3-SAT solver for two-way quantum computers

TL;DR

This paper proposes a practical 3-SAT solver for two-way quantum computers, leveraging CPT symmetry to enhance error correction and potentially solve NP problems more efficiently than traditional quantum algorithms.

Contribution

It introduces a novel approach to implement 2WQC 3-SAT solving with exponential error reduction through linear gate scaling, enhancing error correction and stability.

Findings

Error rate can be exponentially reduced by linearly increasing gates.

2WQC offers improved error correction and stability over traditional quantum methods.

Potential to solve NP problems more efficiently than existing quantum algorithms.

Abstract

While quantum computers assume existence of state preparation process $|0\rangle$, CPT symmetry of physics says that performing such process in CPT symmetry perspective, e.g. reversing used EM impulses ($V(t)\to V(-t)$), we should get its symmetric analog $\langle 0|$, referred here as state postparation - which should provide results as postselection, but with higher success rate. Two-way quantum computers (2WQC) assume having both $|0\rangle$ and $\langle 0|$ pre and postparation. In theory they allow to solve NP problems, however, basic approach would be more difficult than Shor algorithm, which is now far from being practical. This article discusses approach to make practical 2WQC 3-SAT solver, requiring exponential reduction of error rate, what should be achievable through linear increase of the numbers of gates. 2WQC also provides additional error correction capabilities, like more stable Grover algorithm, or mid-circuit enforcement of syndrome to zero, like proposed equalizer enforcing qubit equality.