arXiv subjects

Nobuyuki Yoshioka

Publications and source records attributed to Nobuyuki Yoshioka.

At least 37 records · Page 2Linked to original sources

arXiv2025

Transition from topological to chaos in the nonlinear Su-Schrieffer-Heeger model

Recent studies on topological materials are expanding into the nonlinear regime, while the central principle, namely the bulk-edge correspondence, is yet to be elucidated in the strongly nonlinear regime. Here, we reveal that nonlinear topological edge modes can exhibit the transition to spatial chaos by increasing nonlinearity, which can be a universal mechanism of the breakdown of the bulk-edge correspondence. Specifically, we unveil the underlying dynamical system describing the spatial distribution of zero modes and show the emergence of chaos. We also propose the correspondence between the absolute value of the topological invariant and the dimension of the stable manifold under sufficiently weak nonlinearity. Our results provide a general guiding principle to investigate the nonlinear bulk-edge correspondence that can potentially be extended to arbitrary dimensions.

cond-mat.mes-hall↗

arXiv2025

Characterization of randomness in quantum circuits of continuous gate sets

In the accompanying paper of arXiv:2408.13472, we have established the method of characterizing the maximal order of asymptotic unitary designs generated by symmetric local random circuits, and have explicitly specified the order in the cases of $\mathbb{Z}_2$, U(1), and SU(2) symmetries. Here, we provide full details on the derivation of the main theorems for general symmetry and for concrete symmetries. Furthermore, we consider a general framework where we have access to a finite set of connected compact unitary subgroups, which includes symmetric local unitary gate sets.

quant-ph↗

arXiv2025

Unitary Designs of Symmetric Local Random Circuits

We have established the method of characterizing the unitary design generated by a symmetric local random circuit. Concretely, we have shown that the necessary and sufficient condition for the circuit asymptotically forming a t-design is given by simple integer optimization for general symmetry and locality. By using the result, we explicitly give the maximal order of unitary design under the $\mathbb{Z}_2$, U(1), and SU(2) symmetries for general locality. This work reveals the relation between the fundamental notions of symmetry and locality in terms of randomness.

quant-ph↗

arXiv2025

Faster Quantum Algorithm for Multiple Observables Estimation in Fermionic Problems

Achieving quantum advantage in efficiently estimating collective properties of quantum many-body systems remains a fundamental goal in quantum computing. While the quantum gradient estimation (QGE) algorithm has been shown to achieve doubly quantum enhancement in the precision and the number of observables, it remains unclear whether one benefits in practical applications. In this work, we present a generalized framework of adaptive QGE algorithm, and further propose two variants which enable us to estimate the collective properties of fermionic systems using the smallest cost among existing quantum algorithms. The first method utilizes the symmetry inherent in the target state, and the second method enables estimation in a single-shot manner using the parallel scheme. We show that our proposal offers a quadratic speedup compared with prior QGE algorithms in the task of fermionic partial tomography for systems with limited particle numbers. Furthermore, we provide the numerical demonstration that, for a problem of estimating fermionic 2-RDMs, our proposals improve the number of queries to the target state preparation oracle by a factor of 100 for the nitrogenase FeMo cofactor and by a factor of 500 for Fermi-Hubbard model of 100 sites.

quant-ph↗

arXiv2025

Comprehensive Study on Heisenberg-limited Quantum Algorithms for Multiple Observables Estimation

In the accompanying paper of arXiv:2505.00697, we have presented a generalized scheme of adaptive quantum gradient estimation (QGE) algorithm, and further proposed two practical variants which not only achieve doubly quantum enhancement in query complexity regarding estimation precision and number of observables, but also enable minimal cost to estimate $k$-RDMs in fermionic systems among existing quantum algorithms. Here, we provide full descriptions on the algorithm, and provide theoretical guarantee for the estimation precision in terms of the root mean squared error. Furthermore, we analyze the performance of the quantum amplitude estimation algorithm, another variant of the Heisenberg-limited scaling algorithm, and show how the estimation error is minimized under the circuit structure that resembles the phase estimation algorithm. We finally describe the details for the numerical evaluation of the query complexity of the Heisenberg-limited algorithms and sampling-based methods to make a thorough comparison in the task of estimating fermionic $k$-RDMs.

quant-ph↗

arXiv2025

Hardness of classically sampling quantum chemistry circuits

Significant advances have been made in the study of quantum advantage both in theory and experiment, although these have mostly been limited to artificial setups. In this work, we extend the scope to address quantum advantage in tasks relevant to chemistry and physics. Specifically, we consider the unitary cluster Jastrow (UCJ) ansatz-a variant of the unitary coupled cluster ansatz, which is widely used to solve the electronic structure problem on quantum computers-to show that sampling from the output distributions of quantum circuits implementing the UCJ ansatz is likely to be classically hard. More specifically, we show that there exist UCJ circuits for which classical simulation of sampling cannot be performed in polynomial time, under a reasonable complexity-theoretical assumption that the polynomial hierarchy does not collapse. Our main contribution is to show that a class of UCJ circuits can be used to perform arbitrary instantaneous quantum polynomial-time (IQP) computations, which are already known to be classically hard to simulate under the same complexity assumption. As a side result, we also show that UCJ equipped with post-selection can generate the class post-BQP. Our demonstration, worst-case nonsimulatability of UCJ, would potentially imply quantum advantage in quantum algorithms for chemistry and physics using unitary coupled cluster type ansatzes, such as the variational quantum eigensolver and quantum-selected configuration interaction.

quant-ph↗

arXiv2025

Non-Haar random circuits form unitary designs as fast as Haar random circuits

The unitary design formation in random circuits has attracted considerable attention due to its wide range of practical applications and relevance to fundamental physics. While the formation rates in Haar random circuits have been extensively studied in previous works, it remains an open question how these rates are affected by the choice of local randomizers. In this work, we prove that the circuit depths required for general non-Haar random circuits to form unitary designs are upper bounded by those for the corresponding Haar random circuits, up to a constant factor independent of the system size. This result is derived in a broad range of circuit structures, including one- and higher-dimensional lattices, geometrically non-local configurations, and even extremely shallow circuits with patchwork architectures. We provide specific applications of these results in randomized benchmarking and random circuit sampling, and also discuss their implications for quantum many-body physics. Our work lays the foundation for flexible and robust randomness generation in real-world experiments, and offers new insights into chaotic dynamics in complex quantum systems.

quant-ph↗

arXiv2025

Heisenberg-limited adaptive gradient estimation for multiple observables

In quantum mechanics, measuring the expectation value of a general observable has an inherent statistical uncertainty that is quantified by variance or mean squared error of measurement outcome. While the uncertainty can be reduced by averaging several samples, the number of samples should be minimized when each sample is very costly. This is especially the case for fault-tolerant quantum computing that involves measurement of multiple observables of non-trivial states in large quantum systems that exceed the capabilities of classical computers. In this work, we provide an adaptive quantum algorithm for estimating the expectation values of $M$ general observables within root mean squared error $\varepsilon$ simultaneously, using $\mathcal{O}(\varepsilon^{-1}\sqrt{M}\log M)$ queries to a state preparation oracle of a target state. This remarkably achieves the scaling of Heisenberg limit $1/\varepsilon$, a fundamental bound on the estimation precision in terms of mean squared error, together with the sublinear scaling of the number of observables $M$. The proposed method is an adaptive version of the quantum gradient estimation algorithm and has a resource-efficient implementation due to its adaptiveness. Specifically, the space overhead in the proposed method is $\mathcal{O}(M)$ which is independent from the estimation precision $\varepsilon$ unlike non-iterative algorithms. In addition, our method can avoid the numerical instability problem for constructing quantum circuits in a large-scale task (e.g., $\varepsilon\ll 1$ in our case), which appears in the actual implementation of many algorithms relying on quantum signal processing techniques. Our method paves a new way to precisely understand and predict various physical properties in complicated quantum systems using quantum computers.

quant-ph↗

arXiv2025

Faster computation of nonstabilizerness

The characterization of nonstabilizerness is fruitful due to its application in gate synthesis and classical simulation. In particular, the resource monotone called the stabilizer extent is a useful tool to estimate the simulation cost using rank-based simulators, one of the state-of-the-art simulators of Clifford+$T$ circuits. In this work, we propose faster numerical algorithms to compute the stabilizer extent. Our algorithm utilizes the Column Generation method, which iteratively updates the subset of pure stabilizer states used for calculation. This subset is selected based on the overlaps between all stabilizer states and a target state. In order to update the subset, we make use of a newly proposed subroutine for calculating the stabilizer fidelity that (i) achieves linear time complexity with respect to the number of stabilizer states, (ii) super-exponentially reduces the space complexity by in-place calculation, and (iii) prunes unnecessary states for the computation. As a result, our algorithm can compute the stabilizer fidelity and the stabilizer extent for Haar random pure states up to $n=9$ qubits, which naively requires a memory of 305 EiB. We further show that our algorithm runs faster when the target state vector is real. We prove that the problem size is reduced by $\mathcal{O}(2^n)$ compared to the general cases, which makes it computable for the case of $n=10$ qubits.

quant-ph↗

arXiv2025

Error Crafting in Mixed Quantum Gate Synthesis

In fault-tolerant quantum computing, errors in unitary gate synthesis is comparable with noise inherent in the gates themselves. While mixed synthesis can suppress such coherent errors quadratically, there is no clear understanding on its remnant error, which hinders us from designing a holistic and practical error countermeasure. In this work, we propose that the classical characterizability of synthesis error can be exploited; remnant errors can be crafted to satisfy desirable properties. We prove that we can craft the remnant error of arbitrary single-qubit unitaries to be Pauli and depolarizing errors, while the conventional twirling cannot be applied in general. For Pauli rotation gates, in particular, the crafting enables us to suppress the remnant error up to cubic order, which results in synthesis with a T-count of $\log_2(1/\varepsilon)$ up to accuracy of $\varepsilon=10^{-9}$. Our work opens a novel avenue in quantum circuit design and architecture that orchestrates error countermeasures.

quant-ph↗

arXiv2024

Diagonalization of large many-body Hamiltonians on a quantum processor

The estimation of low energies of many-body systems is a cornerstone of computational quantum sciences. Variational quantum algorithms can be used to prepare ground states on pre-fault-tolerant quantum processors, but their lack of convergence guarantees and impractical number of cost function estimations prevent systematic scaling of experiments to large systems. Alternatives to variational approaches are needed for large-scale experiments on pre-fault-tolerant devices. Here, we use a superconducting quantum processor to compute eigenenergies of quantum many-body systems on two-dimensional lattices of up to 56 sites, using the Krylov quantum diagonalization algorithm, an analog of the well-known classical diagonalization technique. We construct subspaces of the many-body Hilbert space using Trotterized unitary evolutions executed on the quantum processor, and classically diagonalize many-body interacting Hamiltonians within those subspaces. These experiments show that quantum diagonalization algorithms are poised to complement their classical counterpart at the foundation of computational methods for quantum systems.

quant-ph↗

arXiv2024

Robust Angle Finding for Generalized Quantum Signal Processing

Quantum Signal Processing (QSP), together with the quantum singular value transformation, is one of the central quantum algorithms due to its efficiency and generality in many fields including quantum simulation, quantum machine learning, and quantum cryptography. The largest bottleneck of QSP and its family is its difficulty in finding the phase angle sequence for signal processing. We find that this is in particular prominent when one employs the generalized formalism of the QSP, or the GQSP, to employ arbitrary single-qubit unitaries for signal processing operator. In this work, we extend the framework of GQSP and propose a robust angle finding algorithm. The proposed angle finding algorithm, based on Prony's method, successfully generates angle sequence of precision $10^{-13}$ up to polynomial degrees of hundreds within a second. By applying our method to Hamiltonian simulation, we find that the number of calls, or queries, to signal operators are essentially halved compared to the ordinary framework of QSP.

quant-ph↗

arXiv2024

Handbook for Quantifying Robustness of Magic

The nonstabilizerness, or magic, is an essential quantum resource to perform universal quantum computation. Robustness of magic (RoM) in particular characterizes the degree of usefulness of a given quantum state for non-Clifford operation. While the mathematical formalism of RoM can be given in a concise manner, it is extremely challenging to determine the RoM in practice, since it involves superexponentially many pure stabilizer states. In this work, we present efficient novel algorithms to compute the RoM. The crucial technique is a subroutine that achieves the remarkable features in calculation of overlaps between pure stabilizer states: (i) the time complexity per each stabilizer is reduced exponentially, (ii) the space complexity is reduced superexponentially. Based on this subroutine, we present algorithms to compute the RoM for arbitrary states up to $n=7$ qubits on a laptop, while brute-force methods require a memory size of 86 TiB. As a byproduct, the proposed subroutine allows us to simulate the stabilizer fidelity up to $n=8$ qubits, for which naive methods require memory size of 86 PiB so that any state-of-the-art classical computer cannot execute the computation. We further propose novel algorithms that utilize the preknowledge on the structure of target quantum state such as the permutation symmetry of disentanglement, and numerically demonstrate our state-of-the-art results for copies of magic states and partially disentangled quantum states. The series of algorithms constitute a comprehensive ``handbook'' to scale up the computation of the RoM, and we envision that the proposed technique applies to the computation of other quantum resource measures as well.

quant-ph↗

arXiv2024

Measuring multipartite quantum correlations by thermodynamic work extraction

Quantum correlations are at the core of quantum mechanics and play a crucial role in various fields. While bipartite quantum correlations have been extensively studied, multipartite quantum correlations in many-body systems remain elusive due to their complex structure. In particular, a primary challenge lies in the fact that the calculation of multipartite quantum correlation measure often requires exponential cost. In this work, we tackle this problem by adopting a thermodynamic approach; we introduce a measure of multipartite quantum correlations based on the difference in extractable thermodynamic work by global operations and local operations and classical communication (LOCC). This can be regarded as a multipartite generalization of the work deficit, which has attracted attention as a thermodynamic measure of bipartite quantum correlation. A distinguishing feature of the thermodynamic approach to multipartite quantum correlation is that we can compare the degree of quantum correlations with clear operational meaning. Importantly, we develop an efficient calculation method of the multipartite work deficit. This efficient method works for a special class of quantum many-body systems described by matrix product states (MPS), where the numerical cost is shown to be proportional to the system size, significantly reducing the exponential cost required for the direct calculations. We demonstrate this efficient method in the AKLT state and the cluster state, and analytically obtain the exact values of this measure. We further show that a quantum phase transition described by MPS is well captured by the multipartite work deficit. This shows that the multipartite work deficit does not only highlight the fundamental connection between multipartite quantum correlations and quantum thermodynamics, but also serves as an efficiently-computable probe of the structures of quantum many-body systems.

quant-ph↗

arXiv2024

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.

quant-ph↗

arXiv2024

Clifford Group and Unitary Designs under Symmetry

We have generalized the well-known statement that the Clifford group is a unitary 3-design into symmetric cases by extending the notion of unitary design. Concretely, we have proven that a symmetric Clifford group is a symmetric unitary 3-design if and only if the symmetry constraint is described by some Pauli subgroup. We have also found a complete and unique construction method of symmetric Clifford groups with simple quantum gates for Pauli symmetries. For the overall understanding, we have also considered physically relevant U(1) and SU(2) symmetry constraints, which cannot be described by a Pauli subgroup, and have proven that the symmetric Clifford group is a symmetric unitary 1-design but not a 2-design under those symmetries. Our findings are numerically verified by computing the frame potentials, which measure the difference in randomness between the uniform ensemble on the symmetric group of interest and the symmetric unitary group. This work will open a new perspective into quantum information processing such as randomized benchmarking, and give a deep understanding to many-body systems such as monitored random circuits.

quant-ph↗

arXiv2024

Adaptive measurement strategy for quantum subspace methods

Estimation of physical observables for unknown quantum states is an important problem that underlies a wide range of fields, including quantum information processing, quantum physics, and quantum chemistry. In the context of quantum computation, in particular, existing studies have mainly focused on holistic state tomography or estimation on specific observables with known classical descriptions, while this lacks the important class of problems where the estimation target itself relies on the measurement outcome. In this work, we propose an adaptive measurement optimization method that is useful for the quantum subspace methods, namely the variational simulation methods that utilize classical postprocessing on measurement outcomes. The proposed method first determines the measurement protocol for classically simulatable states, and then adaptively updates the protocol of quantum subspace expansion (QSE) according to the quantum measurement result. As a numerical demonstration, we have shown for excited-state simulation of molecules that (i) we are able to reduce the number of measurements by an order of magnitude by constructing an appropriate measurement strategy (ii) the adaptive iteration converges successfully even for a strongly correlated molecule of H$_4$. Our work reveals that the potential of the QSE method can be empowered by elaborated measurement protocols, and opens a path to further pursue efficient quantum measurement techniques in practical computations.

quant-ph↗

arXiv2024

Hunting for quantum-classical crossover in condensed matter problems

The intensive pursuit for quantum advantage in terms of computational complexity has further led to a modernized crucial question: {\it When and how will quantum computers outperform classical computers?} The next milestone is undoubtedly the realization of quantum acceleration in practical problems. Here we provide a clear evidence and arguments that the primary target is likely to be condensed matter physics. Our primary contributions are summarized as follows: 1) Proposal of systematic error/runtime analysis on state-of-the-art classical algorithm based on tensor networks; 2) Dedicated and high-resolution analysis on quantum resource performed at the level of executable logical instructions; 3) Clarification of quantum-classical crosspoint for ground-state simulation to be within runtime of hours using only a few hundreds of thousand physical qubits for 2d Heisenberg and 2d Fermi-Hubbard models, assuming that logical qubits are encoded via the surface code with the physical error rate of $p=10^{-3}$. To our knowledge, we argue that condensed matter problems offer the earliest platform for demonstration of practical quantum advantage that is order-of-magnitude more feasible than ever known candidates, in terms of both qubit counts and total runtime.

quant-ph↗