Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection

• URL: http://arxiv.org/abs/2206.05434v3
• Date: Wed, 27 Dec 2023 00:56:39 GMT
• Title: Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection
• Authors: Ryo Hiromasa, Akihiro Mizutani, Yuki Takeuchi, Seiichiro Tani
• Abstract summary: We show that any problem in $sf PostBQP$ can be solved with only postselections whose probabilities are close to one. We also show that a single rewind operator is sufficient to achieve tasks that are intractable for quantum computation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We define rewinding operators that invert quantum measurements. Then, we define complexity classes ${\sf RwBQP}$, ${\sf CBQP}$, and ${\sf AdPostBQP}$ as sets of decision problems solvable by polynomial-size quantum circuits with a polynomial number of rewinding operators, cloning operators, and adaptive postselections, respectively. Our main result is that ${\sf BPP}^{\sf PP}\subseteq{\sf RwBQP}={\sf CBQP}={\sf AdPostBQP}\subseteq{\sf PSPACE}$. As a byproduct of this result, we show that any problem in ${\sf PostBQP}$ can be solved with only postselections of outputs whose probabilities are polynomially close to one. Under the strongly believed assumption that ${\sf BQP}\nsupseteq{\sf SZK}$, or the shortest independent vectors problem cannot be efficiently solved with quantum computers, we also show that a single rewinding operator is sufficient to achieve tasks that are intractable for quantum computation. In addition, we consider rewindable Clifford and instantaneous quantum polynomial time circuits.

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