Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection

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.Comment: 29 pages, 3 figures, v2: Added Result 3 and improved Result

Computational self-testing for entangled magic states

In the seminal paper [Metger and Vidick, Quantum ’21], they proposed a computational self-testing protocol for Bell states in a single quantum device. Their protocol relies on the fact that the target states are stabilizer states, and hence it is highly non-trivial to reveal whether the other class of quantum states, non-stabilizer states, can be self-tested within their framework. Among non-stabilizer states, magic states are indispensable resources for universal quantum computation. In this letter, we show that a magic state for the CCZ gate can be self-tested while that for the T gate cannot. Our result is applicable to a proof of quantumness, where we can classically verify whether a quantum device generates a quantum state having non zero magic

An emissive charge-transfer excited-state at the well-defined hetero-nanostructure interface of an organic conjugated molecule and two-dimensional inorganic nanosheet

Precise engineering of excited-state interactions between an organic conjugated molecule and a two-dimensional semiconducting inorganic nanosheet, specifically the manipulation of charge-transfer excited (CTE) states, still remains a challenge for state-of-the-art photochemistry. Herein, we report a long-lived, highly emissive CTE state at structurally well-defined hetero-nanostructure interfaces of photoactive pyrene and two-dimensional MoS2 nanosheets via an N-benzylsuccinimide bridge (Py-Bn-MoS2). Spectroscopic measurements reveal that no charge-transfer state is formed in the ground state, but the locally-excited (LE) state of pyrene in Py-Bn-MoS2 efficiently generates an unusual emissive CTE state. Theoretical studies elucidate the interaction of MoS2 vacant orbitals with the pyrene LE state to form a CTE state that shows a distinct solvent dependence of the emission energy. This is the first example of organic-inorganic 2D hetero-nanostructures displaying mixed luminescence properties by an accurate design of the bridge structure, and therefore represents an important step in their applications for energy conversion and optoelectronic devices and sensors