arXiv subjects

Akihito Soeda

Publications and source records attributed to Akihito Soeda.

At least 19 recordsLinked to original sources

arXiv2026

Comparison of unknown unitary channels with multiple queries

Comparison of quantum objects is the task of determining relational properties, such as whether two unknown objects are the same or different, without identifying the objects themselves. Multiple copies of unknown states or multiple queries to unknown channels are natural resources for improving comparison, and the optimal strategy for pure-state comparison with multiple copies is known. For unitary-channel comparison with multiple queries, however, the optimal strategy has been unclear because different queries can be arranged in parallel, sequentially, adaptively, or in more general causal structures. We study comparison of two unknown $d$-dimensional unitary channels using $N_1$ and $N_2$ queries to the two channels, respectively, under the promise that they are either identical Haar-random unitaries or independent Haar-random unitaries. We optimize over valid general testers, a class containing ordinary quantum testers, classically controlled causal orders, and indefinite-causal-order processes. We characterize the optimal minimum-error and one-sided unambiguous comparison probabilities for arbitrary finite query numbers. The upper bound in fact holds for a larger positive relaxation, while the optimum is attained by a valid parallel tester. The optimum is determined by a finite representation-theoretic parameter built from Young diagrams and Littlewood--Richardson coefficients. For fixed $N_1$, the performance is saturated for every $N_2\geq(d-1)N_1$. By contrast, the corresponding pure-state comparison parameter has no finite-$N_2$ saturation and reaches its known-reference limit only asymptotically, yielding continued success-probability improvement in the nontrivial decision regime. This highlights a sharp difference between comparison tasks for states and channels, analogous to distinctions known in quantum discrimination.

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arXiv2026

Promise and Challenges of Distimation

Estimating the quality of raw entangled states and distilling high-fidelity entanglement traditionally require two separate link-layer protocols in a quantum network stack, each consuming its own share of fragile entangled pairs. The recently introduced distimation concept merges these two protocols by directly extracting state estimation data from the classical syndromes generated during entanglement distillation. By removing the dedicated "test-then-distill'' stage, distimation lowers the number of raw entangled pairs required to operate the network, reduces latency, and streamlines the network control plane. The paradigm is especially attractive for near-term hardware platforms, where entanglement generation remains a severe bottleneck. Alongside these promises, distimation introduces new engineering challenges, ranging from accurate local-device modeling to protocols for tracking time-varying sources. This article surveys the core principles of distimation, quantifies expected gains for realistic architectures, and outlines a research roadmap toward making distimation a standard building block in future quantum networks.

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arXiv2026

Parameter Calibration for Reduced-Bandwidth Two-Photon Waveguide-QED Simulations

Waveguide-QED platforms represent one potential approach to scalable quantum technologies, but their simulation remains computationally demanding due to the large number of frequency modes required to describe traveling photons. In practice, increasing the simulated bandwidth rapidly raises the numerical cost, leading to a trade-off between accuracy and tractability. The existing approaches formulated in time-domain indirectly control this trade-off through the choice of time step, which obscures the connection between discretization parameters and the represented spectral window. In this work, we introduce an end-to-end framework to explicitly control the effective bandwidth in waveguide-QED simulations of two-photon scattering. We show that truncating the frequency domain requires consistent shifts of the model parameters, and derive a systematic calibration procedure that preserves the physical accuracy of the reduced model. This enables tuning the central frequency and the bandwidth of the numerical spectrum, leading to a several-fold reduction in the Hilbert space dimension while maintaining physical accuracy. We discuss the limitations of this calibration and relate the finite-bandwidth viewpoint to time-domain discretizations.

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arXiv2026

Renormalization Treatment of IR and UV Cutoffs in Waveguide QED and Implications to Numerical Model Simulation

We present a non-perturbative, first-principles derivation of renormalization relations for waveguide-QED models, explicitly accounting for the infrared (IR) and ultraviolet (UV) cutoffs that are necessarily introduced in numerical simulations. By formulating the atomic dynamics in the time domain, we obtain explicit expressions linking the bare model parameters to the physically observable atomic frequency and decay rate, and verify their consistency with scattering theory. We further connect these results to standard Feynman diagrams, providing a transparent physical interpretation and ensuring the generality of the approach. Finally, we show how these renormalization relations can be used to parameterize simulations with a minimal frequency bandwidth, simultaneously preserving physical accuracy and reducing computational cost, thereby paving the way for efficient and reliable multi-photon light-matter simulations.

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arXiv2025

Efficient graph-diagonal characterization of noisy states distributed over quantum networks via Bell sampling

Graph states are an important class of entangled states that serve as a key resource for distributed information processing and communication in quantum networks. In this work, we propose a protocol that utilizes a Bell sampling subroutine to characterize the diagonal elements in the graph basis of noisy graph states distributed across a network. Our approach offers significant advantages over direct diagonal estimation using unentangled single-qubit measurements in terms of scalability. Specifically, we prove that estimating the full vector of diagonal elements requires a sample complexity that scales linearly with the number of qubits ($\mathcal{O}(n)$), providing an exponential reduction in resource overhead compared to the best known $\mathcal{O}(2^n)$ scaling of direct estimation. Furthermore, we demonstrate that global properties, such as state fidelity, can be estimated with a sample complexity independent of the network size. Finally, we present numerical results indicating that the estimation in practice is more efficient than the derived theoretical bounds. Our work thus establishes a promising technique for efficiently estimating noisy graph states in large networks under realistic experimental conditions.

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arXiv2025

Low Cost Bayesian Experimental Design for Quantum Frequency Estimation with Decoherence

A two-level quantum system evolving under a time-independent Hamiltonian produces oscillatory measurement probabilities. The estimation of the associated frequency is a cornerstone problem in quantum metrology, sensing, calibration and control. In this work, we tackle this task by introducing WES: a Window Expansion Strategy for low cost adaptive Bayesian experimental design. WES employs empirical cost-reduction techniques to keep the optimization overhead low, curb scaling problems, and enable high degrees of parallelism. Unlike previous heuristics, it offers adjustable classical processing costs that determine the performance standard. As a benchmark, we analyze the performance of widely adopted heuristics, comparing them with the fundamental limits of metrology and a baseline random strategy. Numerical simulations show that WES delivers the most reliable performance and fastest learning rate, saturating the Heisenberg limit.

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arXiv2025

A double selection entanglement distillation-based state estimator

With the advent of practical quantum communication networks drawing closer, there is a growing need for reliable estimation protocols that can efficiently characterize quantum resources with minimum resource overhead requirement. A novel approach to this problem is to integrate an estimator into an existing network task, thereby removing the need for an additional characterization protocol. In this work, we show that the measurement statistics of a double selection distillation protocol alone can be used to efficiently estimate the Bell-diagonal parameters of the undistilled states, as well as the resulting distilled states after additional post-processing. We also demonstrate that this novel estimator outperforms the previously proposed distillation-based estimator in terms of resource complexity.

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arXiv2025

Universal adjointation of isometry operations using conversion of quantum supermaps

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 transform 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 the (dual) Clebsch-Gordan transforms, 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.

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arXiv2024

Fast simulation for multi-photon, atomic-ensemble quantum model of linear optical systems addressing the curse of dimensionality

Photons are elementary particles of light in quantum mechanics, whose dynamics can be difficult to gain detailed insights, especially in complex systems. Simulation is a promising tool to resolve this issue, but it must address the curse of dimensionality, namely, that the number of bases increases exponentially in the number of photons. Here we mitigate this dimensionality scaling by focusing on optical systems composed of linear optical objects, modeled as an ensemble of two-level atoms. We decompose the time evolutionary operator on multiple photons into a group of time evolution operators acting on a single photon. Since the dimension of a single-photon time evolution operator is exponentially smaller than that of a multi-photon one in the number of photons, the decomposition enables the multi-photon simulations to be performed at a much lower computational cost. We apply this method to basic single- and multi-photon phenomena, such as Hong-Ou-Mandel interference and violation of the Bell-CHSH inequality, and confirm that the calculated properties are quantitatively comparable to the experimental results. Furthermore, our method visualizes the spatial propagation of photons hence provides insights that aid experiment designs for quantum-enabled technologies.

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arXiv2023

Entanglement-efficient bipartite-distributed quantum computing

In noisy intermediate-scale quantum computing, the limited scalability of a single quantum processing unit (QPU) can be extended through distributed quantum computing (DQC), in which one can implement global operations over two QPUs by entanglement-assisted local operations and classical communication. To facilitate this type of DQC in experiments, we need an entanglement-efficient protocol. To this end, we extend the protocol in [Eisert et. al., PRA, 62:052317(2000)] implementing each nonlocal controlled-unitary gate locally with one maximally entangled pair to a packing protocol, which can pack multiple nonlocal controlled-unitary gates locally using one maximally entangled pair. In particular, two types of packing processes are introduced as the building blocks, namely the distributing processes and embedding processes. Each distributing process distributes corresponding gates locally with one entangled pair. The efficiency of entanglement is then enhanced by embedding processes, which merge two non-sequential distributing processes and hence save the entanglement cost. We show that the structure of distributability and embeddability of a quantum circuit can be fully represented by the corresponding packing graphs and conflict graphs. Based on these graphs, we derive heuristic algorithms for finding an entanglement-efficient packing of distributing processes for a given quantum circuit to be implemented by two parties. These algorithms can determine the required number of local auxiliary qubits in the DQC. We apply these algorithms for bipartite DQC of unitary coupled-cluster circuits and find a significant reduction of entanglement cost through embeddings. This method can determine a constructive upper bound on the entanglement cost for the DQC of quantum circuits.

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arXiv2023

Higher-order quantum transformations of Hamiltonian dynamics

We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our algorithm efficiently simulates linear transformations of any seed Hamiltonian with a bounded energy range consisting of a polynomial number of terms in system size, making use of only controlled-Pauli gates and time-correlated randomness. This algorithm is an instance of quantum functional programming, where the desired function is specified as a concatenation of higher-order quantum transformations. By way of example, we demonstrate the simulation of negative time-evolution and time-reversal, and perform a Hamiltonian learning task.

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arXiv2023

The quantum switch is uniquely defined by its action on unitary operations

The quantum switch is a quantum process that creates a coherent control between different unitary operations, which is often described as a quantum process which transforms a pair of unitary operations $(U_1, U_2)$ into a controlled unitary operation that coherently applies them in different orders as ${\vert {0} \rangle\!\langle {0} \vert} \otimes U_1 U_2 + {\vert {1} \rangle\!\langle {1} \vert} \otimes U_2 U_1$. This description, however, does not directly define its action on non-unitary operations. The action of the quantum switch on non-unitary operations is then chosen to be a ``natural'' extension of its action on unitary operations. In general, the action of a process on non-unitary operations is not uniquely determined by its action on unitary operations. It may be that there could be a set of inequivalent extensions of the quantum switch for non-unitary operations. We prove, however, that the natural extension is the only possibility for the quantum switch for the 2-slot case. In other words, contrary to the general case, the action of the quantum switch on non-unitary operations (as a linear and completely CP preserving supermap) is completely determined by its action on unitary operations. We also discuss the general problem of when the complete description of a quantum process is uniquely determined by its action on unitary operations and identify a set of single-slot processes which are completely defined by their action on unitary operations.

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arXiv2023

Reversing Unknown Qubit-Unitary Operation, Deterministically and Exactly

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 $\textbf{6}$, 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.

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arXiv2023

Universal construction of decoders from encoding black boxes

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.

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arXiv2021

Transferring quantum information between a quantum system with limited control and a quantum computer

We consider a hybrid quantum system consisting of a qubit system continuously evolving according to its fixed own Hamiltonian and a quantum computer. The qubit system couples to a quantum computer through a fixed interaction Hamiltonian, which can only be switched on and off. We present quantum algorithms to approximately transfer quantum information between the qubit system with limited control and the quantum computer under this setting. Our algorithms are programmed by the gate sequences in a closed formula for a given interface interaction Hamiltonian.

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arXiv2021

Optimal quantum discrimination of single-qubit unitary gates between two candidates

We analyze a discrimination problem of a single-qubit unitary gate with two candidates, where the candidates are not provided with their classical description, but their quantum sample is. More precisely, there are three unitary quantum gates -- one target and one sample for each of the two candidates -- whose classical description is unknown except for their dimension. The target gate is chosen equally among the candidates. We obtain the optimal protocol that maximizes the expected success probability, assuming the Haar distribution for the candidates. This problem is originally introduced in Hillery et al. (J. Mod. Opt. 2010), which provides a protocol achieving 7/8 in the expected success probability based on the ``unitary comparison" protocol of Andersson et al. (J. Phys. A 2003). The optimality of the protocol has been an open question since then. We prove the optimality of the comparison protocol, implying that only one of the two samples (one for each candidate) is needed to achieve an optimal discrimination. The optimization includes protocols outside the scope of quantum testers due to the dynamic ordering of the sample and target gates within a given protocol.

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arXiv2021

Controlled quantum operations and combs, and their applications to universal controllization of divisible unitary operations

Unitary operations are a fundamental component of quantum algorithms, but they seem to be far more useful if given with a "quantum control" as a controlled unitary operation. However, quantum operations are not limited to unitary operations. Nevertheless, it is not a priori clear if a controlled form of these general deterministic quantum operations can be well-defined. To provide a novel tool in the toolbox for quantum programming, we propose a mathematically consistent definition of a controlled form of deterministic but non-unitary quantum operations and, more generally, of quantum combs. We propose a "neutralization" comb, which transforms a set of input quantum operations to the identity operation, and study its controlled form based on our definition. We propose two new quantum algorithms for universal controllization of divisible unitary operations utilizing the most coherently controlled neutralization combs.

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arXiv2021

Consequences of preserving reversibility in quantum superchannels

Similarly to quantum states, quantum operations can also be transformed by means of quantum superchannels, also known as process matrices. Quantum superchannels with multiple slots are deterministic transformations whichtake independent quantum operations as inputs. While they are enforced to respect the laws of quantum mechanics, the use of input operations may lack a definite causal order, and characterizations of general superchannels in terms of quantum objects with a physical implementation have been missing. In this paper, we provide a mathematical characterization for pure superchannels with two slots (also known as bipartite pure processes), which are superchannels preserving the reversibility of quantum operations. We show that the reversibility preserving condition restricts all pure superchannels with two slots to be either a quantum circuit only consisting of unitary operations or a coherent superposition of two unitary quantum circuits where the two input operations are differently ordered. The latter may be seen as a generalization of the quantum switch, allowing a physical interpretation for pure two-slot superchannels. An immediate corollary is that purifiable bipartite processes cannot violate device-independent causal inequalities.

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