same time without eliminating the infinite set of classically simulable instances. Further analysis of the tools used in this then shows there exists a language that every (promise) BQP language is one-one reducible to. This language is also not P-bi-immune under very many promises.