3-SAT solver for two-way quantum computers

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.