Papers | Satoshi Yoshida

2024

arXiv
Multicopy quantum state teleportation with application to storage and retrieval of quantum programs

Frédéric Grosshans, Michał Horodecki, Mio Murao, Tomasz Młynik, Marco Túlio Quintino, Michał Studziński, Satoshi Yoshida

arXiv:2409.10393 (2024).

Abs arXiv Bib

This work considers a teleportation task for Alice and Bob in a scenario where Bob cannot perform corrections. In particular, we analyse the task of multicopy state teleportation, where Alice has k identical copies of an arbitrary unknown d-dimensional qudit state |ψ⟩to teleport a single copy of |ψ⟩to Bob using a maximally entangled two-qudit state shared between Alice and Bob without Bob’s correction. Alice may perform a joint measurement on her half of the entangled state and the k copies of |ψ⟩. We prove that the maximal probability of success for teleporting the exact state |ψ⟩to Bob is p(d,k)=k/[d(k-1+d)] and present an explicit protocol to attain this performance. Then, by utilising k copies of an arbitrary target state |ψ⟩, we show how the multicopy state teleportation protocol can be employed to enhance the success probability of storage and retrieval of quantum programs, which aims to universally retrieve the action of an arbitrary quantum channel that is stored in a state. Our proofs make use of group representation theory methods, which may find applications beyond the problems addressed in this work.
@article{frederic2024multicopy, title = {{Multicopy quantum state teleportation with application to storage and retrieval of quantum programs}}, author = {Grosshans, Fr\'ed\'eric and Horodecki, Micha{\l} and Murao, Mio and M{\l}ynik, Tomasz and Quintino, Marco T\'ulio and Studzi\'nski, Micha{\l} and Yoshida, Satoshi}, year = {2024}, }
arXiv
One-to-one Correspondence between Deterministic Port-Based Teleportation and Unitary Estimation

Satoshi Yoshida, Yuki Koizumi, Michał Studziński, Marco Túlio Quintino, Mio Murao

arXiv:2408.11902 (2024).

Abs arXiv Bib

Port-based teleportation is a variant of quantum teleportation, where the receiver can choose one of the ports in his part of the entangled state shared with the sender, but cannot apply other recovery operations. We show that the optimal fidelity of deterministic port-based teleportation (dPBT) using N=n+1 ports to teleport a d-dimensional state is equivalent to the optimal fidelity of d-dimensional unitary estimation using n calls of the input unitary operation. From any given dPBT, we can explicitly construct the corresponding unitary estimation protocol achieving the same optimal fidelity, and vice versa. Using the obtained one-to-one correspondence between dPBT and unitary estimation, we derive the asymptotic optimal fidelity of port-based teleportation given by F = 1-Θ(d^4 N^-2), which improves the previously known result given by 1-O(d^5 N^-2) ≤F ≤1-Ω(d^2 N^-2). We also show that the optimal fidelity of unitary estimation for the case n≤d-1 is F = n+1 \over d^2, and this fidelity is equal to the optimal fidelity of unitary inversion with n≤d-1 calls of the input unitary operation even if we allow indefinite causal order among the calls.
@article{yoshida2024one, title = {{One-to-one Correspondence between Deterministic Port-Based Teleportation and Unitary Estimation}}, author = {Yoshida, Satoshi and Koizumi, Yuki and Studzi\'nski, Micha{\l} and Quintino, Marco T\'ulio and Murao, Mio}, year = {2024}, }
arXiv
Analytical lower bound on the number of queries to a black-box unitary operation in deterministic exact transformations of unknown unitary operations

Tatsuki Odake, Satoshi Yoshida, Mio Murao

arXiv:2405.07625 (2024).

Abs arXiv Bib

Several counter-intuitive go-theorems have recently been shown for transformations of unknown unitary operations; deterministic and exact complex conjugation, inversion, and transposition of a general d-dimensional unknown unitary operation are implementable with a finite number of queries of the black-box unitary operation. However, the minimum numbers of the required queries are not known except for d=2 unitary inversion and unitary transposition (numerical) and unitary conjugation (analytic). In this work, we derive complementary no-go theorems for deterministic and exact implementations of inversion and transposition of a d-dimensional unknown unitary operation under certain numbers of queries. The obtained no-go theorem indicates that the analytical lower bound of the number of queries for unitary inversion is d^2 and that for unitary transposition is 4 for d=2 and d+3 for d≥3. We have developed a new framework that utilizes differentiation to obtain the analytical lower bounds on the number of queries to the black-box unitary operation required to implement a transformation given by a general differentiable function mapping a unitary operation to another unitary operation, which reproduces the lower bound of the number of queries for unitary complex conjugation d−1. As a corollary, we show the relationship between the tightness of the lower bounds and the existence of optimal catalytic transformations, which is a new aspect recently identified in the study of deterministic and exact unitary inversion. Furthermore, we extend our framework to the probabilistic setting where the transformation is required to succeed with a certain probability, thereby showing a possible tradeoff relation between query numbers and the required success probability.
@article{odake2024analytical, title = {{Analytical lower bound on the number of queries to a black-box unitary operation in deterministic exact transformations of unknown unitary operations}}, author = {Odake, Tatsuki and Yoshida, Satoshi and Murao, Mio}, year = {2024}, }
arXiv
Concatenate codes, save qubits

Satoshi Yoshida, Shiro Tamiya, Hayata Yamasaki

arXiv:2402.09606 (2024).

Abs arXiv Bib

The essential requirement for fault-tolerant quantum computation (FTQC) is the total protocol design to achieve a fair balance of all the critical factors relevant to its practical realization, such as the space overhead, the threshold, and the modularity. A major obstacle in realizing FTQC with conventional protocols, such as those based on the surface code and the concatenated Steane code, has been the space overhead, i.e., the required number of physical qubits per logical qubit. Protocols based on high-rate quantum low-density parity-check (LDPC) codes gather considerable attention as a way to reduce the space overhead, but problematically, the existing fault-tolerant protocols for such quantum LDPC codes sacrifice the other factors. Here we construct a new fault-tolerant protocol to meet these requirements simultaneously based on more recent progress on the techniques for concatenated codes rather than quantum LDPC codes, achieving a constant space overhead, a high threshold, and flexibility in modular architecture designs. In particular, under a physical error rate of 0.1%, our protocol reduces the space overhead to achieve the logical CNOT error rates 10^−10 and 10^−24 by more than 90% and 97%, respectively, compared to the protocol for the surface code. Furthermore, our protocol achieves the threshold of 2.4% under a conventional circuit-level error model, substantially outperforming that of the surface code. The use of concatenated codes also naturally introduces abstraction layers essential for the modularity of FTQC architectures. These results indicate that the code-concatenation approach opens a way to significantly save qubits in realizing FTQC while fulfilling the other essential requirements for the practical protocol design.
@article{yoshida2024concatenate, author = {Yoshida, Satoshi and Tamiya, Shiro and Yamasaki, Hayata}, year = {2024}, }
arXiv
Universal adjointation of isometry operations using transformation of quantum supermaps

Satoshi Yoshida, Akihito Soeda, Mio Murao

arXiv:2401.10137 (2024).

Abs arXiv Bib

Identification of possible transformations of quantum objects including quantum states and quantum operations is indispensable in developing quantum algorithms. Universal transformations, defined as input-independent transformations, appear in various quantum applications. Such is the case for universal transformations of unitary operations. However, extending these transformations to non-unitary operations is nontrivial and largely unresolved. Addressing this, we introduce isometry adjointation protocols that convert an input isometry operation into its adjoint operation, which include both unitary operation and quantum state transformations. The paper details the construction of parallel and sequential isometry adjointation protocols, derived from unitary inversion protocols using quantum combs, and achieving optimal approximation error. This error is shown to be independent of the output dimension of the isometry operation. In particular, we explicitly obtain an asymptotically optimal parallel protocol achieving an approximation error ε=Θ(d^2/n), where d is the input dimension of the isometry operation and n is the number of calls of the isometry operation. The research also extends to isometry inversion and universal error detection, employing semidefinite programming to assess optimal performances. The findings suggest that the optimal performance of general protocols in isometry adjointation and universal error detection is not dependent on the output dimension, and that indefinite causal order protocols offer advantages over sequential ones in isometry inversion and universal error detection.
@article{yoshida2024universal, title = {{Universal adjointation of isometry operations using transformation of quantum supermaps}}, author = {Yoshida, Satoshi and Soeda, Akihito and Murao, Mio}, year = {2024}, }

2023

Phys. Rev. Lett.
Reversing Unknown Qubit-Unitary Operation, Deterministically and Exactly

Satoshi Yoshida, Akihito Soeda, Mio Murao

Phys. Rev. Lett. 131, 120602 (2023).

Abs arXiv Journal Bib

We report a deterministic and exact protocol to reverse any unknown qubit-unitary operation, which simulates the time inversion of a closed qubit system. To avoid known no-go results on universal deterministic exact unitary inversion, we consider the most general class of protocols transforming unknown unitary operations within the quantum circuit model, where the input unitary operation is called multiple times in sequence and fixed quantum circuits are inserted between the calls. In the proposed protocol, the input qubit-unitary operation is called 4 times to achieve the inverse operation, and the output state in an auxiliary system can be reused as a catalyst state in another run of the unitary inversion. We also present the simplification of the semidefinite programming for searching the optimal deterministic unitary inversion protocol for an arbitrary dimension presented by M. T. Quintino and D. Ebler [Quantum 6, 679 (2022)]. We show a method to reduce the large search space representing all possible protocols, which provides a useful tool for analyzing higher-order quantum transformations for unitary operations.
@article{yoshida2023reversing, title = {{Reversing Unknown Qubit-Unitary Operation, Deterministically and Exactly}}, author = {Yoshida, Satoshi and Soeda, Akihito and Murao, Mio}, journal = {Phys. Rev. Lett.}, volume = {131}, pages = {120602}, year = {2023}, doi = {10.1103/PhysRevLett.131.120602} }
Quantum
Universal construction of decoders from encoding black boxes

Satoshi Yoshida, Akihito Soeda, Mio Murao

Quantum 7, 957 (2023).

Abs arXiv Journal Bib

Isometry operations encode the quantum information of the input system to a larger output system, while the corresponding decoding operation would be an inverse operation of the encoding isometry operation. Given an encoding operation as a black box from a d-dimensional system to a D-dimensional system, we propose a universal protocol for isometry inversion that constructs a decoder from multiple calls of the encoding operation. This is a probabilistic but exact protocol whose success probability is independent of D. For a qubit (d=2) encoded in n qubits, our protocol achieves an exponential improvement over any tomography-based or unitary-embedding method, which cannot avoid D-dependence. We present a quantum operation that converts multiple parallel calls of any given isometry operation to random parallelized unitary operations, each of dimension d. Applied to our setup, it universally compresses the encoded quantum information to a D-independent space, while keeping the initial quantum information intact. This compressing operation is combined with a unitary inversion protocol to complete the isometry inversion. We also discover a fundamental difference between our isometry inversion protocol and the known unitary inversion protocols by analyzing isometry complex conjugation and isometry transposition. General protocols including indefinite causal order are searched using semidefinite programming for any improvement in the success probability over the parallel protocols. We find a sequential "success-or-draw" protocol of universal isometry inversion for d=2 and D=3, thus whose success probability exponentially improves over parallel protocols in the number of calls of the input isometry operation for the said case.
@article{yoshida2023universal, author = {Yoshida, Satoshi and Soeda, Akihito and Murao, Mio}, journal = {Quantum}, volume = {7}, pages = {957}, year = {2023}, publisher = {Verein zur F{\"o}rderung des Open Access Publizierens in den Quantenwissenschaften}, doi = {10.22331/q-2023-03-20-957} }

2022

Phys. Rev. Res.
Thermodynamic role of main reaction pathway and multi-body information flow in membrane transport

Satoshi Yoshida, Yasushi Okada, Eiro Muneyuki, Sosuke Ito

Phys. Rev. Res. 4, 023229 (2022).

Abs arXiv Journal Bib

The two classes of membrane transport, namely, secondary active and passive transport, are understood as different reaction pathways in the same protein structure, described by the 16-state model in this paper. To quantify the thermodynamic difference between secondary active transport and passive transport, we extend the second law of information thermodynamics of the autonomous demon in the four-state model composed of two subsystems to the 16-state model composed of four subsystems representing the membrane transport. We reduce the 16 states to 4 states and derive the coarse-grained second law of information thermodynamics, which provides an upper bound of the free energy transport by the coarse-grained information flow. We also derive an upper bound on the free energy transport by the multi-body information flow representing the two-body or four-body correlations in the 16-state model by exploiting the cycle decomposition. The coarse-grained information flow and the multi-body information flows express the quantitative difference between secondary active and passive transport. The numerical analysis shows that the coarse-grained information flow is positive for secondary active transport and negative for passive transport. The four-body correlation is dominant in the multi-body information flows for secondary active transport. In contrast, the two-body correlation is dominant for passive transport. This result shows that both the sign of the coarse-grained information flow and the difference of the four-body correlation and the two-body correlation explain the difference of the free energy transport in secondary active and passive transport.
@article{yoshida2022thermodynamic, title = {Thermodynamic role of main reaction pathway and multi-body information flow in membrane transport}, author = {Yoshida, Satoshi and Okada, Yasushi and Muneyuki, Eiro and Ito, Sosuke}, journal = {Phys. Rev. Res.}, volume = {4}, number = {2}, pages = {023229}, year = {2022}, publisher = {APS}, doi = {10.1103/PhysRevResearch.4.023229} }