Pub Date : 2024-12-09DOI: 10.1088/2058-9565/ad985f
Youle Wang and Linyun Cao
Unveiling quantum phase transitions (QPTs) is important for characterising physical systems at low temperatures. However, the detection of these transitions is encumbered by significant challenges, especially in the face of the exponential growth in ground state complexity with system scale. The emergence of quantum machine learning has lately gained traction as a promising method for elucidating the properties of many-body systems, providing a different avenue to study QPT. In this paper, we propose a novel and efficient quantum algorithm for identifying QPT synthesising quantum feature with quantum machine learning. Our approach is anchored in the utilisation of quantum computers to directly encode the kernel matrix into Hilbert spaces, realised by the parallel implementation of the quantum feature map. Specifically, we generate a quantum state encoding the information of ground states of the given quantum systems by employing the parallel quantum feature map. The resultant state preparation circuit is then used to implement a block-encoding of the kernel matrix. Equipped with the associated labels and this encoding, we devise a new quantum support vector machine (QSVM) algorithm, forming the main ingredient of the classifier. The presented method refines the efficiency of the prevailing QSVM algorithm for processing quantum and classical data. We demonstrate the effectiveness of our quantum classifier in predicting QPT within the transverse-field Ising model. The findings affirm the efficacy of quantum machine learning in recognising QPT in many-body systems and offer insights into the design of quantum machine learning algorithms.
{"title":"Quantum phase transition detection via quantum support vector machine","authors":"Youle Wang and Linyun Cao","doi":"10.1088/2058-9565/ad985f","DOIUrl":"https://doi.org/10.1088/2058-9565/ad985f","url":null,"abstract":"Unveiling quantum phase transitions (QPTs) is important for characterising physical systems at low temperatures. However, the detection of these transitions is encumbered by significant challenges, especially in the face of the exponential growth in ground state complexity with system scale. The emergence of quantum machine learning has lately gained traction as a promising method for elucidating the properties of many-body systems, providing a different avenue to study QPT. In this paper, we propose a novel and efficient quantum algorithm for identifying QPT synthesising quantum feature with quantum machine learning. Our approach is anchored in the utilisation of quantum computers to directly encode the kernel matrix into Hilbert spaces, realised by the parallel implementation of the quantum feature map. Specifically, we generate a quantum state encoding the information of ground states of the given quantum systems by employing the parallel quantum feature map. The resultant state preparation circuit is then used to implement a block-encoding of the kernel matrix. Equipped with the associated labels and this encoding, we devise a new quantum support vector machine (QSVM) algorithm, forming the main ingredient of the classifier. The presented method refines the efficiency of the prevailing QSVM algorithm for processing quantum and classical data. We demonstrate the effectiveness of our quantum classifier in predicting QPT within the transverse-field Ising model. The findings affirm the efficacy of quantum machine learning in recognising QPT in many-body systems and offer insights into the design of quantum machine learning algorithms.","PeriodicalId":20821,"journal":{"name":"Quantum Science and Technology","volume":"213 1","pages":""},"PeriodicalIF":6.7,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142793889","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}
Pub Date : 2024-12-05DOI: 10.1088/2058-9565/ad904f
Sören Arlt, Carlos Ruiz-Gonzalez and Mario Krenn
Linear quantum optics is advancing quickly, driven by sources of correlated photon pairs. Multi-photon sources beyond pairs would be a powerful resource, but are a difficult technology to implement. We have discovered a way in which we can combine multiple pair-sources to act analogous to sources of four, six or even eight correlated photons for the creation of highly entangled quantum states and other quantum information tasks. The existence of such setups is interesting from a conceptual perspective, but also offers a useful abstraction for the construction of more complicated photonic experiments, ranging from state generation to complex quantum networks. We show that even just going from probabilistic two-photon sources to effective four-photon sources allows conceptually new experiments for which no other building principles were known before. The setups which inspired the formulation of these abstract building blocks were discovered by a computer algorithm that can efficiently design quantum optics experiments. Our manuscript demonstrates how artificial intelligence can act as a source of inspiration for the scientific discoveries of new ideas and concepts in physics.
{"title":"Emulating multiparticle emitters with pair-sources: digital discovery of a quantum optics building block","authors":"Sören Arlt, Carlos Ruiz-Gonzalez and Mario Krenn","doi":"10.1088/2058-9565/ad904f","DOIUrl":"https://doi.org/10.1088/2058-9565/ad904f","url":null,"abstract":"Linear quantum optics is advancing quickly, driven by sources of correlated photon pairs. Multi-photon sources beyond pairs would be a powerful resource, but are a difficult technology to implement. We have discovered a way in which we can combine multiple pair-sources to act analogous to sources of four, six or even eight correlated photons for the creation of highly entangled quantum states and other quantum information tasks. The existence of such setups is interesting from a conceptual perspective, but also offers a useful abstraction for the construction of more complicated photonic experiments, ranging from state generation to complex quantum networks. We show that even just going from probabilistic two-photon sources to effective four-photon sources allows conceptually new experiments for which no other building principles were known before. The setups which inspired the formulation of these abstract building blocks were discovered by a computer algorithm that can efficiently design quantum optics experiments. Our manuscript demonstrates how artificial intelligence can act as a source of inspiration for the scientific discoveries of new ideas and concepts in physics.","PeriodicalId":20821,"journal":{"name":"Quantum Science and Technology","volume":"47 1","pages":""},"PeriodicalIF":6.7,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142776899","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}
Pub Date : 2024-12-02DOI: 10.1088/2058-9565/ad9499
Francesco Albarelli, Bassano Vacchini and Andrea Smirne
The treatment of quantum thermodynamic systems beyond weak coupling is of increasing relevance, yet extremely challenging. The evaluation of thermodynamic quantities in strong-coupling regimes requires a nonperturbative knowledge of the bath dynamics, which in turn relies on heavy numerical simulations. To tame these difficulties, considering thermal bosonic baths linearly coupled to the open system, we derive expressions for heat, work, and average system-bath interaction energy that only involve the autocorrelation function of the bath and two-time expectation values of system operators. We then exploit the pseudomode approach, which replaces the physical continuous bosonic bath with a small finite number of damped, possibly interacting, modes, to numerically evaluate these relevant thermodynamic quantities. We show in particular that this method allows for an efficient numerical evaluation of thermodynamic quantities in terms of one-time expectation values of the open system and the pseudomodes. We apply this framework to the investigation of two paradigmatic situations. In the first instance, we study the entropy production for a two-level system (TLS) coupled to an ohmic bath, simulated via interacting pseudomodes, allowing for the presence of time-dependent driving. Secondly, we consider a quantum thermal machine composed of a TLS interacting with two thermal baths at different temperatures, showing that an appropriate sinusoidal modulation of the coupling with the cold bath only is enough to obtain work extraction.
{"title":"Pseudomode treatment of strong-coupling quantum thermodynamics","authors":"Francesco Albarelli, Bassano Vacchini and Andrea Smirne","doi":"10.1088/2058-9565/ad9499","DOIUrl":"https://doi.org/10.1088/2058-9565/ad9499","url":null,"abstract":"The treatment of quantum thermodynamic systems beyond weak coupling is of increasing relevance, yet extremely challenging. The evaluation of thermodynamic quantities in strong-coupling regimes requires a nonperturbative knowledge of the bath dynamics, which in turn relies on heavy numerical simulations. To tame these difficulties, considering thermal bosonic baths linearly coupled to the open system, we derive expressions for heat, work, and average system-bath interaction energy that only involve the autocorrelation function of the bath and two-time expectation values of system operators. We then exploit the pseudomode approach, which replaces the physical continuous bosonic bath with a small finite number of damped, possibly interacting, modes, to numerically evaluate these relevant thermodynamic quantities. We show in particular that this method allows for an efficient numerical evaluation of thermodynamic quantities in terms of one-time expectation values of the open system and the pseudomodes. We apply this framework to the investigation of two paradigmatic situations. In the first instance, we study the entropy production for a two-level system (TLS) coupled to an ohmic bath, simulated via interacting pseudomodes, allowing for the presence of time-dependent driving. Secondly, we consider a quantum thermal machine composed of a TLS interacting with two thermal baths at different temperatures, showing that an appropriate sinusoidal modulation of the coupling with the cold bath only is enough to obtain work extraction.","PeriodicalId":20821,"journal":{"name":"Quantum Science and Technology","volume":"26 1","pages":""},"PeriodicalIF":6.7,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142758210","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}
Pub Date : 2024-11-29DOI: 10.1088/2058-9565/ad8fc9
L A Williamson, F Cerisola, J Anders and Matthew J Davis
We show how work can be extracted from number-state coherence in a two-mode Bose–Einstein condensate. With careful tuning of parameters, a sequence of thermodynamically reversible steps transforms a Glauber coherent state into a thermal state with the same energy probability distribution. The work extracted during this process arises entirely from the removal of quantum coherence. More generally, we characterise quantum (from coherence) and classical (remaining) contributions to work output, and find that in this system the quantum contribution can be dominant over a broad range of parameters. The proportion of quantum work output can be further enhanced by squeezing the initial state. Due to the many-body nature of the system, the work from coherence can equivalently be understood as work from entanglement.
{"title":"Extracting work from coherence in a two-mode Bose–Einstein condensate","authors":"L A Williamson, F Cerisola, J Anders and Matthew J Davis","doi":"10.1088/2058-9565/ad8fc9","DOIUrl":"https://doi.org/10.1088/2058-9565/ad8fc9","url":null,"abstract":"We show how work can be extracted from number-state coherence in a two-mode Bose–Einstein condensate. With careful tuning of parameters, a sequence of thermodynamically reversible steps transforms a Glauber coherent state into a thermal state with the same energy probability distribution. The work extracted during this process arises entirely from the removal of quantum coherence. More generally, we characterise quantum (from coherence) and classical (remaining) contributions to work output, and find that in this system the quantum contribution can be dominant over a broad range of parameters. The proportion of quantum work output can be further enhanced by squeezing the initial state. Due to the many-body nature of the system, the work from coherence can equivalently be understood as work from entanglement.","PeriodicalId":20821,"journal":{"name":"Quantum Science and Technology","volume":"37 1","pages":""},"PeriodicalIF":6.7,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142753028","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}
Pub Date : 2024-11-28DOI: 10.1088/2058-9565/ad93fb
Jorge Chávez-Carlos, Miguel A Prado Reynoso, Rodrigo G Cortiñas, Ignacio García-Mata, Victor S Batista, Francisco Pérez-Bernal, Diego A Wisniacki and Lea F Santos
Kerr parametric oscillators are potential building blocks for fault-tolerant quantum computers. They can stabilize Kerr-cat qubits, which offer advantages toward the encoding and manipulation of error-protected quantum information. The recent realization of Kerr-cat qubits made use of the nonlinearity of transmon superconducting circuits and a squeezing drive. Increasing nonlinearities can enable faster gate times, but, as shown here, can also induce chaos and melt the qubit away. We determine the region of validity of the Kerr-cat qubit and discuss how its disintegration could be experimentally detected. The danger zone for parametric quantum computation is also a potential playground for investigating quantum chaos with driven superconducting circuits.
{"title":"Driving superconducting qubits into chaos","authors":"Jorge Chávez-Carlos, Miguel A Prado Reynoso, Rodrigo G Cortiñas, Ignacio García-Mata, Victor S Batista, Francisco Pérez-Bernal, Diego A Wisniacki and Lea F Santos","doi":"10.1088/2058-9565/ad93fb","DOIUrl":"https://doi.org/10.1088/2058-9565/ad93fb","url":null,"abstract":"Kerr parametric oscillators are potential building blocks for fault-tolerant quantum computers. They can stabilize Kerr-cat qubits, which offer advantages toward the encoding and manipulation of error-protected quantum information. The recent realization of Kerr-cat qubits made use of the nonlinearity of transmon superconducting circuits and a squeezing drive. Increasing nonlinearities can enable faster gate times, but, as shown here, can also induce chaos and melt the qubit away. We determine the region of validity of the Kerr-cat qubit and discuss how its disintegration could be experimentally detected. The danger zone for parametric quantum computation is also a potential playground for investigating quantum chaos with driven superconducting circuits.","PeriodicalId":20821,"journal":{"name":"Quantum Science and Technology","volume":"12 1","pages":""},"PeriodicalIF":6.7,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142753106","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}
Pub Date : 2024-11-27DOI: 10.1088/2058-9565/ad9177
Jonathan Z Lu, Lucy Jiao, Kristina Wolinski, Milan Kornjača, Hong-Ye Hu, Sergio Cantu, Fangli Liu, Susanne F Yelin and Sheng-Tao Wang
We propose hybrid digital–analog (DA) learning algorithms on Rydberg atom arrays, combining the potentially practical utility and near-term realizability of quantum learning with the rapidly scaling architectures of neutral atoms. Our construction requires only single-qubit operations in the digital setting and global driving according to the Rydberg Hamiltonian in the analog setting. We perform a comprehensive numerical study of our algorithm on both classical and quantum data, given respectively by handwritten digit classification and unsupervised quantum phase boundary learning. We show in the two representative problems that DA learning is not only feasible in the near term, but also requires shorter circuit depths and is more robust to realistic error models as compared to digital learning schemes. Our results suggest that DA learning opens a promising path towards improved variational quantum learning experiments in the near term.
{"title":"Digital–analog quantum learning on Rydberg atom arrays","authors":"Jonathan Z Lu, Lucy Jiao, Kristina Wolinski, Milan Kornjača, Hong-Ye Hu, Sergio Cantu, Fangli Liu, Susanne F Yelin and Sheng-Tao Wang","doi":"10.1088/2058-9565/ad9177","DOIUrl":"https://doi.org/10.1088/2058-9565/ad9177","url":null,"abstract":"We propose hybrid digital–analog (DA) learning algorithms on Rydberg atom arrays, combining the potentially practical utility and near-term realizability of quantum learning with the rapidly scaling architectures of neutral atoms. Our construction requires only single-qubit operations in the digital setting and global driving according to the Rydberg Hamiltonian in the analog setting. We perform a comprehensive numerical study of our algorithm on both classical and quantum data, given respectively by handwritten digit classification and unsupervised quantum phase boundary learning. We show in the two representative problems that DA learning is not only feasible in the near term, but also requires shorter circuit depths and is more robust to realistic error models as compared to digital learning schemes. Our results suggest that DA learning opens a promising path towards improved variational quantum learning experiments in the near term.","PeriodicalId":20821,"journal":{"name":"Quantum Science and Technology","volume":"3 1","pages":""},"PeriodicalIF":6.7,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142718429","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}
Pub Date : 2024-11-27DOI: 10.1088/2058-9565/ad93fa
Paul Weinbrenner, Patricia Quellmalz, Christian Giese, Luis Flacke, Manuel Müller, Matthias Althammer, Stephan Geprägs, Rudolf Gross and Friedemann Reinhard
Planar scanning probe microscopy is a recently emerging alternative approach to tip-based scanning probe imaging. It can scan an extended planar sensor, such as a polished bulk diamond doped with magnetic-field-sensitive nitrogen-vacancy (NV) centers, in nanometer-scale proximity of a planar sample. So far, this technique has been limited to optical near-field microscopy and has required nanofabrication of the sample of interest. Here we extend this technique to magnetometry using NV centers and present a modification that removes the need for sample-side nanofabrication. We harness this new ability to perform a hitherto infeasible measurement - direct imaging of the three-dimensional vector magnetic field of magnetic vortices in a thin film magnetic heterostructure, based on repeated scanning with NV centers with different orientations within the same scanning probe. Our result opens the door to quantum sensing using multiple qubits within the same scanning probe, a prerequisite for the use of entanglement-enhanced and massively parallel schemes.
{"title":"Planar scanning probe microscopy enables vector magnetic field imaging at the nanoscale","authors":"Paul Weinbrenner, Patricia Quellmalz, Christian Giese, Luis Flacke, Manuel Müller, Matthias Althammer, Stephan Geprägs, Rudolf Gross and Friedemann Reinhard","doi":"10.1088/2058-9565/ad93fa","DOIUrl":"https://doi.org/10.1088/2058-9565/ad93fa","url":null,"abstract":"Planar scanning probe microscopy is a recently emerging alternative approach to tip-based scanning probe imaging. It can scan an extended planar sensor, such as a polished bulk diamond doped with magnetic-field-sensitive nitrogen-vacancy (NV) centers, in nanometer-scale proximity of a planar sample. So far, this technique has been limited to optical near-field microscopy and has required nanofabrication of the sample of interest. Here we extend this technique to magnetometry using NV centers and present a modification that removes the need for sample-side nanofabrication. We harness this new ability to perform a hitherto infeasible measurement - direct imaging of the three-dimensional vector magnetic field of magnetic vortices in a thin film magnetic heterostructure, based on repeated scanning with NV centers with different orientations within the same scanning probe. Our result opens the door to quantum sensing using multiple qubits within the same scanning probe, a prerequisite for the use of entanglement-enhanced and massively parallel schemes.","PeriodicalId":20821,"journal":{"name":"Quantum Science and Technology","volume":"181 1","pages":""},"PeriodicalIF":6.7,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142718430","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}
Pub Date : 2024-11-25DOI: 10.1088/2058-9565/ad934d
Diksha Sharma, Parvinder Singh and Atul Kumar
In this study, we propose the use of quantum information gain (QIG) and fidelity as quantum splitting criteria to construct an efficient and balanced quantum decision tree. QIG is a circuit-based criterion in which angle embedding is used to construct a quantum state, which utilizes quantum mutual information to compute the information between a feature and the class attribute. For the fidelity-based criterion, we construct a quantum state using the occurrence of random events in a feature and its corresponding class. We use the constructed state to further compute fidelity for determining the splitting attribute among all features. Using numerical analysis, our results clearly demonstrate that the fidelity-based criterion ensures the construction of a balanced tree. We further compare the efficiency of our quantum information gain and fidelity-based quantum splitting criteria with different classical splitting criteria on balanced and imbalanced datasets. Our analysis shows that the quantum splitting criteria lead to quantum advantage in comparison to classical splitting criteria for different evaluation metrics.
{"title":"Quantum-inspired attribute selection algorithms","authors":"Diksha Sharma, Parvinder Singh and Atul Kumar","doi":"10.1088/2058-9565/ad934d","DOIUrl":"https://doi.org/10.1088/2058-9565/ad934d","url":null,"abstract":"In this study, we propose the use of quantum information gain (QIG) and fidelity as quantum splitting criteria to construct an efficient and balanced quantum decision tree. QIG is a circuit-based criterion in which angle embedding is used to construct a quantum state, which utilizes quantum mutual information to compute the information between a feature and the class attribute. For the fidelity-based criterion, we construct a quantum state using the occurrence of random events in a feature and its corresponding class. We use the constructed state to further compute fidelity for determining the splitting attribute among all features. Using numerical analysis, our results clearly demonstrate that the fidelity-based criterion ensures the construction of a balanced tree. We further compare the efficiency of our quantum information gain and fidelity-based quantum splitting criteria with different classical splitting criteria on balanced and imbalanced datasets. Our analysis shows that the quantum splitting criteria lead to quantum advantage in comparison to classical splitting criteria for different evaluation metrics.","PeriodicalId":20821,"journal":{"name":"Quantum Science and Technology","volume":"183 1","pages":""},"PeriodicalIF":6.7,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697139","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}
Pub Date : 2024-11-22DOI: 10.1088/2058-9565/ad92a4
Yong Wang, Lijun Liu, Tong Dou, Li Li and Shuming Cheng
Quantum state tomography is a cornerstone of quantum information technologies to characterize and benchmark quantum systems from measurement statistics. In this work, we present an infidelity-based least-squares estimator, which incorporates the state purity information and provides orders of magnitude higher tomography accuracy than previous ones. It is further enhanced with the randomized toolbox of direct fidelity estimation, making it applicable to large-scale quantum systems. We validate the proposed estimators through extensive experiments conducted on the IBM Qiskit simulator. The results also demonstrate that our estimator admits an infidelity scaling with Pauli sample size N for (nearly) pure states. Further, it enables high-precision pure-state tomography for systems of up to 25-qubit states, given some state priors. Our method provides a novel perspective on the union of underlying tomography technique and state properties estimation.
量子态层析成像技术是量子信息技术的基石，它可以从测量统计数据中描述量子系统的特征并为其设定基准。在这项工作中，我们提出了一种基于不保真度的最小二乘估计器，它结合了状态纯度信息，比以往的层析准确度高出几个数量级。它通过直接保真度估计的随机工具箱得到了进一步增强，使其适用于大规模量子系统。我们在 IBM Qiskit 模拟器上进行了大量实验，验证了所提出的估计器。实验结果还证明，我们的估计器对于（近乎）纯态的保真度可随保利样本大小 N 而缩放。此外，它还能在给定一些状态先验的情况下，对多达 25 量子比特的系统进行高精度纯态层析。我们的方法为底层层析技术与状态特性估计的结合提供了一个新的视角。
{"title":"Quantum state tomography based on infidelity estimation","authors":"Yong Wang, Lijun Liu, Tong Dou, Li Li and Shuming Cheng","doi":"10.1088/2058-9565/ad92a4","DOIUrl":"https://doi.org/10.1088/2058-9565/ad92a4","url":null,"abstract":"Quantum state tomography is a cornerstone of quantum information technologies to characterize and benchmark quantum systems from measurement statistics. In this work, we present an infidelity-based least-squares estimator, which incorporates the state purity information and provides orders of magnitude higher tomography accuracy than previous ones. It is further enhanced with the randomized toolbox of direct fidelity estimation, making it applicable to large-scale quantum systems. We validate the proposed estimators through extensive experiments conducted on the IBM Qiskit simulator. The results also demonstrate that our estimator admits an infidelity scaling with Pauli sample size N for (nearly) pure states. Further, it enables high-precision pure-state tomography for systems of up to 25-qubit states, given some state priors. Our method provides a novel perspective on the union of underlying tomography technique and state properties estimation.","PeriodicalId":20821,"journal":{"name":"Quantum Science and Technology","volume":"16 1","pages":""},"PeriodicalIF":6.7,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142684464","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}
Pub Date : 2024-11-21DOI: 10.1088/2058-9565/ad9176
Youle Wang
Kernel principal component analysis (kernel PCA) is a nonlinear dimensionality reduction technique that employs kernel functions to map data into a high-dimensional feature space, thereby extending the applicability of linear PCA to nonlinear data and facilitating the extraction of informative principal components. However, kernel PCA necessitates the manipulation of large-scale matrices, leading to high computational complexity and posing challenges for efficient implementation in big data environments. Quantum computing has recently been integrated with kernel methods in machine learning, enabling effective analysis of input data within intractable feature spaces. Although existing quantum kernel PCA proposals promise exponential speedups, they impose stringent requirements on quantum hardware that are challenging to fulfill. In this work, we propose a quantum algorithm for kernel PCA by establishing a connection between quantum kernel methods and block encoding, thereby diagonalizing the centralized kernel matrix on a quantum computer. The query complexity is logarithmic with respect to the size of the data vector, D, and linear with respect to the size of the dataset. An exponential speedup could be achieved when the dataset consists of a few high-dimensional vectors, wherein the dataset size is polynomial in , with D being significantly large. In contrast to existing work, our algorithm enhances the efficiency of quantum kernel PCA and reduces the requirements for quantum hardware. Furthermore, we have also demonstrated that the algorithm based on block encoding matches the lower bound of query complexity, indicating that our algorithm is nearly optimal. Our research has laid down new pathways for developing quantum machine learning algorithms aimed at addressing tangible real-world problems and demonstrating quantum advantages within machine learning.
核主成分分析（kernel PCA）是一种非线性降维技术，它利用核函数将数据映射到高维特征空间，从而将线性 PCA 的适用性扩展到非线性数据，并促进信息主成分的提取。然而，核 PCA 需要处理大规模矩阵，导致计算复杂度高，为在大数据环境中高效实施带来了挑战。最近，量子计算与机器学习中的内核方法相结合，能够在难以处理的特征空间内对输入数据进行有效分析。虽然现有的量子内核 PCA 提议有望实现指数级的速度提升，但它们对量子硬件提出了严格的要求，要满足这些要求具有挑战性。在这项工作中，我们通过建立量子核方法与块编码之间的联系，提出了核 PCA 的量子算法，从而在量子计算机上对集中核矩阵进行对角。查询复杂度与数据向量 D 的大小成对数关系，与数据集的大小成线性关系。当数据集由几个高维向量组成时，可以实现指数级提速，此时数据集的大小为多项式，而 D 则非常大。与现有研究相比，我们的算法提高了量子核 PCA 的效率，降低了对量子硬件的要求。此外，我们还证明了基于块编码的算法符合查询复杂度的下限，表明我们的算法接近最优。我们的研究为开发量子机器学习算法铺平了新的道路，旨在解决现实世界中的实际问题，并展示机器学习中的量子优势。
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