IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-09-17 DOI: 10.22331/q-2024-09-17-1474

Kazuki Sakamoto, Hayata Morisaki, Junichi Haruna, Etsuko Itou, Keisuke Fujii, Kosuke Mitarai

{"title":"End-to-end complexity for simulating the Schwinger model on quantum computers","authors":"Kazuki Sakamoto, Hayata Morisaki, Junichi Haruna, Etsuko Itou, Keisuke Fujii, Kosuke Mitarai","doi":"10.22331/q-2024-09-17-1474","DOIUrl":"https://doi.org/10.22331/q-2024-09-17-1474","url":null,"abstract":"The Schwinger model is one of the simplest gauge theories. It is known that a topological term of the model leads to the infamous sign problem in the classical Monte Carlo method. In contrast to this, recently, quantum computing in Hamiltonian formalism has gained attention. In this work, we estimate the resources needed for quantum computers to compute physical quantities that are challenging to compute on classical computers. Specifically, we propose an efficient implementation of block-encoding of the Schwinger model Hamiltonian. Considering the structure of the Hamiltonian, this block-encoding with a normalization factor of $mathcal{O}(N^3)$ can be implemented using $mathcal{O}(N+log^2(N/varepsilon))$ T gates. As an end-to-end application, we compute the vacuum persistence amplitude. As a result, we found that for a system size $N=128$ and an additive error $varepsilon=0.01$, with an evolution time $t$ and a lattice spacing a satisfying $t/2a=10$, the vacuum persistence amplitude can be calculated using about $10^{13}$ T gates. Our results provide insights into predictions about the performance of quantum computers in the FTQC and early FTQC era, clarifying the challenges in solving meaningful problems within a realistic timeframe.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"13 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142235250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Reconstruction of Quantum Particle Statistics: Bosons, Fermions, and Transtatistics 重构量子粒子统计：玻色子、费米子和超统计

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-09-12 DOI: 10.22331/q-2024-09-12-1473

Nicolás Medina Sánchez, Borivoje Dakić

{"title":"Reconstruction of Quantum Particle Statistics: Bosons, Fermions, and Transtatistics","authors":"Nicolás Medina Sánchez, Borivoje Dakić","doi":"10.22331/q-2024-09-12-1473","DOIUrl":"https://doi.org/10.22331/q-2024-09-12-1473","url":null,"abstract":"Identical quantum particles exhibit only two types of statistics: bosonic and fermionic. Theoretically, this restriction is commonly established through the symmetrization postulate or (anti)commutation constraints imposed on the algebra of creation and annihilation operators. The physical motivation for these axioms remains poorly understood, leading to various generalizations by modifying the mathematical formalism in somewhat arbitrary ways. In this work, we take an opposing route and classify quantum particle statistics based on operationally well-motivated assumptions. Specifically, we consider that a) the standard (complex) unitary dynamics defines the set of single-particle transformations, and b) phase transformations act locally in the space of multi-particle systems. We develop a complete characterization, which includes bosons and fermions as basic statistics with minimal symmetry. Interestingly, we have discovered whole families of novel statistics (dubbed transtatistics) accompanied by hidden symmetries, generic degeneracy of ground states, and spontaneous symmetry breaking – effects that are (typically) absent in ordinary statistics.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"35 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142174657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Adaptive Online Learning of Quantum States 量子态的自适应在线学习

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-09-12 DOI: 10.22331/q-2024-09-12-1471

Xinyi Chen, Elad Hazan, Tongyang Li, Zhou Lu, Xinzhao Wang, Rui Yang

引用次数: 0

The Complexity of Being Entangled 纠缠的复杂性

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-09-12 DOI: 10.22331/q-2024-09-12-1472

Stefano Baiguera, Shira Chapman, Giuseppe Policastro, Tal Schwartzman

{"title":"The Complexity of Being Entangled","authors":"Stefano Baiguera, Shira Chapman, Giuseppe Policastro, Tal Schwartzman","doi":"10.22331/q-2024-09-12-1472","DOIUrl":"https://doi.org/10.22331/q-2024-09-12-1472","url":null,"abstract":"Nielsen's approach to quantum state complexity relates the minimal number of quantum gates required to prepare a state to the length of geodesics computed with a certain norm on the manifold of unitary transformations. For a bipartite system, we investigate binding complexity, which corresponds to norms in which gates acting on a single subsystem are free of cost. We reduce the problem to the study of geodesics on the manifold of Schmidt coefficients, equipped with an appropriate metric. Binding complexity is closely related to other quantities such as distributed computing and quantum communication complexity, and has a proposed holographic dual in the context of AdS/CFT. For finite dimensional systems with a Riemannian norm, we find an exact relation between binding complexity and the minimal Rényi entropy. We also find analytic results for the most commonly used non-Riemannian norm (the so-called $F_1$ norm) and provide lower bounds for the associated notion of state complexity ubiquitous in quantum computation and holography. We argue that our results are valid for a large class of penalty factors assigned to generators acting across the subsystems. We demonstrate that our results can be borrowed to study the usual complexity (not-binding) for a single spin for the case of the $F_1$ norm which was previously lacking from the literature. Finally, we derive bounds for multi-partite binding complexities and the related (continuous) circuit complexity where the circuit contains at most $2$-local interactions.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"17 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142174628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Efficient Classical Shadow Tomography through Many-body Localization Dynamics 通过多体定位动力学实现高效经典阴影断层扫描

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-09-11 DOI: 10.22331/q-2024-09-11-1467

Tian-Gang Zhou, Pengfei Zhang

{"title":"Efficient Classical Shadow Tomography through Many-body Localization Dynamics","authors":"Tian-Gang Zhou, Pengfei Zhang","doi":"10.22331/q-2024-09-11-1467","DOIUrl":"https://doi.org/10.22331/q-2024-09-11-1467","url":null,"abstract":"Classical shadow tomography serves as a potent tool for extracting numerous properties from quantum many-body systems with minimal measurements. Nevertheless, prevailing methods yielding optimal performance for few-body operators necessitate the application of random two-qubit gates, a task that can prove challenging on specific quantum simulators such as ultracold atomic gases. In this work, we introduce an alternative approach founded on the dynamics of many-body localization, a phenomenon extensively demonstrated in optical lattices. Through an exploration of the shadow norm – both analytically, employing a phenomenological model, and numerically, utilizing the TEBD algorithm – we demonstrate that our scheme achieves remarkable efficiency comparable to shallow circuits or measurement-induced criticality, resulting in a significant improvement in the exponential exponent compared to the previous classical shadow protocol. Our findings are corroborated through direct numerical simulations encompassing the entire sampling and reconstruction processes. Consequently, our results present a compelling methodology for analyzing the output states of quantum simulators.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"38 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142166208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exact results on finite size corrections for surface codes tailored to biased noise 针对偏置噪声的表面代码有限尺寸修正的精确结果

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-09-11 DOI: 10.22331/q-2024-09-11-1468

Yinzi Xiao, Basudha Srivastava, Mats Granath

{"title":"Exact results on finite size corrections for surface codes tailored to biased noise","authors":"Yinzi Xiao, Basudha Srivastava, Mats Granath","doi":"10.22331/q-2024-09-11-1468","DOIUrl":"https://doi.org/10.22331/q-2024-09-11-1468","url":null,"abstract":"The code-capacity threshold of a scalable quantum error correcting stabilizer code can be expressed as a thermodynamic phase transition of a corresponding random-bond Ising model. Here we study the XY and XZZX surface codes under phase-biased noise, $p_x=p_y=p_z/(2eta)$, with $etageq 1/2$, and total error rate $p=p_x+p_y+p_z$. By appropriately formulating the boundary conditions, in the rotated code geometry, we find exact solutions at a special disordered point, $p=frac{1+eta^{-1}}{2+eta^{-1}}gtrsim 0.5$, for arbitrary odd code distance $d$, where the codes reduce to one-dimensional Ising models. The total logical failure rate is given by $P_{f}=frac{3}{4}-frac{1}{4}e^{-2d_Z,text{artanh}(1/2eta)}$, where $d_{Z}=d^2$ and $d$ for the two codes respectively, is the effective code distance for pure phase-flip noise. As a consequence, for code distances $dll eta$, and error rates near the threshold, the XZZX code is effectively equivalent to the phase-flip correcting repetition code over $d$ qubits. The large finite size corrections for $d_Z lt eta$ also make threshold extractions, from numerical calculations at moderate code distances, unreliable. We show that calculating thresholds based not only on the total logical failure rate, but also independently on the phase- and bit-flip logical failure rates, gives a more confident estimate. Using this method for the XZZX code with a tensor-network based decoder and code distances up to $dapprox 100$, we find that the thresholds converge to a single value at moderate bias ($eta=30, 100$), at an error rate above the hashing bound.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"48 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142166209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Hadamard gate cannot be replaced by a resource state in universal quantum computation 在通用量子计算中，哈达玛门不能被资源态取代

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-09-11 DOI: 10.22331/q-2024-09-11-1470

Benjamin D. M. Jones, Noah Linden, Paul Skrzypczyk

引用次数: 0

The Fractal-Lattice Hubbard Model 分形晶格哈伯德模型

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-09-11 DOI: 10.22331/q-2024-09-11-1469

Monica Conte, Vinicius Zampronio, Malte Röntgen, Cristiane Morais Smith

{"title":"The Fractal-Lattice Hubbard Model","authors":"Monica Conte, Vinicius Zampronio, Malte Röntgen, Cristiane Morais Smith","doi":"10.22331/q-2024-09-11-1469","DOIUrl":"https://doi.org/10.22331/q-2024-09-11-1469","url":null,"abstract":"Here, we investigate the fractal-lattice Hubbard model using various numerical methods: exact diagonalization, the self-consistent diagonalization of a (mean-field) Hartree-Fock Hamiltonian and state-of-the-art Auxiliary-Field Quantum Monte Carlo. We focus on the Sierpinski triangle with Hausdorff dimension $1.58$ and consider several generations. In the tight-binding limit, we find compact localised states, which are also explained in terms of symmetry and linked to the formation of a ferrimagnetic phase at weak interaction. Simulations at half-filling revealed the persistence of this type of magnetic order for every value of interaction strength and a Mott transition for U/t $sim$ 4.5. In addition, we found a remarkable dependence on the Hausdorff dimension regarding $i)$ the number of compact localised states in different generations, $ii)$ the scaling of the total many-body ground-state energy in the tight-binding limit, and $iii)$ the density of the states at the corners of the lattice for specific values of electronic filling. Moreover, in the presence of an intrinsic spin-orbit coupling, the zero-energy compact localized states become entangled and give rise to inner and outer corner modes.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"49 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142166210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

SQuADDS: A validated design database and simulation workflow for superconducting qubit design SQuADDS：用于超导量子比特设计的经过验证的设计数据库和仿真工作流程

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-09-09 DOI: 10.22331/q-2024-09-09-1465

Sadman Shanto, Andre Kuo, Clark Miyamoto, Haimeng Zhang, Vivek Maurya, Evangelos Vlachos, Malida Hecht, Chung Wa Shum, Eli Levenson-Falk

引用次数: 0

Quantum-enhanced mean value estimation via adaptive measurement 通过自适应测量进行量子增强均值估计

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-09-09 DOI: 10.22331/q-2024-09-09-1463

Kaito Wada, Kazuma Fukuchi, Naoki Yamamoto

{"title":"Quantum-enhanced mean value estimation via adaptive measurement","authors":"Kaito Wada, Kazuma Fukuchi, Naoki Yamamoto","doi":"10.22331/q-2024-09-09-1463","DOIUrl":"https://doi.org/10.22331/q-2024-09-09-1463","url":null,"abstract":"Quantum-enhanced (i.e., higher performance by quantum effects than any classical methods) mean value estimation of observables is a fundamental task in various quantum technologies; in particular, it is an essential subroutine in quantum computing algorithms. Notably, the quantum estimation theory identifies the ultimate precision of such an estimator, which is referred to as the quantum Cramér-Rao (QCR) lower bound or equivalently the inverse of the quantum Fisher information. Because the estimation precision directly determines the performance of those quantum technological systems, it is highly demanded to develop a generic and practically implementable estimation method that achieves the QCR bound. Under imperfect conditions, however, such an ultimate and implementable estimator for quantum mean values has not been developed. In this paper, we propose a quantum-enhanced mean value estimation method in a depolarizing noisy environment that asymptotically achieves the QCR bound in the limit of a large number of qubits. To approach the QCR bound in a practical setting, the method adaptively optimizes the amplitude amplification and a specific measurement that can be implemented without any knowledge of state preparation. We provide a rigorous analysis for the statistical properties of the proposed adaptive estimator such as consistency and asymptotic normality. Furthermore, several numerical simulations are provided to demonstrate the effectiveness of the method, particularly showing that the estimator needs only a modest number of measurements to almost saturate the QCR bound.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"48 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

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