arXiv subjects

Hayata Yamasaki

Publications and source records attributed to Hayata Yamasaki.

At least 37 records · Page 2Linked to original sources

arXiv2026

Classical simulation and quantum resource theory of non-Gaussian optics

We propose efficient algorithms for classically simulating Gaussian unitaries and measurements applied to non-Gaussian initial states. The constructions are based on decomposing the non-Gaussian states into linear combinations of Gaussian states. We use an extension of the covariance matrix formalism to efficiently track relative phases in the superpositions of Gaussian states. We get an exact simulation algorithm, which costs quadratically with the number of Gaussian states required to represent the initial state, and an approximate simulation algorithm, which costs linearly with the $l_1$ norm of the coefficients associated with the superposition. We define measures of non-Gaussianity quantifying this simulation cost, which we call the Gaussian rank and the Gaussian extent. From the perspective of quantum resource theories, we investigate the properties of this type of non-Gaussianity measure and compute optimal decompositions for states relevant to continuous-variable quantum computing.

quant-ph↗

arXiv2026

Constant-space-overhead fault-tolerant quantum input/output and communication

Fault-tolerant capacities quantify the ability of a quantum channel to reliably transmit information when every component of the encoding and decoding procedure is noisy. Earlier work analyzed achievable communication rates under such noise using fault-tolerant implementations based on concatenated codes with a single logical qubit. In this work, we develop an alternative approach using concatenations of quantum Hamming codes, which offer constant space overhead by encoding many logical qubits simultaneously. We introduce modular techniques for implementing fault-tolerant circuits with quantum input/output interfaces using the concatenated quantum Hamming code. These tools enable an analysis of fault-tolerant entanglement-assisted communication that is not only simpler, but also yields substantially higher achievable communication rates than previous methods, owing to the limited noise correlations in syndrome qubits of high-rate quantum Hamming codes.

quant-ph↗

arXiv2025

Characterizing Space-Constrained Implementability of Quantum Instruments via Signaling Conditions

Scaling up the number of qubits available on quantum processors remains technically demanding even in the long term; it is therefore crucial to clarify the number of qubits required to implement a given quantum operation. For the most general class of quantum operations, known as quantum instruments, the qubit requirements are not well understood, especially when mid-circuit measurements and delayed input preparation are permitted. In this work, we characterize lower and upper bounds on the number of qubits required to implement a given quantum instrument in terms of the causal structure of the instrument. We further apply our results to entanglement distillation protocols based on stabilizer codes and show that, in these cases, the lower and upper bounds coincide, so the optimal qubit requirement is determined. In particular, we compute that the optimal number of qubits is 3 for the $[[9,1,3]]$-code-based protocol and 4 for the $[[5,1,3]]$-code-based protocol.

quant-ph↗

arXiv2025

Generalized Quantum Stein's Lemma for Classical-Quantum Dynamical Resources

Channel conversion constitutes a pivotal paradigm in information theory and its applications to quantum physics, providing a unified problem setting that encompasses celebrated results such as Shannon's noisy-channel coding theorem. Quantum resource theories (QRTs) offer a general framework to study such problems under a prescribed class of operations, such as those for encoding and decoding. In QRTs, quantum states serve as static resources, while quantum channels give rise to dynamical resources. A recent major advance in QRTs is the generalized quantum Stein's lemma, which characterizes the optimal error exponent in hypothesis testing to discriminate resource states from free states, enabling a reversible QRT framework for static resources where asymptotic conversion rates are fully determined by the regularized relative entropy of resource. However, applications of QRTs to channel conversion require a framework for dynamical resources. The earlier extension of the reversible framework to a fundamental class of dynamical resources, represented by classical-quantum (CQ) channels, relied on state-based techniques and imposed an asymptotic continuity assumption on operations, which prevented its applicability to conventional channel coding scenarios. To overcome this problem, we formulate and prove a generalized quantum Stein's lemma directly for CQ channels, by developing CQ-channel counterparts of the core proof techniques used in the state setting. Building on this result, we construct a reversible QRT framework for CQ channel conversion that does not require the asymptotic continuity assumption, and show that this framework applies to the analysis of channel coding scenarios. These results establish a fully general toolkit for CQ channel discrimination and conversion, enabling their broad application to core conversion problems for this fundamental class of channels.

quant-ph↗

arXiv2025

Doubly-polylog-time-overhead fault-tolerant quantum computation by a polylog-time parallel minimum-weight perfect matching decoder

Reducing space and time overheads of fault-tolerant quantum computation (FTQC) has been receiving increasing attention as it is crucial for the development of quantum computers and also plays a fundamental role in understanding the feasibility and limitations of realizing quantum advantages. Shorter time overheads are particularly essential for demonstrating quantum computational speedups without compromising runtime advantages. However, surpassing the conventional polylogarithmic (polylog) scaling of time overheads has remained a significant challenge, since it requires addressing all potential bottlenecks, including the nonzero runtime of classical computation for decoding in practical implementations. In this work, we construct a protocol that achieves FTQC with doubly polylog time overhead while maintaining the conventional polylog space overhead. The key to our approach is the development of a highly parallelizable minimum-weight perfect matching (MWPM) decoder, which achieves a polylog parallel runtime in terms of the code size while providing theoretical guarantees on threshold existence and overhead bounds. Our protocol integrates this decoder with a topological-code protocol that incorporates single-shot decoding for efficient syndrome extraction; furthermore, we concatenate this with the concatenated Steane codes to guarantee the existence of the threshold while avoiding a backlog problem, enabling us to achieve doubly polylog time overheads even when accounting for the decoder's runtime. These results suggest the feasibility of surpassing the conventional polylog-time-overhead barrier, opening a new frontier in low-overhead FTQC.

quant-ph↗

arXiv2025

Transversal Surface-Code Game Powered by Neutral Atoms

Neutral atom technologies have opened the door to novel theoretical advances in surface-code protocols for fault-tolerant quantum computation (FTQC), offering a compelling alternative to lattice surgery by leveraging transversal gates. However, a crucial gap remains between the theory of FTQC and its practical realization on neutral atom systems; most critically, a key theoretical requirement -- that syndrome extraction must be performed frequently enough to keep error accumulation below a threshold constant -- is difficult to satisfy in a scalable manner in conventional zoned approach. In this work, we develop a comprehensive theoretical framework that closes such a gap, bridging theoretical advances in surface-code fault-tolerant protocols with capabilities of neutral atoms. Building on the "game of surface code" framework originally developed for superconducting qubits, we introduce an alternative game-based paradigm for transversal-gate FTQC that harnesses the unique strengths of neutral atom arrays. The game rules are designed to enable syndrome extraction at any intermediate step during logical gate implementation, ensuring compatibility with the threshold theorem. We further present an efficient method for designing resource state factories tailored to transversal-gate FTQC. As an application, our framework offers a systematic methodology and high-level abstraction for resource estimation and optimization, demonstrating that space-time performance competitive with a baseline lattice-surgery-based approach on superconducting qubits is possible, even when physical operations on neutral atoms are orders of magnitude slower. These results establish a solid foundation that bridges the theory and experiment of FTQC powered by neutral atoms, charting a well-founded pathway toward scalable, fault-tolerant quantum computers and setting practical directions for technological development.

quant-ph↗

arXiv2025

Concatenate codes, save qubits

The essential requirement for fault-tolerant quantum computation (FTQC) is the total protocol design to achieve a fair balance of all the critical factors relevant to its practical realization, such as the space overhead, the threshold, and the modularity. A major obstacle in realizing FTQC with conventional protocols, such as those based on the surface code and the concatenated Steane code, has been the space overhead, i.e., the required number of physical qubits per logical qubit. Protocols based on high-rate quantum low-density parity-check (LDPC) codes gather considerable attention as a way to reduce the space overhead, but problematically, the existing fault-tolerant protocols for such quantum LDPC codes sacrifice the other factors. Here we construct a new fault-tolerant protocol to meet these requirements simultaneously based on more recent progress on the techniques for concatenated codes rather than quantum LDPC codes, achieving a constant space overhead, a high threshold, and flexibility in modular architecture designs. In particular, under a physical error rate of $0.1\%$, our protocol reduces the space overhead to achieve the logical CNOT error rates $10^{-10}$ and $10^{-24}$ by more than $90 \%$ and $96 \%$, respectively, compared to the protocol for the surface code. Furthermore, our protocol achieves the threshold of $2.5 \%$ under a conventional circuit-level error model, substantially outperforming that of the surface code. The use of concatenated codes also naturally introduces abstraction layers essential for the modularity of FTQC architectures. These results indicate that the code-concatenation approach opens a way to significantly save qubits in realizing FTQC while fulfilling the other essential requirements for the practical protocol design.

quant-ph↗

arXiv2025

Generalized Quantum Stein's Lemma and Second Law of Quantum Resource Theories

The second law of thermodynamics is the cornerstone of physics, characterizing the convertibility between thermodynamic states through a single function, entropy. Given the universal applicability of thermodynamics, a fundamental question in quantum information theory is whether an analogous second law can be formulated to characterize the convertibility of resources for quantum information processing by a single function. In 2008, a promising formulation was proposed, linking resource convertibility to the optimal performance of a variant of the quantum version of hypothesis testing. Central to this formulation was the generalized quantum Stein's lemma, which aimed to characterize this optimal performance by a measure of quantum resources, the regularized relative entropy of resource. If proven valid, the generalized quantum Stein's lemma would lead to the second law for quantum resources, with the regularized relative entropy of resource taking the role of entropy in thermodynamics. However, in 2023, a logical gap was found in the original proof of this lemma, casting doubt on the possibility of such a formulation of the second law. In this work, we address this problem by developing alternative techniques to successfully prove the generalized quantum Stein's lemma under a smaller set of assumptions than the original analysis. Based on our proof, we reestablish and extend the second law of quantum resource theories, applicable to both static resources of quantum states and a fundamental class of dynamical resources represented by classical-quantum (CQ) channels. These results resolve the fundamental problem of bridging the analogy between thermodynamics and quantum information theory.

quant-ph↗

arXiv2025

Taming Recoil Effect in Cavity-Assisted Quantum Interconnects

Photon recoil is one of the fundamental limitations for high-fidelity control of trapped-atom qubits such as neutral atoms and trapped ions. In this work, we derive an analytical model for efficiently evaluating the motion-induced infidelity in remote entanglement generation protocols. Our model is applicable for various photonic qubit encodings such as polarization, time bin, and frequency, and with arbitrary initial motional states, thus providing a crucial theoretical tool for realizing high-fidelity quantum networking. For the case of tweezer-trapped neutral atoms, our results indicate that operating in the bad-cavity regime with cavity decay rate exceeding atom-photon coupling rate, and near-ground-state cooling with motional quanta below 1, are desired to suppress the motion-induced infidelity sufficiently below the 1% level required for efficient quantum networking. Finite temperature effects can be mitigated efficiently by detection time filtering at the moderate cost of success probability and network speed. These results extend the understanding of infidelity sources in remote entanglement generation protocols, establishing a concrete path towards fault-tolerant quantum networking with scalable trapped-atom qubit systems.

physics.atom-ph↗

arXiv2025

Energy-Consumption Advantage of Quantum Computation

Energy consumption in solving computational problems has been gaining growing attention as one of the key performance measures for computers. Quantum computation is known to offer advantages over classical computation in terms of various computational resources; however, proving its energy-consumption advantage has been challenging due to the lack of a theoretical foundation linking the physical concept of energy with the computer-scientific notion of complexity for quantum computation. To bridge this gap, we introduce a general framework for studying the energy consumption of quantum and classical computation, based on a computational model conventionally used for studying query complexity in computational complexity theory. Within this framework, we derive an upper bound for the achievable energy consumption of quantum computation, accounting for imperfections in implementation appearing in practice. As part of this analysis, we construct a protocol for Landauer erasure with finite precision in a finite number of steps, which constitutes a contribution of independent interest. Additionally, we develop techniques for proving a nonzero lower bound of energy consumption of classical computation, based on the energy-conservation law and Landauer's principle. Using these general bounds, we rigorously prove that quantum computation achieves an exponential energy-consumption advantage over classical computation for solving a paradigmatic computational problem -- Simon's problem. Furthermore, we propose explicit criteria for experimentally demonstrating this energy-consumption advantage of quantum computation, analogous to the experimental demonstrations of quantum computational supremacy. These results establish a foundational framework and techniques to explore the energy consumption of computation, opening an alternative way to study the advantages of quantum computation.

quant-ph↗

arXiv2025

Time-Efficient Constant-Space-Overhead Fault-Tolerant Quantum Computation

Scaling up quantum computers to attain substantial speedups over classical computing requires fault tolerance. Conventionally, protocols for fault-tolerant quantum computation demand excessive space overheads by using many physical qubits for each logical qubit. A more recent protocol using quantum analogues of low-density parity-check codes needs only a constant space overhead that does not grow with the number of logical qubits. However, the overhead in the processing time required to implement this protocol grows polynomially with the number of computational steps. To address these problems, here we introduce an alternative approach to constant-space-overhead fault-tolerant quantum computing using a concatenation of multiple small-size quantum codes rather than a single large-size quantum low-density parity-check code. We develop techniques for concatenating different quantum Hamming codes with growing sizes. As a result, we construct a low-overhead protocol to achieve constant space overhead and only quasi-polylogarithmic time overhead simultaneously. Our protocol is fault tolerant even if a decoder has a non-constant runtime, unlike the existing constant-space-overhead protocol. This code concatenation approach will make possible a large class of quantum speedups within feasibly bounded space overhead yet negligibly short time overhead.

quant-ph↗

arXiv2024

Polylog-time- and constant-space-overhead fault-tolerant quantum computation with quantum low-density parity-check codes

A major challenge in fault-tolerant quantum computation (FTQC) is to reduce both space overhead -- the large number of physical qubits per logical qubit -- and time overhead -- the long physical gate sequences per logical gate. We prove that a protocol using non-vanishing-rate quantum low-density parity-check (LDPC) codes, combined with concatenated Steane codes, achieves constant space overhead and polylogarithmic time overhead, even when accounting for non-zero classical computation time. This protocol offers an improvement over existing constant-space-overhead protocols, which have polynomial time overhead using quantum LDPC codes and quasi-polylogarithmic time overhead using concatenated quantum Hamming codes. To ensure the completeness of this proof, we develop a technique called partial circuit reduction, which enables error analysis for the entire fault-tolerant circuit by examining smaller parts composed of a few gadgets. With this technique, we resolve a previously unaddressed logical gap in the existing arguments and complete the proof of the threshold theorem for the constant-space-overhead protocol with quantum LDPC codes. Our work highlights that the quantum-LDPC-code approach can realize FTQC with a negligibly small slowdown and a bounded overhead of physical qubits, similar to the code-concatenation approach, underscoring the importance of a comprehensive comparison of the future realizability of these two approaches.

quant-ph↗

arXiv2024

Efficient decoding of stabilizer code by single-qubit local operations and classical communication

We construct a protocol for extracting distributed one-qubit quantum information encoded in a stabilizer code of multiple qubits, only by single-qubit local operations and classical communication (LOCC) without global operations or entanglement resources. This protocol achieves efficient extraction within a polynomial time in terms of the number of physical qubits. We apply this protocol to a setting of quantum information splitting where a subset of spatially separated parties cooperate by classical communication to extract quantum information shared among all the parties. For this task, our LOCC extraction protocol allows designing hierarchical information access structures among the parties, where the minimum number of parties required to cooperate depends on the location of extracting the shared quantum information. These results provide a fundamental building block of distributed quantum information processing that requires access to distributed quantum information encoded in the stabilizer codes.

quant-ph↗

arXiv2024

Continuous-Variable Fault-Tolerant Quantum Computation under General Noise

The quantum error-correcting code in the continuous-variable (CV) system attracts much attention due to its flexibility and high resistance against specific noise. However, the theory of fault tolerance in CV systems is premature and lacks the general strategy to translate the noise in CV systems into the noise in logical qubits, leading to severe restrictions on the correctable noise models. In this paper, we show that the Markovian-type noise in CV systems is translated into the Markovian-type noise in the logical qubits through the Gottesman-Kitaev-Preskill code with an explicit bound on the noise strength. Combined with the established threshold theorem of the concatenated code against Markovian-type noise, we show that CV quantum computation has a fault-tolerant threshold against general Markovian-type noise, closing the existing crucial gap in CV quantum computation. We also give a new insight into the fact that careful management of the energy of the state is required to achieve fault tolerance in the CV system.

quant-ph↗

arXiv2024

Constant-Overhead Magic State Distillation

Magic state distillation is a crucial yet resource-intensive process in fault-tolerant quantum computation. The protocol's overhead, defined as the number of input magic states required per output magic state with an error rate below $ε$, typically grows as $\mathcal{O}(\log^γ(1/ε))$. Achieving smaller overheads, i.e., smaller exponents $γ$, is highly desirable; however, all existing protocols require polylogarithmically growing overheads with some $γ> 0$, and identifying the smallest achievable exponent $γ$ for distilling magic states of qubits has remained challenging. To address this issue, we develop magic state distillation protocols for qubits with efficient, polynomial-time decoding that achieve an $\mathcal{O}(1)$ overhead, meaning the optimal exponent $γ= 0$; this improves over the previous best of $γ\approx 0.678$ due to Hastings and Haah. In our construction, we employ algebraic geometry codes to explicitly present asymptotically good quantum codes for $2^{10}$-dimensional qudits that support transversally implementable logical gates in the third level of the Clifford hierarchy. The use of asymptotically good codes with non-vanishing rate and relative distance leads to the constant overhead. These codes can be realised by representing each $2^{10}$-dimensional qudit as a set of $10$ qubits, using stabiliser operations on qubits. The $10$-qubit magic states distilled with these codes can be converted to and from conventional magic states for the controlled-controlled-$Z$ ($CCZ$) and $T$ gates on qubits with only a constant overhead loss, making it possible to achieve constant-overhead distillation of such standard magic states for qubits. These results resolve the fundamental open problem in quantum information theory concerning the construction of magic state distillation protocols with the optimal exponent.

quant-ph↗

arXiv2024

Improved bounds on quantum uncommon information

In classical information theory, channel capacity quantifies the maximum number of messages that can be reliably transmitted using shared information. An equivalent concept, termed uncommon information, represents the number of messages required to be exchanged to completely share all information in common. However, this equivalence does not extend to quantum information theory. Specifically, quantum uncommon information is operationally defined as the minimal amount of entanglement required for the quantum communication task of quantum state exchange, where two parties exchange quantum states to share all quantum messages in common. Currently, an analytical closed-form expression for the quantum uncommon information remains undetermined. In this work, by investigating underlying characterization of the quantum uncommon information, we derive improved bounds on it. To obtain these bounds, we develop a subspace exchange strategy that leverages a common subspace of two parties to identify the unnecessary qubits for exchange. We also consider a referee-assisted exchange, wherein a referee aids two parties in efficiently performing the quantum state exchange. Our bounds provide more precise estimations for the quantum uncommon information. Furthermore, we demonstrate that the subspace technique is a versatile tool for characterizing uncommon information not only in the bipartite scenario but also in various multi-partite ones.

quant-ph↗

arXiv2024

Scalable Networking of Neutral-Atom Qubits: Nanofiber-Based Approach for Multiprocessor Fault-Tolerant Quantum Computer

Neutral atoms are among the leading platforms toward realizing fault-tolerant quantum computation (FTQC). However, scaling up a single neutral-atom device beyond $\sim 10^4$ atoms to meet the demands of FTQC for practical applications remains a challenge. To overcome this challenge, we clarify the criteria and technological requirements for further scaling based on multiple neutral atom quantum processing units (QPUs) connected through photonic networking links. Our quantitative analysis shows that nanofiber optical cavities have the potential as an efficient atom-photon interface to enable fast entanglement generation between atoms in distinct neutral-atom modules, allowing multiple neutral-atom QPUs to operate cooperatively without sacrificing computational speed. Using state-of-the-art millimeter-scale nanofiber cavities with the finesse of thousands, over a hundred atoms can be coupled to the cavity mode with an optical tweezer array, with expected single-atom cooperativity exceeding 100 for telecom-band transition of ytterbium atoms. This enables efficient time-multiplexed entanglement generation with a predicted Bell pair generation rate of 100 kHz while maintaining a small footprint for channel multiplexing. These proposals and results indicate a promising pathway for building large-scale multiprocessor fault-tolerant quantum computers using neutral atoms, nanofiber optical cavities, and fiber-optic networks.

quant-ph↗

arXiv2024

Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories

Quantum resource theories (QRTs) provide a unified framework to analyze quantum properties as resources for achieving advantages in quantum information processing. The generalized robustness and the weight of resource have been gaining increasing attention as useful resource quantifiers. However, the existing analyses of these measures were restricted to the cases where convexity of the set of free states is assumed, and physically motivated resources do not necessarily satisfy this restriction. In this paper, we give characterizations of robustness- and weight-based measures in general QRTs without convexity restriction through two different yet related approaches. On the one hand, we characterize the generalized robustness and the weight of resource by introducing a nonlinear witness. We show a general construction of new witness observables that detect the resourcefulness of a given state from multiple copies of the state and, using these witnesses, we provide operational interpretations of the above resource measures even without any convexity assumption. On the other hand, we find that the generalized robustness and the weight of resource can also be interpreted as the worst-case maximum advantage in variants of channel-discrimination and channel-exclusion tasks, respectively, where the set of free states consists of several convex subsets corresponding to multiple restrictions. We further extend these results to QRTs for quantum channels and quantum instruments. These characterizations show that every quantum resource exhibits an advantage for the corresponding tasks, even in general QRTs without convexity assumption. Thus, we establish the usefulness of robustness-based and weight-based techniques beyond the conventional scope of convex QRTs, leading to a better understanding of the general structure of QRTs.

quant-ph↗