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quantum state and process tomography via adaptive measurements

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Science China(Physics,Mechanics & Astronomy) 2016年第10期59卷 25-32页

作者： HengYan Wang WenQiang Zheng NengKun Yu KeRen Li DaWei Lu Tao Xin Carson Li ZhengFeng Ji David Kribs Bei Zeng XinHua Peng JiangFeng Du Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics University of Science and Technology of ChinaHefei 230026China Department of Applied Physics Zhejiang University of TechnologyHangzhou 310023China Institute for Quantum Computing University of WaterlooWaterloo N2L 3G1Canada 4Department of Mathematics&Statistics University of GuelphGuelph N1G 2W1Canada Centre for Quantum Computation&Intelligent Systems Faculty of Engineering and Information TechnologyUniversity of Technology SydneySydney NSW 2007Australia State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics Tsinghua UniversityBeijing 100084China Department of Physics University of GuelphGuelph N1G 2W1Canada State Key Laboratory of Computer Science Institute of SoftwareChinese Academy of SciencesBeijing 100190China Canadian Institute for Advanced Research Toronto M5G 1Z8Canada

We investigate quantum state tomography(QST) for pure states and quantum process tomography(QPT) for unitary channels via adaptive measurements. For a quantum system with a d-dimensional Hilbert space, we first propose an adaptive protocol where only 2d. 1 measurement outcomes are used to accomplish the QST for all pure states. This idea is then extended to study QPT for unitary channels, where an adaptive unitary process tomography(AUPT) protocol of d2+d.1measurement outcomes is constructed for any unitary channel. We experimentally implement the AUPT protocol in a 2-qubit nuclear magnetic resonance system. We examine the performance of the AUPT protocol when applied to Hadamard gate, T gate(/8 phase gate), and controlled-NOT gate,respectively, as these gates form the universal gate set for quantum information processing purpose. As a comparison, standard QPT is also implemented for each gate. Our experimental results show that the AUPT protocol that reconstructing unitary channels via adaptive measurements significantly reduce the number of experiments required by standard QPT without considerable loss of fidelity.

关键词： quantum tomography state reconstruction nuclear magnetic resonance

quantum insertion-deletion channels

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arXiv 2019年

作者： Leahy, Janet Touchette, Dave Yao, Penghui University of Calgary Institute for Quantum Computing Department of Combinatorics and Optimization University of Waterloo Perimeter Institute for Theoretical Physics State Key Laboratory for Novel Software Technology Nanjing University Nanjing210023 China

We introduce a model of quantum insertion-deletion (insdel) channels. Insdel channels are meant to represent, for example, synchronization errors arising in data transmission. In the classical setting, they represent a strict generalization of the better-understood corruption error channels, and until recently, had mostly resisted effort toward a similar understanding as their corruption counterparts. They have received considerable attention in recent years. Very recently, Haeupler and Shahrasbi developed a framework, using what they call synchronisation strings, that allows one to turn insdel-type errors into corruption-type errors. These can then be handled by the use of standard error-correcting codes. We show that their framework can be extended to the quantum setting, providing a way to turn quantum insdel errors into quantum corruption errors, which can be handled with standard quantum error-correcting codes. Copyright © 2019, The Authors. All rights reserved.

关键词： Crime

Distinguishing unitary gates on the IBM quantum processor

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arXiv 2018年

作者： Liu, Shusen Li, Yinan Duan, Runyao School of Data and Computer Science Sun Yat-sen University Guangzhou Guangdong510006 China Centre for Quantum Software and Information Faculty of Engineering and Information Technology University of Technology SydneyNSW2007 Australia Centrum Wiskunde & Informatica and Research Center for Quantum Software Netherlands Institute for Quantum Computing Baidu Inc. Beijing100193 China

An unknown unitary gates, which is secretly chosen from several known ones, can always be distinguished perfectly. In this paper, we implement such a task on IBM's quantum processor. More precisely, we experimentally demonstrate the discrimination of two qubit unitary gates, the identity gate and the 2/3π-phase shift gate, using two discrimination schemes - the parallel scheme and the sequential scheme. We program these two schemes on the ibmqx4, a 5-qubit superconducting quantum processor via IBM cloud, with the help of the QSI modules [S. Liu et al., arXiv:1710.09500, 2017]. We report that both discrimination schemes achieve success probabilities at least 85%. Copyright © 2018, The Authors. All rights reserved.

关键词： Program processors

quantum phase processing and its applications in estimating phase and entropies

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Physical Review A 2023年第6期108卷 062413-062413页

作者： Youle Wang Lei Zhang Zhan Yu Xin Wang Institute for Quantum Computing Baidu Research Beijing 100193 China School of Software Nanjing University of Information Science and Technology Nanjing 210044 China Thrust of Artificial Intelligence Information Hub Hong Kong University of Science and Technology (Guangzhou) Guangdong 511455 China Centre for Quantum Technologies National University of Singapore 117543 Singapore

quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates and make quantum algorithms fundamentally different from their classical counterparts. Based on this unique principle of quantum computing, we develop an algorithmic toolbox, quantum phase processing, that can directly apply arbitrary trigonometric transformations to eigenphases of a unitary operator. The quantum phase processing circuit is constructed simply, consisting of single-qubit rotations and controlled unitaries, typically using only one ancilla qubit. Besides the capability of phase transformation, quantum phase processing in particular can extract the eigeninformation of quantum systems by simply measuring the ancilla qubit, making it naturally compatible with indirect measurement. quantum phase processing complements another powerful framework known as quantum singular value transformation and leads to more intuitive and efficient quantum algorithms for solving problems that are particularly phase related. As a notable application, we propose a quantum phase estimation algorithm without quantum Fourier transform, which requires the fewest ancilla qubits and matches the best performance so far. We further exploit the power of our method by investigating a plethora of applications in Hamiltonian simulation, entanglement spectroscopy, and quantum entropy estimation, demonstrating improvements or optimality for almost all cases.

关键词： Machine learning quantum algorithms quantum simulation

quantum Self-Attention Neural Networks for Text Classification

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arXiv 2022年

作者： Li, Guangxi Zhao, Xuanqiang Wang, Xin Institute for Quantum Computing Baidu Research Beijing100193 China Centre for Quantum Software and Information University of Technology SydneyNSW2007 Australia QICI Department of Computer Science The University of Hong Kong Hong Kong Nansha China

An emerging direction of quantum computing is to establish meaningful quantum applications in various fields of artificial intelligence, including natural language processing (NLP). Although some efforts based on syntactic analysis have opened the door to research in quantum NLP (QNLP), limitations such as heavy syntactic preprocessing and syntax-dependent network architecture make them impracticable on larger and real-world data sets. In this paper, we propose a new simple network architecture, called the quantum self-attention neural network (QSANN), which can compensate for these limitations. Specifically, we introduce the self-attention mechanism into quantum neural networks and then utilize a Gaussian projected quantum self-attention serving as a sensible quantum version of self-attention. As a result, QSANN is effective and scalable on larger data sets and has the desirable property of being implementable on near-term quantum devices. In particular, our QSANN outperforms the best existing QNLP model based on syntactic analysis as well as a simple classical self-attention neural network in numerical experiments of text classification tasks on public data sets. We further show that our method exhibits robustness to low-level quantum noises and showcases resilience to quantum neural network architectures. © 2022, CC BY.

关键词： Network architecture

Model checking quantum continuous-time Markov chains

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arXiv 2021年

作者： Xu, Ming Mei, Jingyi Guan, Ji Yu, Nengkun Shanghai Key Lab of Trustworthy Computing East China Normal University China State Key Lab of Computer Science Institute of Software Chinese Academy of Sciences China Centre for Quantum Software and Information University of Technology Sydney Australia

Verifying quantum systems has attracted a lot of interests in the last decades. In this paper, we initialised the model checking of quantum continuous-time Markov chain (QCTMC). As a real-time system, we specify the temporal properties on QCTMC by signal temporal logic (STL). To effectively check the atomic propositions in STL, we develop a state-of-art real root isolation algorithm under Schanuel's conjecture;further, we check the general STL formula by interval operations with a bottom-up fashion, whose query complexity turns out to be linear in the size of the input formula by calling the real root isolation algorithm. A running example of an open quantum walk is provided to demonstrate our method. © 2021, CC BY.

关键词： Continuous time systems

Uniqueness of quantum states compatible with given measurement results

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Physical Review A 2013年第1期88卷 012109-012109页

作者： Jianxin Chen Hillary Dawkins Zhengfeng Ji Nathaniel Johnston David Kribs Frederic Shultz Bei Zeng Department of Mathematics & Statistics University of Guelph Guelph Ontario Canada Institute for Quantum Computing University of Waterloo Waterloo Ontario Canada State Key Laboratory of Computer Science Institute of Software Chinese Academy of Sciences Beijing China Mathematics Department Wellesley College Wellesley Massachusetts 02481 USA

We discuss the uniqueness of quantum states compatible with given measurement results for a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same measurement results and (2) no other state, pure or mixed, is compatible with the same measurement results. For case (1), it was known that for a d-dimensional Hilbert space, there exists a set of 4d−5 observables that uniquely determines any pure state. We show that for case (2), 5d−7 observables suffice to uniquely determine any pure state. Thus, there is a gap between the results for (1) and (2), and we give some examples to illustrate this. Unique determination of a pure state by its reduced density matrices (RDMs), a special case of determination by observables, is also discussed. We improve the best-known bound on local dimensions in which almost all pure states are uniquely determined by their RDMs for case (2). We further discuss circumstances where (1) can imply (2). We use convexity of the numerical range of operators to show that when only two observables are measured, (1) always implies (2). More generally, if there is a compact group of symmetries of the state space which has the span of the observables measured as the set of fixed points, then (1) implies (2). We analyze the possible dimensions for the span of such observables. Our results extend naturally to the case of low-rank quantum states.

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Symmetric extension of two-qubit states

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Physical Review A 2014年第3期90卷 032318-032318页

作者： Jianxin Chen Zhengfeng Ji David Kribs Norbert Lütkenhaus Bei Zeng Department of Mathematics and Statistics University of Guelph Guelph Ontario Canada Institute for Quantum Computing University of Waterloo Waterloo Ontario Canada UTS-AMSS Joint Research Laboratory for Quantum Computation and Quantum Information Processing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China State Key Laboratory of Computer Science Institute of Software Chinese Academy of Sciences Beijing China Department of Physics and Astronomy University of Waterloo Waterloo Ontario Canada

A bipartite state ρAB is symmetric extendible if there exists a tripartite state ρABB′ whose AB and AB′ marginal states are both identical to ρAB. Symmetric extendibility of bipartite states is of vital importance in quantum information because of its central role in separability tests, one-way distillation of Einstein-Podolsky-Rosen pairs, one-way distillation of secure keys, quantum marginal problems, and antidegradable quantum channels. We establish a simple analytic characterization for symmetric extendibility of any two-qubit quantum state ρAB; specifically, tr(ρB2)≥tr(ρAB2)−4detρAB. As a special case we solve the bosonic three-representability problem for the two-body reduced density matrix.

关键词： Distillation

quantum advantage with noisy shallow circuits in 3D

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arXiv 2019年

作者： Bravyi, Sergey Gosset, David Konig, Robert Tomamichel, Marco IBM T. J. Watson Research Center Yorktown Heights United States Department of Combinatorics and Optimization Institute for Quantum Computing University of Waterloo Waterloo Canada Institute for Advanced Study and Zentrum Mathematik Technical University of Munich Munich Germany Centre for Quantum Software and Information and School of Software University of Technology Sydney Sydney Australia

Prior work has shown that there exists a relation problem which can be solved with certainty by a constant-depth quantum circuit composed of geometrically local gates in two dimensions, but cannot be solved with high probability by any classical constant depth circuit composed of bounded fan-in gates. Here we provide two extensions of this result. Firstly, we show that a separation in computational power persists even when the constant-depth quantum circuit is restricted to geometrically local gates in one dimension. The corresponding quantum algorithm is the simplest we know of which achieves a quantum advantage of this type. It may also be more practical for future implementations. Our second, main result, is that a separation persists even if the shallow quantum circuit is corrupted by noise. We construct a relation problem which can be solved with near certainty using a noisy constant-depth quantum circuit composed of geometrically local gates in three dimensions, provided the noise rate is below a certain constant threshold value. On the other hand, the problem cannot be solved with high probability by a noise-free classical circuit of constant depth. A key component of the proof is a quantum error-correcting code which admits constant-depth logical Clifiord gates and single-shot logical state preparation. We show that the surface code meets these criteria. To this end, we provide a protocol for single-shot logical state preparation in the surface code which may be of independent interest. Copyright © 2019, The Authors. All rights reserved.

关键词： quantum theory