arXiv subjects

Suguru Endo

Publications and source records attributed to Suguru Endo.

At least 19 recordsLinked to original sources

arXiv2026

Linear optical Bell state measurement for rotation-symmetric cat codes

Rotation-symmetric cat (RS-cat) codes are a bosonic-code platform for quantum information processing, combining finite-energy realizability with robustness against photon loss through their discrete rotational symmetry. For applications in long-distance quantum communication and fusion-based quantum computation (FBQC), efficient Bell state measurement (BSM) is a key primitive. In this work, we consider a BSM protocol for RS-cat codes using only a half beam splitter (HBS) and photon-number-resolving detectors (PNRDs). By exploiting the characteristic photon-number structure induced by the discrete rotational symmetry of RS-cat codes, our protocol extracts both photon-number modulo and phase information for Bell-state discrimination. We show that, under ideal loss-free conditions, the proposed BSM protocol becomes deterministic for arbitrary symmetry order $N$ for sufficiently large amplitudes $\alpha$. We further numerically evaluate the success probability under photon loss and identify the loss regime in which higher-order RS-cat codes provide an advantage. Finally, we show that post-selection can enhance the success probability.

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arXiv2026

Systematic construction of digital autonomous quantum error correction for state preparation and error suppression via conditional Gaussian operations

In continuous-variable quantum computing, autonomous quantum error correction (QEC) can dissipatively steer a noisy quantum state into a target state or manifold, enabling robust quantum information processing without explicit syndrome measurements and feedback. Here, we propose a nullifier-based digital autonomous QEC enabled by conditional Gaussian operations. By designing jump operators for target nullifiers and compiling the resulting Lindbladian into a Trotterized sequence of elementary conditional Gaussian operations, we demonstrate two use cases: (i) deterministic preparation of non-Gaussian resource states for universal computation, including finitely squeezed cubic phase states and approximate trisqueezed states, and (ii) autonomous suppression of dephasing error for cat and squeezed cat states. We provide explicit gate decompositions for the required conditional Gaussian operations and numerically evaluate the performance under realistic imperfections, including photon loss in the bosonic mode and ancillary-qubit decoherence. Our results clarify the resource requirements and trade-offs, such as circuit depth, time-step choices, and the required set of conditional Gaussian operations, for scalable, gate-level implementations of autonomous state preparation and error suppression.

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arXiv2026

Error-Mitigated Hamiltonian Simulation: Complexity Analysis and Optimization for Near-Term and Early-Fault-Tolerant Quantum Computers

Simulating real-time dynamics under a Hamiltonian is a central goal of quantum information science. While numerous Hamiltonian-simulation quantum algorithms have been proposed, the effects of physical noise have rarely been incorporated into their performance analysis, despite the non-negligible noise levels of quantum devices. We present an end-to-end complexity analysis of noisy Hamiltonian simulation combined with quantum error mitigation (QEM) to answer how many circuit runs are required to reach a given target accuracy. Because the QEM sampling overhead grows exponentially with the circuit depth while the algorithmic error decreases with it, the circuit depth becomes an optimization variable, and we derive an analytic depth-selection rule for two algorithm families. For the order-$k$ Suzuki--Trotter formula, the optimized cost exhibits a critical error $\epsilon_c$, below which the required number of circuit runs grows exponentially. QEM improves the noise dependence of $\epsilon_c$ from sublinear to $k$th-power scaling, an exponent improvement by a factor of $k+1$. For randomized-LCU-based simulation, optimizing the repetition number yields a square-root improvement in the simulation-time dependence of the sampling-overhead exponent over the standard parameter choice. We further quantify the noise-characterization cost required for error mitigation via gate set tomography and the recently proposed space-time noise inversion method, showing that the latter can significantly reduce this cost.

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arXiv2026

Quantum Error Mitigation Simulates General Non-Hermitian Dynamics

While non-Hermitian Hamiltonians enable exotic dynamical phenomena, implementing their nonunitary time evolution on near-term quantum devices remains challenging. We propose a hardware-friendly protocol that simulates non-Hermitian dynamics without ancillas, controlled time evolution, or continuous monitoring. The protocol combines a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) evolution via classical Gaussian white-noise averaging with stochastic quantum error mitigation (QEM) to cancel the jump contribution at the level of expectation values. The mitigation layer uses only single-qubit operations. We validate the method through numerical simulations of an asymmetric-hopping model and an open {\it XXZ} spin chain with non-Hermitian boundary fields. Our work provides a programmable and ancilla-free framework for investigating exotic dynamics beyond the class of completely positive and trace-preserving dynamics using QEM.

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arXiv2025

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits

Quantum circuit cutting and knitting are divide-and-conquer methods that enable large-scale quantum computations on hardware with limited qubit resources and connectivity by decomposing a target computation into smaller local experiments. Existing methods, however, typically incur a sampling overhead that grows exponentially with the number of cut locations, leaving open the question of whether this barrier is intrinsic. Here we show that this barrier is not universal by introducing a learning-based cutting protocol tailored to the target observable. At each cut, the protocol locally learns a Heisenberg-picture effective observable that captures the downstream information relevant to the final measurement and uses it to construct an observable-adaptive cut. This replaces the multiplicative variance amplification of conventional cutting with additive bias accumulation controlled by local learning accuracy. We apply this framework to finite tree-structured circuits. For any finite rooted tree with $K$ cut wires and cut-system dimension at most $d$, the protocol estimates the target expectation value within additive error $\epsilon$ with high probability using $\widetilde{O}(d^3K^3/\epsilon^2)$ measurements, including the local learning cost. Moreover, for two-layer trees with $R$ cut wires, we prove an information-theoretic exponential separation between our learning-based protocol and learning-free wire-cutting protocols based on pre-specified randomized cutting rules: even with arbitrary classical post-processing, any such learning-free protocol requires $\Omega((d+1)^R/\epsilon^2)$ measurements, whereas our protocol uses $\widetilde{O}(d^3R^3/\epsilon^2)$. These results identify local learning, rather than the tree structure alone, as the key mechanism driving the exponential-to-polynomial reduction in sampling overhead.

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arXiv2025

Trade-offs between Quantum and Classical Resources in the Linear Combination of Unitaries

The randomized linear combination of unitaries (LCU) method with many applications to early fault-tolerant quantum computing algorithms has been proposed. This quantum algorithm computes the same expectation values as the original, fully coherent LCU algorithm using a shallower quantum circuit with a single ancilla qubit, at the cost of a quadratically larger sampling overhead. In this work, we propose a quantum algorithm intermediate between the original and randomized LCU that manages the trade-off between the sampling overhead and circuit complexity. Our algorithm divides the set of unitary operators into several groups and then randomly samples LCU circuits from these groups to evaluate the target expectation value. Notably, we reveal that across all grouping strategies, the mechanism of the sampling overhead reduction can be solely characterized by a metric we call the reduction factor. Moreover, we analytically prove an underlying monotonicity of the reduction factor in the group size: larger group sizes entail smaller sampling overhead. Finally, our framework enables a more flexible algorithmic design by systematically yielding intermediate implementations of LCU-based algorithms; we provide intermediate implementations of non-Hermitian dynamics simulation, ground-state property estimation, and quantum error detection. Besides, we demonstrate this principle by deriving intermediate trade-off scaling in sample complexity and ancillary space for quantum linear system solver.

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arXiv2025

Data-driven adaptive quantum error mitigation for probability distribution

Quantum error mitigation (QEM) has been proposed as a class of hardware-friendly error suppression techniques. While QEM has been primarily studied for mitigating errors in the estimation of expectation values of observables, recent works have explored its application to estimating noiseless probability distributions. In this work, we propose two protocols to improve the accuracy of QEM for probability distributions, inspired by techniques in software engineering. The first is the N-version programming method, which compares probability distributions obtained via different QEM strategies and excludes the outlier distribution, certifying the feasibility of the error-mitigated distributions. The second is a consistency-based method for selecting an appropriate extrapolation strategy. Specifically, we prepare $K$ data points at different error rates, choose $L<K$ of them for extrapolation, and evaluate error-mitigated results for all $\binom{K}{L}$ possible choices. We then select the extrapolation method that yields the smallest variance in the error-mitigated results. This procedure can also be applied bitstring-wise, enabling adaptive error mitigation for each probability in the distribution.

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arXiv2025

Non-Markovianity in Quantum Information Processing: Interplay with Quantum Error Mitigation

Non-Markovian dynamics are typically present in the dynamics of open quantum systems. Despite the rich structure of non-Markovian dynamics, their relevance to quantum information processing (QIP) has been rarely discussed. In this work, we demonstrate that the negativity of the dynamics, a characteristic of non-Markovian dynamics, naturally arises in quantum error correction (QEC) and quantum teleportation. The negativity in open quantum systems is naturally attributed to the information backflow from the environment. We partition the whole Hilbert space into the logical subsystem and the gauge subsystem. The logical subsystem stores the quantum information for QIP, while the gauge subsystem stores the information for recovery of the logical information, i.e., the syndrome measurement outcomes for quantum error correction and Bell measurement outcomes for successful teleportation. We then show that the negativity in quantum information processing appears as a consequence of the feedback operation based on the measurement outcomes of the gauge subsystem. Finally, we show that the negativity of non-Markovianity in QIP reduces the sampling cost of quantum error mitigation (QEM), shedding light on the importance of combination strategies of QEC and QEM in a practical QIP.

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arXiv2025

Exploiting Translational Symmetry for Quantum Computing with Squeezed Cat Qubits

Translational symmetry plays an essential role in bosonic quantum error correction (QEC), most notably in the Gottesman-Kitaev-Preskill code. Squeezed cat (SC) codes provide a complementary platform, combining approximate protection against physical errors with the noise bias of cat codes, but a hardware-efficient route to exploit their translational symmetry for QEC has been lacking. Here we show that this symmetry provides a practical route to autonomous QEC and universal quantum computation with SC codes. We then propose a QEC protocol that autonomously restores states driven out of the code space by physical errors, even though translational symmetry along a single direction does not uniquely define the code space. Using a subsystem decomposition based on squeezed displaced Fock states, we analytically characterize the relaxation rate toward the code space induced by the protocol, thereby estimating the QEC-cycle rate required for effective error suppression. Within the same framework, we propose deterministic preparation of logical states, logical gates, and logical-$Z$ readout with improved error scaling. These results establish translational symmetry as a new perspective for approaching quantum computation with SC qubits.

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arXiv2025

Data-Efficient Error Mitigation for Physical and Algorithmic Errors in a Hamiltonian Simulation

Quantum dynamics simulation via Hamilton simulation algorithms is one of the most crucial applications in the quantum computing field. While this task has been relatively considered the target in the fault-tolerance era, the experiment for demonstrating utility by an IBM team simulates the dynamics of an Ising-type quantum system with the Trotter-based Hamiltonian simulation algorithm with the help of quantum error mitigation. In this study, we propose the data-efficient 1D extrapolation method to mitigate not only physical errors but also algorithmic errors of Trotterized quantum circuits in both the near-term and early fault-tolerant eras. Our proposed extrapolation method uses expectation values obtained by Trotterized circuits, where the Trotter number is selected to minimize both physical and algorithmic errors according to the circuit's physical error rate. We also propose a method that combines the data-efficient 1D extrapolation with purification QEM methods, which improves accuracy more at the expense of multiple copies of quantum states or the depth of the quantum circuit. Using the 1D transverse-field Ising model, we numerically demonstrate our proposed methods and confirm that our proposed extrapolation method suppresses both statistical and systematic errors more than the previous extrapolation method.

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arXiv2024

Unitary-transformed projective squeezing: applications for circuit-knitting and state-preparation of non-Gaussian states

Continuous-variable (CV) quantum computing is a promising candidate for quantum computation because it can, even with one mode, utilize infinite-dimensional Hilbert spaces and can efficiently handle continuous values. Although photonic platforms have been considered as a leading platform for CV computation, hybrid systems that use both qubits and bosonic modes, e.g., superconducting hardware, have shown significant advances because they can prepare non-Gaussian states by utilizing the nonlinear interaction between the qubits and the bosonic modes. However, the size of hybrid hardware is currently restricted. Moreover, the fidelity of the non-Gaussian state is also restricted. This work extends the projective squeezing method to establish a formalism for projecting quantum states onto the states that are unitary-transformed from the squeezed vacuum at the expense of the sampling cost. Based on this formalism, we propose methods for simulating larger quantum devices and projecting states onto the cubic phase state, a typical non-Gaussian state, with a higher squeezing level and higher nonlinearity. To make implementation practical, we can, by leveraging the interactions in hybrid systems of qubits and bosonic modes, apply the smeared projector by using either the linear-combination-of-unitaries or virtual quantum error detection algorithms. We numerically verify the performance of our methods and show that projection can suppress the effect of photon-loss errors.

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arXiv2024

$N$-Party Hadamard Test for Distributed Quantum Computation

Quantum computers promise computational advantages over classical computers, but hardware-imposed limitations remain a major obstacle. The Hadamard test mitigates these limitations by estimating expectation values associated with resource-intensive quantum operations using simple quantum circuits at the cost of additional classical sampling, and therefore underlies many quantum algorithms. However, in distributed quantum computing (DQC), which offers a promising route to scalability, its use is hindered by the need for nonlocal controlled operations. Here we introduce an $N$-party Hadamard test for DQC that estimates the same expectation values as the standard Hadamard test without implementing nonlocal controlled operations. The protocol instead uses pre-shared entanglement together with local operations and classical communication, which are standard resources in DQC settings. To demonstrate its utility, we apply it to unitary operations for clustered Hamiltonian simulation and to projectors for stabilizer-state preparation, showing lower sampling overheads than previous approaches by exploiting pre-shared entangled ancilla states. Moreover, we numerically demonstrate Bell-state preparation from Werner states to show favorable sampling efficiency and noise robustness relative to conventional purification, circuit knitting/cutting, and probabilistic error cancellation. Our work provides a general strategy for bringing Hadamard-test-based algorithms to DQC, facilitating practical and flexible quantum computation.

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arXiv2024

Projective squeezing for translation symmetric bosonic codes

The design of translation symmetric bosonic codes, e.g., Gottesmann-Kitaev-Preskill and squeezed cat codes, is robust against photon loss, but the computation accuracy is limited by the available squeezing level. Here, we introduce the \textit{projective squeezing} (PS) method for computing outcomes for a higher squeezing level by revealing that a linear combination of displacement operators with periodic displacement values constitutes the smeared projector onto the better code space; we also show the analytical relationship between the increased squeezing level and the projection probability. We introduce concrete implementation methods for PS based on linear-combination-of-unitaries and virtual quantum error detection. We also numerically verify our analytical arguments and show that our protocol can mitigate the effect of photon loss.

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arXiv2024

Hardware-Efficient Bosonic Quantum Computing with Photon-loss Detection Capability

Bosonic quantum systems offer the hardware-efficient construction of error detection/error correction codes by using the infinitely large Hilbert space. However, due to the encoding, arbitrary gate rotations usually require magic state teleportation or complicated optimized pulse sequences involving an ancilla qubit. Here, we propose a simple and hardware-efficient bosonic 02 error detection code that allows for the implementation of arbitrary X and Z rotations and a controlled phase gate by using a Kerr nonlinear resonator. Our code can detect a single photon loss, and we observe significant error suppression by simulating the frequently used hardware-efficient ansatz quantum circuit in near-term quantum computing.

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arXiv2023

Virtual quantum error detection

Quantum error correction and quantum error detection necessitate syndrome measurements to detect errors. Performing syndrome measurements for each stabilizer generator can be a significant overhead, considering the fact that the readout fidelity in the current quantum hardware is generally lower than gate fidelity. Here, by generalizing a quantum error mitigation method known as symmetry expansion, we propose a protocol called virtual quantum error detection (VQED). This method virtually allows for evaluating computation results corresponding to post-selected quantum states obtained through quantum error detection during circuit execution, without implementing syndrome measurements. Unlike conventional quantum error detection, which requires the implementation of Hadamard test circuits for each stabilizer generator, our VQED protocol can be performed with a constant depth shallow quantum circuit with an ancilla qubit, irrespective of the number of stabilizer generators. Furthermore, for some simple error models, the computation results obtained using VQED are robust against the noise that occurred during the operation of VQED, and our method is fully compatible with other error mitigation schemes, enabling further improvements in computation accuracy and facilitating high-fidelity quantum computing.

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arXiv2023

Density matrix representation of hybrid tensor networks for noisy quantum devices

The hybrid tensor network (HTN) method is a general framework allowing for the construction of an effective wavefunction with the combination of classical tensors and quantum tensors, i.e., amplitudes of quantum states. In particular, hybrid tree tensor networks (HTTNs) are very useful for simulating larger systems beyond the available size of the quantum hardware. However, while the realistic quantum states in NISQ hardware are highly likely to be noisy, this framework is formulated for pure states. In this work, as well as discussing the relevant methods, i.e., Deep VQE and entanglement forging under the framework of HTTNs, we investigate the noisy HTN states by introducing the expansion operator for providing the description of the expansion of the size of simulated quantum systems and the noise propagation. This framework enables the general tree HTN states to be explicitly represented and their physicality to be discussed. We also show that the expectation value of a measured observable exponentially vanishes with the number of contracted quantum tensors. Our work will lead to providing the noise-resilient construction of HTN states.

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arXiv2023

Resource-efficient Generalized Quantum Subspace Expansion

Realizing practical quantum computing requires overcoming a number of computation errors and the limitation of device size, which have intensively been tackled by quantum error mitigation (QEM) these days. As a unified approach of noise-agnostic QEM, generalized quantum subspace expansion (GSE) has lately been proposed to be remarkably robust against stochastic and coherent errors, integrating quantum subspace expansion and virtual state purification. However, the requirement in GSE to perform entangled measurements between copies of the quantum states remains a significant drawback under the current situation of quantum devices with a restricted number of qubits and their connectivity. In this work, we propose ``Dual-GSE'', a resource-efficient implementation of GSE to circumvent this overhead by constructing an ansatz of error-mitigated quantum states via dual-state purification without state copies. Remarkably, the proposed method can further simulate larger quantum systems beyond the size of available quantum hardware, achieved by a suitable ansatz construction inspired by the divide-and-conquer strategy that classically reintroduces the effect of entanglement. While classically forging the entanglement comes with additional cost, the total sampling overhead can be notably reduced by reusing the same Pauli expectation values among divided-and-conquered subsystems. We comprehensively analyze the advantages and overhead of Dual-GSE and perform numerical simulations of the eight-qubit transverse-field Ising model under various setups. Our results demonstrate that Dual-GSE estimates the ground state energy with high accuracy under gate noise with low mitigation overhead and practical sampling cost.

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arXiv2023

Localized Virtual Purification

Analog and digital quantum simulators can efficiently simulate quantum many-body systems that appear in natural phenomena. However, experimental limitations of near-term devices still make it challenging to perform the entire process of quantum simulation. The purification-based quantum simulation methods can alleviate the limitations in experiments such as the cooling temperature and noise from the environment, while this method has the drawback that it requires global entangled measurement with a prohibitively large number of measurements that scales exponentially with the system size. In this Letter, we propose that we can overcome these problems by restricting the entangled measurements to the vicinity of the local observables to be measured, when the locality of the system can be exploited. We provide theoretical guarantees that the global purification operation can be replaced with local operations under some conditions, in particular for the task of cooling and error mitigation. We furthermore give a numerical verification that the localized purification is valid even when conditions are not satisfied. Our method bridges the fundamental concept of locality with quantum simulators, and therefore expected to open a path to unexplored quantum many-body phenomena.

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