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arXiv:2409.03785

Optimization of Postselection in Quantum Algorithms: A Two-Way Quantum Computing Approach

Linden, Alex, Betül Gül

Published Aug 30, 2024• 0 citations
arXivHTMLPDF

Abstract

Postselection is an operation that allows the selection of specific measurement outcomes. It serves as a powerful theoretical tool for enhancing the performance of existing quantum algorithms. Despite recent developments such as time reversal in quantum measurements and IBM's mid-circuit measurements, postselection continues to face significant challenges, most notably poor, often exponential, scaling. This study investigates how Two-Way Quantum Computing (2WQC) offers potential solutions to these challenges. By introducing the concept of postparation and enabling dynamic quantum state control, 2WQC has the potential to mitigate scaling issues and improve the practicality of postselection, thereby fostering advancements in the field of quantum algorithms.

DOI
10.48550/arxiv.2409.03785

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Postselection is an operation that allows the selection of specific measurement outcomes. It serves as a powerful theoretical tool for enhancing the performance of existing quantum algorithms. Despite recent developments such as time reversal in quantum measurements and IBM's mid-circuit measurements, postselection continues to face significant challenges, most notably poor, often exponential, scaling. This study investigates how Two-Way Quantum Computing (2WQC) offers potential solutions to these challenges. By introducing the concept of postparation and enabling dynamic quantum state control, 2WQC has the potential to mitigate scaling issues and improve the practicality of postselection, thereby fostering advancements in the field of quantum algorithms.
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While quantum computers assume existence of state preparation process ∣0⟩|0\rangle∣0⟩, CPT symmetry of physics says that performing such process in CPT symmetry perspective, e.g. reversing used EM impulses (V(t)→V(−t)V(t)\to V(-t)V(t)→V(−t)), we should get its symmetric analog ⟨0∣\langle 0|⟨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⟩|0\rangle∣0⟩ and ⟨0∣\langle 0|⟨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.
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We study quantum measurements with preselection and postselection, and derive the precise expressions of the measurement results without any restriction on the coupling strength. For a qubit system, we derive the maximum measurement results by choosing appropriate initial and finial states. Significant amplification effect is obtained when the interaction between the system and the measuring device is very weak; and typical ideal quantum measurement results are obtained when the interaction is strong. The improvement of the signal-to-noise ratio (SNR) and the enhancement of the measure sensitivity (MS) by weak measurements are studied. Without considering the probability decrease due to postselection, the SNR and the MS can both be significantly improved by weak measurements; surprisingly, neither SNR nor MS can be effectively improved when the probability decrease is considered.