arXiv subjects

Riki Toshio

Publications and source records attributed to Riki Toshio.

15 recordsLinked to original sources

arXiv2026

Adaptive Window Decoding based on Spatiotemporal Complementary Gap

Real-time decoding plays a crucial role in practical fault-tolerant quantum computing. Window decoding, in which the decoding problem is divided into windows, is a promising approach. While reducing the window size is desirable for faster decoding, each window contains a buffer region whose size must typically be at least the code distance to avoid degrading the logical error rate, which limits how much the window can shrink. In this paper, we propose an adaptive decoding scheme in which window decoding is first performed with a small buffer size and a decoding confidence (soft information) is computed; if the confidence is low, the buffer size is enlarged and decoding is redone. This approach reduces the average decoding time, since most shots are decoded with a small buffer. A central challenge in realizing this scheme is that existing forms of soft information are not directly applicable to window decoding, especially with a small buffer. We address this challenge by introducing a new form of soft information, the spatiotemporal complementary gap, specifically designed for this setting. Numerical simulations demonstrate that the proposed scheme reduces the average buffer size by approximately 40% while maintaining the logical error rate.

quant-ph↗

arXiv2026

Enabling Chemically Accurate Quantum Phase Estimation in the Early Fault-Tolerant Regime

Quantum simulation of molecular electronic structure is one of the most promising applications of quantum computing. However, achieving chemically accurate predictions for strongly correlated systems requires quantum phase estimation (QPE) on fault-tolerant quantum computing (FTQC) devices. Existing resource estimates for typical FTQC architectures suggest that such calculations demand millions of physical qubits, thereby placing them beyond the reach of near-term devices. Here, we investigate the feasibility of performing QPE for chemically relevant molecular systems in an early-FTQC regime, characterized by partial fault tolerance, constrained qubit budgets, and limited circuit depth. Our framework is based on single-ancilla, Trotter-based QPE implementations combined with partially randomized time evolution. Within this framework, we develop a novel Hamiltonian optimization strategy, termed unitary weight concentration, that reduces algorithmic cost by reshaping linear-combination-of-unitaries representations. Applying this framework to active-space models of iron-sulfur clusters, cytochrome P450 active sites, and CO$_2$-utilization catalysts, we perform end-to-end resource estimation using the latest version of the space-time efficient analog rotation (STAR) architecture. Our results indicate that ground-state energy estimation for active spaces of approximately 20 to 50 spatial orbitals, well beyond the reach of classical full configuration interaction, is achievable using $\sim 10^5$ physical qubits, with runtimes on the order of days to weeks. These findings demonstrate that while full-fledged fault-tolerant quantum computers will be required for even larger molecular simulations, chemically meaningful quantum chemistry problems are already within reach in an experimentally relevant, early-FTQC regime.

quant-ph↗

arXiv2026

STAR-Magic Mutation: Even More Efficient Analog Rotation Gates for Early Fault-Tolerant Quantum Computer

We introduce STAR-magic mutation, an efficient protocol for implementing logical rotation gates on early fault-tolerant quantum computers. This protocol judiciously combines two of the latest state preparation protocols: transversal multi-rotation protocol and magic state cultivation. It achieves a logical rotation gate with a favorable error scaling of $\mathcal{O}(\theta_L^{2(1-\Theta(1/d))}p_{\text{ph}})$, while requiring only the ancillary space of a single surface code patch. Here, $\theta_L$ is the logical rotation angle, $p_{\text{ph}}$ is the physical error rate, and $d$ is the code distance. This scaling marks a significant improvement over the previous state-of-the-art, $\mathcal{O}(\theta_L p_{\text{ph}})$, making our protocol particularly powerful for implementing a sequence of small-angle rotation gates, like Trotter-based circuits. Notably, for $\theta_L \lesssim 10^{-5}$, our protocol achieves a two-order-of-magnitude reduction in both the execution time and the error rate of analog rotation gates compared to the standard $T$-gate synthesis using cultivated magic states. Building upon this protocol, we also propose a novel quantum computing architecture designed for early fault-tolerant quantum computers, dubbed ``STAR ver.~3". It employs a refined circuit compilation strategy based on Clifford+$T$+$\phi$ gate set, rather than the conventional Clifford+$T$ or Clifford+$\phi$ gate sets. We establish a theoretical bound on the feasible circuit size on this architecture and illustrate its capabilities by analyzing the spacetime costs for simulating the dynamics of quantum many-body systems. Specifically, we demonstrate that our architecture can simulate biologically-relevant molecules or lattice models at scales beyond the reach of exact classical simulation, with only a few hundred thousand physical qubits, even assuming a realistic error rate of $p_{\text{ph}}=10^{-3}$.

quant-ph↗

arXiv2026

Even More Efficient Soft-Output Decoding with Extra-Cluster Growth and Early Stopping

In fault-tolerant quantum computing, soft outputs from real-time decoders play a crucial role in improving decoding accuracy, post-selecting magic states, and accelerating lattice surgery. A recent paper by Meister et al. [arXiv:2405.07433 (2024)] proposed an efficient method to evaluate soft outputs for cluster-based decoders, including the Union-Find (UF) decoder. However, in parallel computing environments, its computational complexity is comparable to or even surpasses that of the UF decoder itself, resulting in a substantial overhead. Furthermore, this method requires global information about the decoding graph, making it poorly suited for existing hardware implementations of the UF decoder on Field-Programmable Gate Arrays (FPGAs). In this paper, to alleviate these issues, we develop more efficient methods for evaluating high-quality soft outputs in cluster-based decoders by introducing several early-stopping techniques. Our central idea is that the precise value of a large soft output is often unnecessary in practice. Based on this insight, we introduce two types of novel soft-outputs: the bounded cluster gap and the extra-cluster gap. The former reduces the computational complexity of Meister's method by terminating the calculation at an early stage. Our numerical simulations show that this method achieves improved scaling with code distance $d$ compared to the original proposal. The latter, the extra-cluster gap, quantifies decoder reliability by performing a small, additional growth of the clusters obtained by the decoder. This approach offers the significant advantage of enabling soft-output computation without modifying the existing architecture of FPGA-implemented UF decoders. These techniques offer lower computational complexity and higher hardware compatibility, laying a crucial foundation for future real-time decoders with soft outputs.

quant-ph↗

arXiv2025

Decoder Switching: Breaking the Speed-Accuracy Tradeoff in Real-Time Quantum Error Correction

The realization of fault-tolerant quantum computers hinges on the construction of high-speed, high-accuracy, real-time decoding systems. The persistent challenge lies in the fundamental trade-off between speed and accuracy: efforts to improve the decoder's accuracy often lead to unacceptable increases in decoding time and hardware complexity, while attempts to accelerate decoding result in a significant degradation in logical error rate. To overcome this challenge, we propose a novel framework, decoder switching, which balances these competing demands by combining a faster, soft-output decoder ("weak decoder") with a slower, high-accuracy decoder ("strong decoder"). In usual rounds, the weak decoder processes error syndromes and simultaneously evaluates its reliability via soft information. Only when encountering a decoding window with low reliability do we switch to the strong decoder to achieve more accurate decoding. Numerical simulations suggest that this framework can achieve accuracy comparable to, or even surpassing, that of the strong decoder, while maintaining an average decoding time on par with the weak decoder. We also develop an online decoding scheme tailored to our framework, named double window decoding, and elucidate the criteria for preventing an exponential slowdown of quantum computation. These findings break the long-standing speed-accuracy trade-off, paving the way for scalable real-time decoding devices.

quant-ph↗

arXiv2025

Efficient magic state cultivation with lattice surgery

Magic state distillation plays a crucial role in fault-tolerant quantum computation and represents a major bottleneck. In contrast to traditional logical-level distillation, physical-level distillation offers significant overhead reduction by enabling direct implementation with physical gates. Magic state cultivation is a state-of-the-art physical-level distillation protocol that is compatible with the square-grid connectivity and yields high-fidelity magic states. However, it relies on the complex grafted code, which incurs substantial spacetime overhead and complicates practical implementation. In this work, we propose an efficient cultivation-based protocol compatible with the square-grid connectivity. We reduce the spatial overhead by avoiding the grafted code and further reduce the average spacetime overhead by utilizing code expansion and enabling early rejection. Numerical simulations show that, with a color code distance of 3 and a physical error probability of $10^{-3}$, our protocol achieves a logical error probability for the resulting magic state comparable to that of magic state cultivation ($\approx 3 \times 10^{-6}$), while requiring about half the spacetime overhead. Our work provides an efficient and simple distillation protocol suitable for megaquop use cases and early fault-tolerant devices.

quant-ph↗

arXiv2025

Runtime reduction in lattice surgery utilizing time-like soft information

Runtime optimization of the quantum computing within a given computational resource is important to achieve practical quantum advantage. In this paper, we propose a runtime reduction protocol for the lattice surgery, which utilizes the soft information corresponding to the logical measurement error. Our proposal is a simple two-step protocol: operating the lattice surgery with the small number of syndrome measurement cycles, and reexecuting it with full syndrome measurement cycles in cases where the time-like soft information catches logical error symptoms. We firstly discuss basic features of the time-like complementary gap as the concrete example of the time-like soft information based on numerical results. Then, we show that our protocol surpasses the existing runtime reduction protocol called temporally encoded lattice surgery (TELS) for the most cases. In addition, we confirm that the combination of our protocol and the TELS protocol can reduce the runtime further, over 50% in comparison to the naive serial execution of the lattice surgery. The proposed protocol in this paper can be applied to any quantum computing architecture based on the lattice surgery, and we expect that this will be one of the fundamental building blocks of runtime optimization to achieve practical scale quantum computing.

quant-ph↗

arXiv2024

Practical quantum advantage on partially fault-tolerant quantum computer

Achieving quantum speedups in practical tasks remains challenging for current noisy intermediate-scale quantum (NISQ) devices. These devices always encounter significant obstacles such as inevitable physical errors and the limited scalability of current near-term algorithms. Meanwhile, assuming a typical architecture for fault-tolerant quantum computing (FTQC), realistic applications inevitably require a vast number of qubits, typically exceeding $10^6$, which seems far beyond near-term realization. In this work, to bridge the gap between the NISQ and FTQC eras, we propose an alternative approach to achieve practical quantum advantages on early-FTQC devices. Our framework is based on partially fault-tolerant logical operations to minimize spatial overhead and avoids the costly distillation techniques typically required for executing non-Clifford gates. To this end, we develop a space-time efficient state preparation protocol to generate an ancillary non-Clifford state consumed for implementing an analog rotation gate with an arbitrary small angle $θ$ and a remarkably low worst-case error rate below $\mathcal{O}(|θ| p_{\text{ph}})$, where $p_{\text{ph}}$ is the physical error rate. Furthermore, we propose several error suppression schemes tailored to our preparation protocol, which are essential to minimize the overhead for mitigating errors. Based on this framework, we present several promising applications that leverage the potential of our framework, including the Trotter simulation and quantum phase estimation (QPE). Notably, we demonstrate that our framework allows us to perform the QPE for $(8\times 8)$-site Hubbard model with fewer than $4.9\times 10^4$ qubits and an execution time of 9 days (or 12 minutes with full parallelization) under $p_{\text{ph}}=10^{-4}$, which is significantly faster than recent classical estimation with tensor network techniques (DMRG and PEPS).

quant-ph↗

arXiv2024

Compilation of Trotter-Based Time Evolution for Partially Fault-Tolerant Quantum Computing Architecture

Achieving practical quantum speedup with limited resources is a crucial challenge in both academic and industrial communities. To address this, a partially fault-tolerant quantum computing architecture called ``space-time efficient analog rotation quantum computing architecture (STAR architecture)'' has been recently proposed. This architecture focuses on minimizing resource requirements while maximizing the precision of non-Clifford gates, essential for universal quantum computation. However, non-deterministic processes such as the repeat-until-success (RUS) protocol and state injection can introduce significant computational overhead. Therefore, optimizing the logical circuit to minimize this overhead by using efficient fault-tolerant operations is essential. This paper presents an efficient method for simulating the time evolution of the 2D Hubbard model Hamiltonian, a promising application of the STAR architecture. We present two techniques, parallel injection protocol and adaptive injection region updating, to reduce unnecessary time overhead specific to our architecture. By integrating these with the existing fSWAP technique, we develop an efficient Trotter-based time evolution operation for the 2D Hubbard model. Our analysis reveals an acceleration of over 10 times compared to naive serial compilation. This optimized compilation enables us to estimate the computational resources required for quantum phase estimation of the 2D Hubbard model. For devices with a physical error rate of $p_{\rm phys} = 10^{-4}$, we estimate that approximately $6.5 \times 10^4$ physical qubits are required to achieve faster ground state energy estimation of the $8\times8$ Hubbard model compared to classical computation.

quant-ph↗

arXiv2023

Path integral approach to universal dynamics of reservoir computers

In this work, we give a characterization of the reservoir computer (RC) by the network structure, especially the probability distribution of random coupling constants. First, based on the path integral method, we clarify the universal behavior of the random network dynamics in the thermodynamic limit, which depends only on the asymptotic behavior of the second cumulant generating functions of the network coupling constants. This result enables us to classify the random networks into several universality classes, according to the distribution function of coupling constants chosen for the networks. Interestingly, it is revealed that such a classification has a close relationship with the distribution of eigenvalues of the random coupling matrix. We also comment on the relation between our theory and some practical choices of random connectivity in the RC. Subsequently, we investigate the relationship between the RC's computational power and the network parameters for several universality classes. We perform several numerical simulations to evaluate the phase diagrams of the steady reservoir states, common-signal-induced synchronization, and the computational power in the chaotic time series inference tasks. As a result, we clarify the close relationship between these quantities, especially a remarkable computational performance near the phase transitions, which is realized even near a non-chaotic transition boundary. These results may provide us with a new perspective on the designing principle for the RC.

cond-mat.dis-nn↗

arXiv2022

Plasmonic quantum nonlinear Hall effect in noncentrosymmetric 2D materials

We investigate an interplay between quantum geometrical effects and surface plasmons through surface plasmonic structures, based on an electron hydrodynamic theory. First we demonstrate that the quantum nonlinear Hall effect can be dramatically enhanced over a very broad range of frequency by utilizing plasmonic resonances and near-field effects of grating gates. Under the resonant condition, the enhancement becomes several orders of magnitude larger than the case without the nanostructures, while the peaks of high-harmonic plasmons expand broadly and emerge under the off-resonant condition, leading to a remarkably broad spectrum. Furthermore, we clarify a universal relation between the photocurrent induced by the Berry curvature dipole and the optical absorption, which is essential for computational material design of long-wavelength photodetectors. Next we discuss a novel mechanism of geometrical photocurrent, which originates from an anomalous force induced by oscillating magnetic fields and is described by the dipole moment of orbital magnetic moments of Bloch electrons in the momentum space. Our theory is relevant to 2D quantum materials such as layered WTe${}_2$ and twisted bilayer graphene, thereby providing a promising route toward a novel type of highly sensitive, broadband terahertz photodetectors.

cond-mat.mes-hall↗

arXiv2021

Nonreciprocal electron hydrodynamics under magnetic fields: applications to nonreciprocal surface magnetoplasmons

Recent experiments have elucidated that novel nonequilibrium states inherent in the so-called hydrodynamic regime are realized in ultrapure metals with sufficiently strong momentum-conserving scattering. In this letter, we formulate a theory of electron hydrodynamics with broken inversion symmetry under magnetic fields and find that novel terms emerge in hydrodynamic equations which play a crucial role for the realization of the nonreciprocal responses. Specifically, we clarify that there exist a novel type of nonreciprocal collective modes dubbed nonreciprocal surface magnetoplasmons arising from an interplay between magnetic fields and the orbital magnetic moment. We reveal that these nonreciprocal collective modes indeed give rise to the nonreciprocity in magneto-optical responses such as the reflectivity. The physics discussed here will bridge the two important notions of magnetoplasmonics and nonreciprocity in electron hydrodynamic materials with inversion symmetry breaking and magnetic fields.

cond-mat.mes-hall↗

arXiv2021

Vorticity-induced anomalous Hall effect in electron fluid

We develop a hydrodynamic theory for an electron system exhibiting the anomalous Hall effect, and show that an additional anomalous Hall effect is induced by a vorticity generated near boundaries. We calculate the momentum flux and force proportional to the electric field using linear response theory. The hydrodynamic equation is obtained by replacing the local electric field with the electric current, focusing on a scale that is sufficiently larger than the mean free path. It is demonstrated that there is a coupling between a vorticity of an electric current and a magnetization which generates a pressure from non-uniform vorticity. Taking into account Hall viscosity and relaxation forces, a non-uniform flow near a boundary and an additional Hall force are calculated. The additional anomalous Hall force is opposite to conventional anomalous Hall force, resulting in a sign reversal in thin systems.

cond-mat.mes-hall↗

arXiv2020

Anomalous Hydrodynamic Transport in Interacting Noncentrosymmetric Metals

In highly conductive metals with sufficiently strong momentum-conserving scattering, the electron momentum is regarded as a long-lived quantity, whose dynamics is described by an emergent hydrodynamic theory. In this paper, we develop an electron hydrodynamic theory for noncentrosymmetric metals, where a novel class of electron fluids is realized by lowering crystal symmetries and the resulting geometrical effects. The obtained hydrodynamic equation suggests a nontrivial analogy between electron fluids in noncentrosymmetric metals and chiral fluids in vacuum, and predicts novel hydrodynamic transport phenomena, that is, asymmetric Poiseuille flow and anomalous edge current. Our theory also gives a hydrodynamic description of the counterpart of various anomalous transport phenomena such as the quantum nonlinear Hall effect. Furthermore, we give a symmetry consideration on the hydrodynamic equation and propose several experimental setups to realize such anomalous hydrodynamic transport in the existing hydrodynamic materials, including bilayer graphene and Weyl semimetals.

cond-mat.mes-hall↗

arXiv2019

Nonlocal optical responses of ultrapure metals in the hydrodynamic regime

Our conventional understanding of optical responses in metals has been based on the Drude theory. In recent years, however, it has become possible to prepare ultrapure metallic samples where the electron-electron scattering becomes the most dominant process governing transport and thus the Drude theory, where momentum-relaxing scatterings such as electron-impurity scattering are assumed to be dominant, is no longer valid. This regime is called the hydrodynamic regime and described by an emergent hydrodynamic theory. Here, we develop a basic framework of optical responses in the hydrodynamic regime. Based on the hydrodynamic equation, we reveal the existence of a ``hydrodynamic mode'' resulting from the viscosity effect and compute the reflectance and the transmittance in three-dimensional electron fluids. Our theory also describes how to probe the hydrodynamic effects and measure the viscosity through simple optical techniques.

cond-mat.mes-hall↗