Pub Date : 2026-01-15DOI: 10.1038/s41534-025-01177-9
Su Direkci, Ran Finkelstein, Manuel Endres, Tuvia Gefen
Optimal phase estimation protocols require complex state preparation and readout schemes, generally unavailable or unscalable in many quantum platforms. We develop a scheme that achieves near-optimal precision up to a constant overhead for Bayesian phase estimation, using simple digital quantum circuits with depths scaling logarithmically with the number of qubits. This is done by approximating the optimal initial states with products of Greenberger-Horne-Zeilinger states for Gaussian prior phase distributions with arbitrary widths. We study various protocols that employ this class of states with different levels of measurement and post-processing complexities, and obtain improvement compared to previously proposed schemes. We then use our scheme to address phase slip errors and laser noise, which impose a major limitation in Bayesian phase estimation and atomic clocks. Based on our scheme, we develop an efficient protocol to suppress this noise that outperforms existing methods.
{"title":"Heisenberg-limited Bayesian phase estimation with low-depth digital quantum circuits","authors":"Su Direkci, Ran Finkelstein, Manuel Endres, Tuvia Gefen","doi":"10.1038/s41534-025-01177-9","DOIUrl":"https://doi.org/10.1038/s41534-025-01177-9","url":null,"abstract":"Optimal phase estimation protocols require complex state preparation and readout schemes, generally unavailable or unscalable in many quantum platforms. We develop a scheme that achieves near-optimal precision up to a constant overhead for Bayesian phase estimation, using simple digital quantum circuits with depths scaling logarithmically with the number of qubits. This is done by approximating the optimal initial states with products of Greenberger-Horne-Zeilinger states for Gaussian prior phase distributions with arbitrary widths. We study various protocols that employ this class of states with different levels of measurement and post-processing complexities, and obtain improvement compared to previously proposed schemes. We then use our scheme to address phase slip errors and laser noise, which impose a major limitation in Bayesian phase estimation and atomic clocks. Based on our scheme, we develop an efficient protocol to suppress this noise that outperforms existing methods.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"21 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145968741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
Pub Date : 2026-01-15DOI: 10.1038/s41534-026-01181-7
Maxwell Gold, Jianlong Lin, Eric Chitambar, Elizabeth A. Goldschmidt
Quantum emitter-based schemes for the generation of photonic graph states offer a promising, resource-efficient methodology for realizing distributed quantum computation and communication protocols on near-term hardware. We present a heralded scheme for making photonic graph states that is compatible with the typically poor photon collection from state-of-the-art coherent quantum emitters. We demonstrate that the construction time for large graph states can be polynomial in the photon collection efficiency, as compared to the exponential scaling of current emitter-based schemes, which assume deterministic photon collection. The additional overhead here consists of an extra spin qubit plus one additional spin-spin entangling gate per photon added to the graph. While the proposed scheme requires both non-demolition measurement and efficient storage of photons in order to generate graph states for arbitrary applications, we show that many useful tasks, including measurement-based quantum computation, can be implemented without these requirements. As a use case of our scheme, we construct a protocol for secure two-party computation that can be implemented efficiently on current hardware. Estimates of the fidelity to produce graph states used in the computation are given assuming current and near-term fidelities for highly coherent quantum emitters.
{"title":"Heralded photonic graph states with inefficient quantum emitters","authors":"Maxwell Gold, Jianlong Lin, Eric Chitambar, Elizabeth A. Goldschmidt","doi":"10.1038/s41534-026-01181-7","DOIUrl":"https://doi.org/10.1038/s41534-026-01181-7","url":null,"abstract":"Quantum emitter-based schemes for the generation of photonic graph states offer a promising, resource-efficient methodology for realizing distributed quantum computation and communication protocols on near-term hardware. We present a heralded scheme for making photonic graph states that is compatible with the typically poor photon collection from state-of-the-art coherent quantum emitters. We demonstrate that the construction time for large graph states can be polynomial in the photon collection efficiency, as compared to the exponential scaling of current emitter-based schemes, which assume deterministic photon collection. The additional overhead here consists of an extra spin qubit plus one additional spin-spin entangling gate per photon added to the graph. While the proposed scheme requires both non-demolition measurement and efficient storage of photons in order to generate graph states for arbitrary applications, we show that many useful tasks, including measurement-based quantum computation, can be implemented without these requirements. As a use case of our scheme, we construct a protocol for secure two-party computation that can be implemented efficiently on current hardware. Estimates of the fidelity to produce graph states used in the computation are given assuming current and near-term fidelities for highly coherent quantum emitters.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"30 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145968743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
Despite the monogamous nature of nonlocal correlations, in a Bell test involving three parties A, B, and C, the nonlocality in two bipartite subsystems (e.g., AB and BC) may force the remaining bipartite subsystem (e.g., AC) to exhibit nonlocality. Although this intriguing effect of nonlocality transitivity has been identified in the non-quantum non-signaling world since 2011, whether such transitivity could manifest within quantum theory has remained unresolved. Here, we answer this open problem affirmatively—both analytically and numerically—at the level of quantum states, thereby showing that a quantum-realizable notion of nonlocality transitivity exists. In our analytic construction, we prove and use the fact that copies of the W-state marginals uniquely determine the global compatible state, thus establishing another instance when the parts determine the whole. Moreover, we present a simple method to construct quantum states and correlations that are nonlocal in all their non-unipartite marginals. We also discuss the implications of our results in (semi-) device-independent cryptographic and certification tasks.
{"title":"Nonlocality of quantum states can be transitive","authors":"Kai-Siang Chen, Gelo Noel M. Tabia, Chung-Yun Hsieh, Yu-Chun Yin, Yeong-Cherng Liang","doi":"10.1038/s41534-025-01173-z","DOIUrl":"https://doi.org/10.1038/s41534-025-01173-z","url":null,"abstract":"Despite the monogamous nature of nonlocal correlations, in a Bell test involving three parties A, B, and C, the nonlocality in two bipartite subsystems (e.g., AB and BC) may force the remaining bipartite subsystem (e.g., AC) to exhibit nonlocality. Although this intriguing effect of nonlocality transitivity has been identified in the non-quantum non-signaling world since 2011, whether such transitivity could manifest within quantum theory has remained unresolved. Here, we answer this open problem affirmatively—both analytically and numerically—at the level of quantum states, thereby showing that a quantum-realizable notion of nonlocality transitivity exists. In our analytic construction, we prove and use the fact that copies of the W-state marginals uniquely determine the global compatible state, thus establishing another instance when the parts determine the whole. Moreover, we present a simple method to construct quantum states and correlations that are nonlocal in all their non-unipartite marginals. We also discuss the implications of our results in (semi-) device-independent cryptographic and certification tasks.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"6 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145947683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
Pub Date : 2026-01-10DOI: 10.1038/s41534-025-01162-2
Riccardo Molteni, Casper Gyurik, Vedran Dunjko
Quantum computers are believed to bring computational advantages in simulating quantum many-body systems. However, recent works have shown that classical machine learning algorithms are able to predict numerous properties of quantum systems with classical data. Despite examples of learning tasks with provable quantum advantages being proposed, they all involve cryptographic functions and do not represent any physical scenarios encountered in laboratory settings. In this paper, we prove quantum advantages for the physically relevant task of learning quantum observables from classical (measured-out) data. We consider two types of observables: first, we prove a learning advantage for linear combinations of Pauli strings, then we extend our results to a broader case of unitarily parametrized observables. For each case, we delineate sharp boundaries separating physically relevant tasks that admit efficient classical learning from those for which a quantum computer remains necessary for data analysis. Unlike previous works, our classical hardness results rely only on the weaker assumption that $$BQP$$BQP hard processes cannot be simulated by polynomial-size classical circuits, and we also provide a nontrivial quantum learning algorithm. Our results clarify when quantum resources are useful for learning problems in quantum many-body physics, and suggest practical directions in which quantum learning improvements may emerge.
量子计算机被认为在模拟量子多体系统方面具有计算优势。然而，最近的研究表明，经典的机器学习算法能够用经典数据预测量子系统的许多特性。尽管提出了具有可证明的量子优势的学习任务示例，但它们都涉及加密功能，并且不代表在实验室环境中遇到的任何物理场景。在本文中，我们证明了量子在从经典（测量）数据中学习量子可观测物的物理相关任务中的优势。我们考虑两种类型的可观察对象：首先，我们证明了泡利弦线性组合的学习优势，然后我们将我们的结果扩展到更广泛的单参数化可观察对象的情况。对于每种情况，我们都划定了明确的界限，将物理相关的任务区分开来，这些任务允许有效的经典学习，而量子计算机仍然需要进行数据分析。与以前的工作不同，我们的经典硬度结果仅依赖于一个较弱的假设，即$$BQP$$ B Q P硬过程不能被多项式大小的经典电路模拟，并且我们还提供了一个非平凡的量子学习算法。我们的研究结果阐明了量子资源何时对量子多体物理中的学习问题有用，并提出了量子学习改进可能出现的实际方向。
{"title":"Exponential quantum advantages in learning quantum observables from classical data","authors":"Riccardo Molteni, Casper Gyurik, Vedran Dunjko","doi":"10.1038/s41534-025-01162-2","DOIUrl":"https://doi.org/10.1038/s41534-025-01162-2","url":null,"abstract":"Quantum computers are believed to bring computational advantages in simulating quantum many-body systems. However, recent works have shown that classical machine learning algorithms are able to predict numerous properties of quantum systems with classical data. Despite examples of learning tasks with provable quantum advantages being proposed, they all involve cryptographic functions and do not represent any physical scenarios encountered in laboratory settings. In this paper, we prove quantum advantages for the physically relevant task of learning quantum observables from classical (measured-out) data. We consider two types of observables: first, we prove a learning advantage for linear combinations of Pauli strings, then we extend our results to a broader case of unitarily parametrized observables. For each case, we delineate sharp boundaries separating physically relevant tasks that admit efficient classical learning from those for which a quantum computer remains necessary for data analysis. Unlike previous works, our classical hardness results rely only on the weaker assumption that <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$BQP$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mstyle> <mml:mi>B</mml:mi> <mml:mi>Q</mml:mi> <mml:mi>P</mml:mi> </mml:mstyle> </mml:math> </jats:alternatives> </jats:inline-formula> hard processes cannot be simulated by polynomial-size classical circuits, and we also provide a nontrivial quantum learning algorithm. Our results clarify when quantum resources are useful for learning problems in quantum many-body physics, and suggest practical directions in which quantum learning improvements may emerge.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"85 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145938230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
Pub Date : 2026-01-08DOI: 10.1038/s41534-025-01176-w
Xiao-Xi Yao, Yusuf Turek
We introduce a protocol for generating non-Gaussian (nG) states via postselected weak measurement. The scheme involves injecting an arbitrary quantum state and a single photon into the signal and idler ports of an interferometer with a third-order nonlinear medium. An nG state is conditionally produced at the signal output, heralded by single-photon detection in an idler output channel. The protocol exploits a weak cross-Kerr interaction, with effective single-photon nonlinearity enhanced by weak-value amplification. By tuning the weak value of the idler photon number operator within experimentally feasible parameters, diverse nG states can be generated with high fidelity. Specific examples include photon-added coherent states, displaced and squeezed number states, and intermediate nG states from coherent and squeezed vacuum inputs. Furthermore, the protocol enables enhancement of non-Gaussianity and enlargement of Schrödinger cat (SC) states when ideal SC states are used as input. Our results provide an alternative route for conditional generation of tunable nG states, with potential applications in quantum information processing and state engineering.
{"title":"Non-Gaussian state preparation and enhancement using weak-value amplification","authors":"Xiao-Xi Yao, Yusuf Turek","doi":"10.1038/s41534-025-01176-w","DOIUrl":"https://doi.org/10.1038/s41534-025-01176-w","url":null,"abstract":"We introduce a protocol for generating non-Gaussian (nG) states via postselected weak measurement. The scheme involves injecting an arbitrary quantum state and a single photon into the signal and idler ports of an interferometer with a third-order nonlinear medium. An nG state is conditionally produced at the signal output, heralded by single-photon detection in an idler output channel. The protocol exploits a weak cross-Kerr interaction, with effective single-photon nonlinearity enhanced by weak-value amplification. By tuning the weak value of the idler photon number operator within experimentally feasible parameters, diverse nG states can be generated with high fidelity. Specific examples include photon-added coherent states, displaced and squeezed number states, and intermediate nG states from coherent and squeezed vacuum inputs. Furthermore, the protocol enables enhancement of non-Gaussianity and enlargement of Schrödinger cat (SC) states when ideal SC states are used as input. Our results provide an alternative route for conditional generation of tunable nG states, with potential applications in quantum information processing and state engineering.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"21 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145919918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
Pub Date : 2026-01-07DOI: 10.1038/s41534-025-01170-2
Aaron Miller, Adam Glos, Zoltán Zimborás
Quantum computers hold great promise for efficiently simulating Fermionic systems, benefiting fields like quantum chemistry and materials science. To achieve this, algorithms typically begin by choosing a Fermion-to-qubit mapping to encode the Fermionic problem in the qubits of a quantum computer. In this work, we introduce ‘Treespilation,’ a technique for efficiently mapping Fermionic systems using a large family of favourable tree-based mappings while minimising a generic cost function to reduce quantum simulation overhead. We use this technique to minimise the number of CNOT gates required to simulate approximate chemical groundstate circuits and observe significant reductions, up to 74%, in CNOT counts on full connectivity. For devices with limited qubit connectivity, we observe similar reductions in CNOT counts, often surpassing the full connectivity CNOT count for circuits encoded with the Jordan-Wigner mapping. We observed similar reductions when applied to reducing the Pauli weight of Hubbard model Hamiltonians.
{"title":"Treespilation: architecture- and state-optimised fermion-to-qubit mappings","authors":"Aaron Miller, Adam Glos, Zoltán Zimborás","doi":"10.1038/s41534-025-01170-2","DOIUrl":"https://doi.org/10.1038/s41534-025-01170-2","url":null,"abstract":"Quantum computers hold great promise for efficiently simulating Fermionic systems, benefiting fields like quantum chemistry and materials science. To achieve this, algorithms typically begin by choosing a Fermion-to-qubit mapping to encode the Fermionic problem in the qubits of a quantum computer. In this work, we introduce ‘Treespilation,’ a technique for efficiently mapping Fermionic systems using a large family of favourable tree-based mappings while minimising a generic cost function to reduce quantum simulation overhead. We use this technique to minimise the number of CNOT gates required to simulate approximate chemical groundstate circuits and observe significant reductions, up to 74%, in CNOT counts on full connectivity. For devices with limited qubit connectivity, we observe similar reductions in CNOT counts, often surpassing the full connectivity CNOT count for circuits encoded with the Jordan-Wigner mapping. We observed similar reductions when applied to reducing the Pauli weight of Hubbard model Hamiltonians.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"40 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145908420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
Pub Date : 2026-01-03DOI: 10.1038/s41534-025-01163-1
Donghwa Lee, Bohdan Bilash, Jaehak Lee, Hyang-Tag Lim, Yosep Kim, Seung-Woo Lee, Yong-Su Kim
We demonstrate a two-qubit variational quantum eigensolver (VQE) implementation using two spatially separated single-photon processors connected via a 3 km optical fiber network. Our approach leverages local operations on pre-shared entanglement to evaluate two-qubit Hamiltonians. By incorporating parameterized weak measurement operations within the local operations framework, we enable access to the complete Hilbert space across distributed quantum processors – a capability typically requiring complex non-local operations. Our experimental results show accurate ground state energy estimation for Hamiltonians including H-He+ cation and the Schwinger model, validating both the necessity of weak measurements and high-quality entanglement in distributed quantum computing. This work establishes a promising direction for resource-efficient, scalable quantum network architectures that maintain full computational capabilities through local operations and controlled entanglement manipulation.
{"title":"Distributed photonic variational quantum eigensolver with parameterized weak measurements","authors":"Donghwa Lee, Bohdan Bilash, Jaehak Lee, Hyang-Tag Lim, Yosep Kim, Seung-Woo Lee, Yong-Su Kim","doi":"10.1038/s41534-025-01163-1","DOIUrl":"https://doi.org/10.1038/s41534-025-01163-1","url":null,"abstract":"We demonstrate a two-qubit variational quantum eigensolver (VQE) implementation using two spatially separated single-photon processors connected via a 3 km optical fiber network. Our approach leverages local operations on pre-shared entanglement to evaluate two-qubit Hamiltonians. By incorporating parameterized weak measurement operations within the local operations framework, we enable access to the complete Hilbert space across distributed quantum processors – a capability typically requiring complex non-local operations. Our experimental results show accurate ground state energy estimation for Hamiltonians including H-He+ cation and the Schwinger model, validating both the necessity of weak measurements and high-quality entanglement in distributed quantum computing. This work establishes a promising direction for resource-efficient, scalable quantum network architectures that maintain full computational capabilities through local operations and controlled entanglement manipulation.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"35 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
Pub Date : 2025-12-31DOI: 10.1038/s41534-025-01167-x
Jian-Peng Dou, Feng Lu, Xiao-Wen Shang, Hao Tang, Xian-Min Jin
In a study of amplifying atomic spin waves, we observe a nontrivial phenomenon: The spin wave stored in moving atoms has a capability of absorbing energy from an external light source, and exhibits a regeneration process. We demonstrate that this regeneration significantly enhances the lifetime and retrieval efficiency of the spin wave, while concurrently the noise is effectively suppressed. Our results suggest that the regeneration mechanism holds promise for mitigating the pronounced decoherence typically encountered in spin waves carried by room-temperature media, therefore offering potential applications in the realms of quantum information and precision measurements at ambient conditions.
{"title":"Regeneration of spin wave in moving atoms","authors":"Jian-Peng Dou, Feng Lu, Xiao-Wen Shang, Hao Tang, Xian-Min Jin","doi":"10.1038/s41534-025-01167-x","DOIUrl":"https://doi.org/10.1038/s41534-025-01167-x","url":null,"abstract":"In a study of amplifying atomic spin waves, we observe a nontrivial phenomenon: The spin wave stored in moving atoms has a capability of absorbing energy from an external light source, and exhibits a regeneration process. We demonstrate that this regeneration significantly enhances the lifetime and retrieval efficiency of the spin wave, while concurrently the noise is effectively suppressed. Our results suggest that the regeneration mechanism holds promise for mitigating the pronounced decoherence typically encountered in spin waves carried by room-temperature media, therefore offering potential applications in the realms of quantum information and precision measurements at ambient conditions.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"27 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
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