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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