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quantum Algorithm for Petz Recovery Channels and Pretty Good Measurements

Physical Review Letters 2022年第22期128卷 220502-220502页

作者： András Gilyén Seth Lloyd Iman Marvian Yihui Quek Mark M. Wilde Institute for Quantum Information and Matter California Institute of Technology Pasadena California 91125 USA Simons Institute for the Theory of Computing Berkeley California 94720 USA Department of Mechanical Engineering and Research Laboratory of Electronics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Department of Physics and Department of Electrical and Computer Engineering Duke University Durham North Carolina 27708 USA Information Systems Laboratory Stanford University Stanford California 94305 USA Hearne Institute for Theoretical Physics Department of Physics and Astronomy and Center for Computation and Technology Louisiana State University Baton Rouge Louisiana 70803 USA Stanford Institute for Theoretical Physics Stanford University Stanford California 94305 USA

The Petz recovery channel plays an important role in quantum information science as an operation that approximately reverses the effect of a quantum channel. The pretty good measurement is a special case of the Petz recovery channel, and it allows for near-optimal state discrimination. A hurdle to the experimental realization of these vaunted theoretical tools is the lack of a systematic and efficient method to implement them. This Letter sets out to rectify this lack: Using the recently developed tools of quantum singular value transformation and oblivious amplitude amplification, we provide a quantum algorithm to implement the Petz recovery channel when given the ability to perform the channel that one wishes to reverse. Moreover, we prove that, in some sense, our quantum algorithm’s usage of the channel implementation cannot be improved by more than a quadratic factor. Our quantum algorithm also provides a procedure to perform pretty good measurements when given multiple copies of the states that one is trying to distinguish.

关键词： quantum algorithms quantum channels quantum error correction

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A Hierarchy for Replica quantum Advantage

arXiv

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arXiv 2021年

作者： Chen, Sitan Cotler, Jordan Huang, Hsin-Yuan Li, Jerry Department of Electrical Engineering and Computer Sciences University of California Berkeley BerkeleyCA United States Simons Institute for the Theory of Computing BerkeleyCA United States Society of Fellows Harvard University CambridgeMA United States Black Hole Initiative Harvard University CambridgeMA United States Institute for Quantum Information and Matter Caltech PasadenaCA United States Department of Computing and Mathematical Sciences Caltech PasadenaCA United States Microsoft Research RedmondWA United States

We prove that given the ability to make entangled measurements on at most k replicas of an n-qubit state ρ simultaneously, there is a property of ρ which requires at least order 2n measurements to learn. However, the same property only requires one measurement to learn if we can make an entangled measurement over a number of replicas polynomial in k, n. Because the above holds for each positive integer k, we obtain a hierarchy of tasks necessitating progressively more replicas to be performed efficiently. We introduce a powerful proof technique to establish our results, and also use this to provide new bounds for testing the mixedness of a quantum state. Copyright © 2021, The Authors. All rights reserved.

关键词： quantum entanglement

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Testing integrability with a single bit of quantum information

引用

Physical Review A 2003年第2期68卷 022302-022302页

作者： David Poulin Raymond Laflamme G. J. Milburn Juan Pablo Paz Perimeter Institute for Theoretical Physics 35 King Street N. Waterloo Ontario Canada N2J 2W9 Institute for Quantum Computing University of Waterloo Waterloo Ontario Canada N2L 3G1 Centre for Quantum Computer Technology School of Physical Science The University of Queensland Queensland 4072 Australia Departamento de Física “J.J. Giambiagi ” FCEN UBA Pabell on 1 Ciudad Universitaria 1428 Buenos Aires Argentina Theory Division MS B213 Los Alamos National Laboratory Los Alamos New Mexico 87545 USA

We show that deterministic quantum computing with a single bit can determine whether the classical limit of a quantum system is chaotic or integrable using O(N) physical resources, where N is the dimension of the Hilbert space of the system under study. This is a square-root improvement over all known classical procedures. Our study relies strictly on the random matrix conjecture. We also present numerical results for the nonlinear kicked top.

关键词： quantum theory

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Entanglement area law for one-dimensional gauge theories and bosonic systems

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Physical Review A 2023年第4期108卷 042422-042422页

作者： Nilin Abrahamsen Yu Tong Ning Bao Yuan Su Nathan Wiebe Simons Institute for the Theory of Computing University of California Berkeley Berkeley California 94720-2190 USA Department of Mathematics University of California Berkeley Berkeley California 94720 USA Computational Science Initiative Brookhaven National Laboratory Upton New York 11973 USA Google Quantum AI Venice California 90291 USA Department of Computer Science University of Toronto Toronto Canada M5S 3E1 Pacific Northwest National Laboratory Richland Washington 99354 USA

We prove an entanglement area law for a class of one-dimensional quantum systems involving infinite-dimensional local Hilbert spaces. This class of quantum systems includes bosonic models and lattice gauge theories in one spatial dimension. Our proof relies on results concerning the robustness of the ground state and spectral gap to the truncation of Hilbert space, applied within the approximate-ground-state projector (AGSP) framework. Our result provides theoretical justification for using tensor networks to study the ground-state properties of quantum systems with infinite local degrees of freedom.

关键词： quantum entanglement

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Experimental Simulation of Loop quantum Gravity on a Photonic Chip

Experimental Simulation of Loop Quantum Gravity on a Photoni...

引用

quantum 2.0, quantum 2024 in quantum 2.0 Conference and Exhibition

作者： Anguita, Malaquias Correa van der Meer, Reinier Huang, Zichang Qu, Dongxue Hooijschuur, Peter Liu, Hongguang Han, Muxin Renema, Jelmer J. Cohen, Lior MESA+ Institute for Nanotechnology University of Twente P.O.box 217 Enschede7500 AE Netherlands State Key Laboratory of Surface Physics Department of Physics Center for Field Theory and Particle Physics Institute for Nanoelectronic devices and Quantum computing Fudan University Shanghai200433 China Department of Physics Florida Atlantic University 777 Glades Road Boca RatonFL33431 United States Department Physik Institut für Quantengravitation Theoretische Physik III Friedrich-Alexander Universität Erlangen-Nürnberg Staudtstr. 7/B2 Erlangen91058 Germany Department of Electrical Computer and Energy Engineering University of Colorado Boulder BoulderCO80309 United States

We experimentally simulate a basic transition amplitude of Loop quantum Gravity on an integrated photonic chip, and show that this amplitude falls within 4% error from the theoretical prediction. © 2024 The Autho... 详细信息

ISBN: (纸本)9781557525185

关键词： Photonic integrated circuits

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Linear combination of Hamiltonian simulation for nonunitary dynamics with optimal state preparation cost

arXiv

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arXiv 2023年

作者： An, Dong Liu, Jin-Peng Lin, Lin Joint Center for Quantum Information and Computer Science University of Maryland MD20742 United States Department of Mathematics University of California BerkeleyCA94720 United States Simons Institute for the Theory of Computing University of California BerkeleyCA94720 United States Center for Theoretical Physics Massachusetts Institute of Technology CambridgeMA02139 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Challenge Institute for Quantum Computation University of California BerkeleyCA94720 United States

We propose a simple method for simulating a general class of non-unitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem, or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving non-unitary processes, such as the quantum singular value transformation. The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters. Copyright © 2023, The Authors. All rights reserved.

关键词： Hamiltonians

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Laser Seeding Attack In quantum Key Distribution

arXiv

引用

arXiv 2019年

作者： Huang, Anqi Navarrete, Álvaro Shi-Hai, Sun Chaiwongkhot, Poompong Curty, Marcos Makarov, Vadim Institute for Quantum Information & State Key Laboratory of High Performance Computing College of Computer National University of Defense Technology Changsha410073 China Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada EI Telecomunicación Department of Signal Theory and Communications University of Vigo VigoE-36310 Spain School of Physics and Astronomy Sun Yat-Sen University Zhuhai519082 China Department of Physics and Astronomy University of Waterloo WaterlooONN2L 3G1 Canada Russian Quantum Center Skolkovo Moscow121205 Russia Shanghai Branch National Laboratory for Physical Sciences at Microscale and CAS Center for Excellence in Quantum Information University of Science and Technology of China Shanghai201315 China NTI Center for Quantum Communications National University of Science and Technology MISiS Moscow119049 Russia

quantum key distribution (QKD) based on the laws of quantum physics allows the secure distribution of secret keys over an insecure channel. Unfortunately, imperfect implementations of QKD compromise its information-theoretical security. Measurement-device-independent quantum key distribution (MDI-QKD) is a promising approach to remove all side channels from the measurement unit, which is regarded as the "Achilles’ heel" of QKD. An essential assumption in MDI-QKD is however that the sources are trusted. Here we experimentally demonstrate that a practical source based on a semiconductor laser diode is vulnerable to a laser seeding attack, in which light injected from the communication line into the laser results in an increase of the intensities of the prepared states. The unnoticed increase of intensity may compromise the security of QKD, as we show theoretically for the prepare-and-measure decoy-state BB84 and MDI-QKD protocols. Our theoretical security analysis is general and can be applied to any vulnerability that increases the intensity of the emitted pulses. Moreover, a laser seeding attack might be launched as well against decoy-state based quantum cryptographic protocols beyond QKD. Copyright © 2019, The Authors. All rights reserved.

关键词： quantum cryptography

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Purely quantum algorithms for calculating determinant and inverse of matrix and solving linear algebraic systems

arXiv

引用

arXiv 2024年

作者： Zenchuk, Alexander I. Bochkin, Georgii A. Qi, Wentao Kumar, Asutosh Wu, Junde Federal Research Center of Problems of Chemical Physics and Medicinal Chemistry RAS Moscow reg. Chernogolovka142432 Russia Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-sen University Guangzhou510006 China Department of Physics Gaya College Gaya Rampur823001 India P.G. Department of Physics Magadh University Bodh Gaya824234 India School of Mathematical Sciences Zhejiang University Hangzhou310027 China

We propose quantum algorithms that are fundamentally quantum in nature for the computation of the determinant and inverse of an (N−1)×(N−1) matrix, with a computational depth of O(N2 log N). This approach is a straightforward modification of the existing algorithm for determining the determinant of an N × N matrix, which operates with a depth of O(N log2 N). The core concept involves encoding each row of the matrix into a pure state of a quantum system. In addition, we use the representation of the elements of the inverse matrix in terms of algebraic complements. This algorithm, in conjunction with the matrix multiplication algorithm discussed in the appendix, facilitates solving systems of linear algebraic equations with a depth of O(N log2 N). The measurement of the ancilla state yielding an output of 1 occurs with a probability of approximately 2−O(N log N), and eliminates the extraneous data generated during the computation. We provide suitable circuit designs for all three algorithms, each estimated to require O(N log N) in terms of space, specifically the number of qubits utilized in the circuit. © 2024, CC BY-NC-ND.

关键词： Inverse problems

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Security boundaries of an optical power limiter for protecting quantum key distribution systems

arXiv

引用

arXiv 2023年

作者： Peng, Qingquan Gao, Binwu Zaitsev, Konstantin Wang, Dongyang Ding, Jiangfang Liu, Yingwen Liao, Qin Guo, Ying Huang, Anqi Wu, Junjie Institute for Quantum Information State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Changsha410073 China School of Automation Central South University Changsha410083 China China Greatwall Research Institute China Greatwall Technology Group Co. Ltd. Shenzhen518057 China Russian Quantum Center Skolkovo Moscow121205 Russia NTI Center for Quantum Communications National University of Science and Technology MISiS Moscow119049 Russia Vigo Quantum Communication Center University of Vigo Vigo Spain Escuela de Ingeniería de Telecomunicación Department of Signal Theory and Communications University of Vigo Vigo Spain atlanTTic Research Center University of Vigo Vigo Spain College of Computer Science and Electronic Engineering Hunan University Changsha410082 China School of Computer Science Beijing University of Posts and Telecommunications Beijing100876 China

Unauthorized light injection has always been a vital threat to the practical security of a quantum key distribution (QKD) system. An optical power limiter (OPL) based on the thermo-optical defocusing effect has been proposed and implemented, limiting the injected hacking light. As a hardware countermeasure, the performance of the OPL under various light-injection attacks shall be tested to clarify the security boundary before being widely deployed. To investigate the OPL’s security boundary in quantum cryptography, we comprehensively test and analyse the behavior of OPL under continuous-wave (c.w.) light-injection attacks and pulse illumination attacks with pulses’ repetition rate at 0.5-Hz, 40-MHz, and 1-GHz. The testing results illuminate the security boundary of the OPL, which allows one to properly employ the OPL in the use cases. The methodology of testing and analysis proposed here is applicable to other power-limitation components in a QKD system. Copyright © 2023, The Authors. All rights reserved.

关键词： Pulse repetition rate

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Auxiliary-free replica shadow estimation

arXiv

引用

arXiv 2024年

作者： Liu, Qing Li, Zihao Yuan, Xiao Zhu, Huangjun Zhou, You Key Laboratory for Information Science of Electromagnetic Waves Ministry of Education Fudan University Shanghai200433 China State Key Laboratory of Surface Physics Department of Physics Fudan University Shanghai200433 China Institute for Nanoelectronic Devices and Quantum Computing Fudan University Shanghai200433 China Center for Field Theory and Particle Physics Fudan University Shanghai200433 China Center on Frontiers of Computing Studies Peking University Beijing100871 China School of Computer Science Peking University Beijing100871 China

Efficiently measuring nonlinear properties, like the entanglement spectrum, is a significant yet challenging task from quantum information processing to many-body physics. Current methodologies often suffer from an exponential scaling of the sampling cost or require auxiliary qubits and deep quantum circuits. To address these limitations, we propose an efficient auxiliary-free replica shadow (AFRS) framework, which leverages the power of the joint entangling operation on a few input replicas while integrating the mindset of shadow estimation. We rigorously prove that AFRS can offer exponential improvements in estimation accuracy compared with the conventional shadow method, and facilitate the simultaneous estimation of various nonlinear properties, unlike the destructive swap test. Additionally, we introduce an advanced local-AFRS variant tailored to estimating local observables with even constant-depth local quantum circuits, which significantly simplifies the experimental realization compared with the general swap test. Our work paves the way for the application of AFRS on near-term quantum hardware, opening new avenues for efficient and practical quantum measurements. © 2024, CC BY.

关键词： quantum entanglement

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