John Tanner, Jason Pye, and Jingbo Wang
"Learning out-of-time-ordered correlators with classical kernel methods"
PHYSICAL REVIEW B 111, 144301 (2025)
Abstract
Out-of-time-ordered correlators (OTOCs) are widely used to investigate information scrambling in quantum systems. However, directly computing OTOCs with classical computers is an expensive procedure. This is due to the need to classically simulate the dynamics of quantum many-body systems, which entails computational costs that scale rapidly with system size. Similarly, exact simulation of the dynamics with a quantum computer (QC) will either only be possible for short times with noisy intermediate-scale quantum devices or require a fault-tolerant QC which is currently beyond technological capabilities. This motivates a search for alternative approaches to determine OTOCs and related quantities. In this paper, we explore four parameterized sets of Hamiltonians describing local one-dimensional quantum systems of interest in condensed matter physics. For each set, we investigate whether classical kernel methods can accurately learn the XZ-OTOC and a particular sum of OTOCs as functions of the Hamiltonian parameters. We frame the problem as a regression task, generating small batches of labeled data with classical tensor network methods for quantum many-body systems with up to 40 qubits. Using this data, we train a variety of standard kernel machines and observe that the Laplacian and radial basis function kernels perform best, achieving a coefficient of determination (R2) on testing sets of at least 0.7167, with averages between 0.8112 and 0.9822 for the various sets of Hamiltonians, together with small root mean squared error and mean absolute error. Hence, after training, the models can replace further uses of tensor networks for calculating an OTOC function of a system within the parameterized sets. Accordingly, the proposed method can assist with extensive evaluations of an OTOC function.
Josh Green and Jingbo Wang
"Quantum Encoding of Structured Data with Matrix Product States"
arXiv:2502.16464 (2025)
Abstract
Quantum computing faces a fundamental challenge: the amplitude encoding of an arbitrary n-qubit state vector generally requires {\Omega}(2n) gate operations. We can, however, form dimensionality-reduced representations of quantum states using matrix product states (MPS), providing a promising pathway to the efficient amplitude encoding of states with limited entanglement entropy. In this paper, we explore the capabilities of MPS representations to encode a wide range of functions and images using O(n)-depth circuits without any ancilla qubits, computed with the so-called Matrix Product Disentangler algorithm with tensor network optimisation. We find that MPS-based state preparation enables the efficient encoding of functions up to low-degree piecewise polynomials with accuracy exceeding 99.99% accuracy. We also showcase a novel approach to encoding structured image data based on MPS approximations of the discrete wavelet transform (DWT) representation, which is shown to prepare a 128x128 ChestMNIST image on 14 qubits with fidelity exceeding 99.1% on a circuit with a total depth of just 425 single-qubit rotation and two-qubit CNOT gates.
Yusen Wu, Bujiao Wu, Yanqi Song, Xiao Yuan, Jingbo Wang
"Learning the complexity of weakly noisy quantum states",
ICLR 2025 – International Conference on Learning Representations (31.75% acceptance rate)
Abstract
Quantifying the complexity of quantum states is a longstanding key problem in various subfields of science, ranging from quantum computing to the black-hole theory. The lower bound on quantum pure state complexity has been shown to grow linearly with system size (Haferkamp et al., 2022). However, extending this result to noisy circuit environments, which better reflect real quantum devices, re- mains an open challenge. In this paper, we explore the complexity of weakly noisy quantum states via the quantum learning method. We present an efficient learning algorithm, that leverages the classical shadow representation of target quantum states, to predict the circuit complexity of weakly noisy quantum states. Our al- gorithm is proved to be optimal in terms of sample complexity accompanied with polynomial classical processing time. Our result builds a bridge between the learn- ing algorithm and quantum state complexity, meanwhile highlighting the power of learning algorithm in characterizing intrinsic properties of quantum states.
2024
Josh Green and Jingbo Wang
"The awe-inspiring power of quantum computers"
Frontiers for Young Minds, 12, 1335355 (2024)
Abstract
Quantum computing is an emerging field of research and technology that harnesses a science called quantum mechanics to create computers with revolutionary capabilities. Although existing quantum computers are limited in size and prone to significant errors, future quantum computers might be capable of performing tasks that were once considered unimaginable using even the world’s most powerful supercomputers. This means that quantum computers could revolutionize many important areas of our lives! In this article, we will explore quantum computing by first reviewing how our current computers work. Then, we will dive into what makes quantum computers potentially far more powerful. We will especially focus on the source of their immense power: the ability of tiny particles to be in multiple states at the same time!
Qu, Dengke; Matwiejew, Edric; Wang, Kunkun; Wang, Jingbo; Xue, Peng
"Experimental implementation of quantum-walk-based portfolio optimisation",
Quantum Science and Technology (IF 6.568) , vol. 9, pp. 025014, 2024.
Abstract
The application of quantum algorithms has attracted much attention as it holds the promise of solving practical problems that are intractable to classical algorithms. One such application is the recent development of a quantum-walk-based optimization algorithm approach to portfolio optimization under the modern portfolio theory framework. In this paper, we demonstrate an experimental realization of the alternating phase-shift and continuous-time quantum walk unitaries that underpin this quantum algorithm using optical networks and single photons. The experimental analysis confirms that the probability of states corresponding to high-quality solutions is efficiently amplified by increasing the number of phase-shift and quantum walk iterations. This work provides strong evidence for practical applications of quantum-walk-based algorithms such as financial portfolio optimization.
Zhuang, Shengxin; Tanner, John; Wu, Yusen; Huynh, Du Q.; Cadet, Wei Liu Xavier F.; Fontaine, Nicolas; Charton, Philippe; Damour, Cedric; Cadet, Frederic; Wang, Jingbo
"Non-Hemolytic Peptide Classification Using A Quantum Support Vector Machine",
Quantum Information Processing 23 (11), 379, 2024
Abstract
Quantum machine learning (QML) is one of the most promising applications of quantum computation. However, it is still unclear whether quantum advantages exist when the data is of a classical nature and the search for practical, real-world applications of QML remains active. In this work, we apply the well-studied quantum support vector machine (QSVM), a powerful QML model, to a binary classification task which classifies peptides as either hemolytic or non-hemolytic. Using three peptide datasets, we apply and contrast the performance of the QSVM, numerous classical SVMs, and the best published results on the same peptide classification task, out of which the QSVM performs best. The contributions of this work include (i) the first application of the QSVM to this specific peptide classification task, (ii) an explicit demonstration of QSVMs outperforming the best published results attained with classical machine learning models on this classification task and (iii) empirical results showing that the QSVM is capable of outperforming many (and possibly all) classical SVMs on this classification task. This foundational work paves the way to verifiable quantum advantages in the field of computational biology and facilitates safer therapeutic development.
Sotelo, R., Giusto, E., Nakamura, Y., & Wang, J.
"The 2nd Workshop on Quantum in Consumer Technology At IEEE Quantum Week"
IEEE Consumer Electronics Magazine, 13(5), 1-2, 2024; https://doi.org/10.1109/MCE.2024.3407740
Abstract
The 2nd Workshop on Quantum in Consumer Technology, held during the IEEE Quantum Week 2023, continued to explore the integration and application of quantum technologies in consumer electronics. Organized by the Quantum in Consumer Technology Technical Committee (QCT TC) of the IEEE Consumer Technology Society (CTSoc), this year's workshop featured two insightful panels discussing the cutting-edge advancements and applications of quantum technologies that aim to revolutionize consumer products and services.
Quantum Convolutional Neural Network (QCNN) has achieved significant success in solving various complex problems, such as quantum many-body physics and image recognition. In comparison to the classical Convolutional Neural Network (CNN) model, the QCNN model requires excellent numerical performance or efficient computational resources to showcase its potential quantum advantages, particularly in classical data processing tasks. In this paper, we propose a computationally resource-efficient QCNN model referred to as RE-QCNN. Specifically, through a comprehensive analysis of the complexity associated with the forward and backward propagation processes in the quantum convolutional layer, our results demonstrate a significant reduction in computational resources required for this layer compared to the classical CNN model. Furthermore, our model is numerically benchmarked on recognizing images from the MNIST and Fashion-MNIST datasets, achieving high accuracy in these multi-class classification tasks.
Quantum Federated Learning (QFL) enables collaborative training of a Quantum Machine Learning (QML) model among multiple clients possessing quantum computing capabilities, without the need to share their respective local data. However, the limited availability of quantum computing resources poses a challenge for each client to acquire quantum computing capabilities. This raises a natural question: Can quantum computing capabilities be deployed on the server instead? In this paper, we propose a QFL framework specifically designed for classical clients, referred to as CCQFL, in response to this question. In each iteration, the collaborative training of the QML model is assisted by the shadow tomography technique, eliminating the need for quantum computing capabilities of clients. Specifically, the server constructs a classical representation of the QML model and transmits it to the clients. The clients encode their local data onto observables and use this classical representation to calculate local gradients. These local gradients are then utilized to update the parameters of the QML model. We evaluate the effectiveness of our framework through extensive numerical simulations using handwritten digit images from the MNIST dataset. Our framework provides valuable insights into QFL, particularly in scenarios where quantum computing resources are scarce.
Y Wu, JB Wang, Y Li
"Quantum Computing for Option Portfolio Analysis"
arXiv:2406.00486 (2024)
Abstract
In this paper, we introduce an efficient and end-to-end quantum algorithm tailored for computing the Value-at-Risk (VaR) and conditional Value-at-Risk (CVar) for a portfolio of European options. Our focus is on leveraging quantum computation to overcome the challenges posed by high dimensionality in VaR and CVaR estimation. While our innovative quantum algorithm is designed primarily for estimating portfolio VaR and CVaR for European options, we also investigate the feasibility of applying a similar quantum approach to price American options. Our analysis reveals a quantum 'no-go' theorem within the current algorithm, highlighting its limitation in pricing American options. Our results indicate the necessity of investigating alternative strategies to resolve the complementarity challenge in pricing American options in future research.
2025
John Tanner, Jason Pye, and Jingbo Wang
"Learning out-of-time-ordered correlators with classical kernel methods"
PHYSICAL REVIEW B 111, 144301 (2025)
Abstract
Out-of-time-ordered correlators (OTOCs) are widely used to investigate information scrambling in quantum systems. However, directly computing OTOCs with classical computers is an expensive procedure. This is due to the need to classically simulate the dynamics of quantum many-body systems, which entails computational costs that scale rapidly with system size. Similarly, exact simulation of the dynamics with a quantum computer (QC) will either only be possible for short times with noisy intermediate-scale quantum devices or require a fault-tolerant QC which is currently beyond technological capabilities. This motivates a search for alternative approaches to determine OTOCs and related quantities. In this paper, we explore four parameterized sets of Hamiltonians describing local one-dimensional quantum systems of interest in condensed matter physics. For each set, we investigate whether classical kernel methods can accurately learn the XZ-OTOC and a particular sum of OTOCs as functions of the Hamiltonian parameters. We frame the problem as a regression task, generating small batches of labeled data with classical tensor network methods for quantum many-body systems with up to 40 qubits. Using this data, we train a variety of standard kernel machines and observe that the Laplacian and radial basis function kernels perform best, achieving a coefficient of determination (R2) on testing sets of at least 0.7167, with averages between 0.8112 and 0.9822 for the various sets of Hamiltonians, together with small root mean squared error and mean absolute error. Hence, after training, the models can replace further uses of tensor networks for calculating an OTOC function of a system within the parameterized sets. Accordingly, the proposed method can assist with extensive evaluations of an OTOC function.
Josh Green and Jingbo Wang
"Quantum Encoding of Structured Data with Matrix Product States"
arXiv:2502.16464 (2025)
Abstract
Quantum computing faces a fundamental challenge: the amplitude encoding of an arbitrary n-qubit state vector generally requires {\Omega}(2n) gate operations. We can, however, form dimensionality-reduced representations of quantum states using matrix product states (MPS), providing a promising pathway to the efficient amplitude encoding of states with limited entanglement entropy. In this paper, we explore the capabilities of MPS representations to encode a wide range of functions and images using O(n)-depth circuits without any ancilla qubits, computed with the so-called Matrix Product Disentangler algorithm with tensor network optimisation. We find that MPS-based state preparation enables the efficient encoding of functions up to low-degree piecewise polynomials with accuracy exceeding 99.99% accuracy. We also showcase a novel approach to encoding structured image data based on MPS approximations of the discrete wavelet transform (DWT) representation, which is shown to prepare a 128x128 ChestMNIST image on 14 qubits with fidelity exceeding 99.1% on a circuit with a total depth of just 425 single-qubit rotation and two-qubit CNOT gates.
Yusen Wu, Bujiao Wu, Yanqi Song, Xiao Yuan, Jingbo Wang
"Learning the complexity of weakly noisy quantum states",
ICLR 2025 – International Conference on Learning Representations (31.75% acceptance rate)
Abstract
Quantifying the complexity of quantum states is a longstanding key problem in various subfields of science, ranging from quantum computing to the black-hole theory. The lower bound on quantum pure state complexity has been shown to grow linearly with system size (Haferkamp et al., 2022). However, extending this result to noisy circuit environments, which better reflect real quantum devices, re- mains an open challenge. In this paper, we explore the complexity of weakly noisy quantum states via the quantum learning method. We present an efficient learning algorithm, that leverages the classical shadow representation of target quantum states, to predict the circuit complexity of weakly noisy quantum states. Our al- gorithm is proved to be optimal in terms of sample complexity accompanied with polynomial classical processing time. Our result builds a bridge between the learn- ing algorithm and quantum state complexity, meanwhile highlighting the power of learning algorithm in characterizing intrinsic properties of quantum states.
2024
Josh Green and Jingbo Wang
"The awe-inspiring power of quantum computers"
Frontiers for Young Minds, 12, 1335355 (2024)
Abstract
Quantum computing is an emerging field of research and technology that harnesses a science called quantum mechanics to create computers with revolutionary capabilities. Although existing quantum computers are limited in size and prone to significant errors, future quantum computers might be capable of performing tasks that were once considered unimaginable using even the world’s most powerful supercomputers. This means that quantum computers could revolutionize many important areas of our lives! In this article, we will explore quantum computing by first reviewing how our current computers work. Then, we will dive into what makes quantum computers potentially far more powerful. We will especially focus on the source of their immense power: the ability of tiny particles to be in multiple states at the same time!
Qu, Dengke; Matwiejew, Edric; Wang, Kunkun; Wang, Jingbo; Xue, Peng
"Experimental implementation of quantum-walk-based portfolio optimisation",
Quantum Science and Technology (IF 6.568) , vol. 9, pp. 025014, 2024.
Abstract
The application of quantum algorithms has attracted much attention as it holds the promise of solving practical problems that are intractable to classical algorithms. One such application is the recent development of a quantum-walk-based optimization algorithm approach to portfolio optimization under the modern portfolio theory framework. In this paper, we demonstrate an experimental realization of the alternating phase-shift and continuous-time quantum walk unitaries that underpin this quantum algorithm using optical networks and single photons. The experimental analysis confirms that the probability of states corresponding to high-quality solutions is efficiently amplified by increasing the number of phase-shift and quantum walk iterations. This work provides strong evidence for practical applications of quantum-walk-based algorithms such as financial portfolio optimization.
Zhuang, Shengxin; Tanner, John; Wu, Yusen; Huynh, Du Q.; Cadet, Wei Liu Xavier F.; Fontaine, Nicolas; Charton, Philippe; Damour, Cedric; Cadet, Frederic; Wang, Jingbo
"Non-Hemolytic Peptide Classification Using A Quantum Support Vector Machine",
Quantum Information Processing 23 (11), 379, 2024
Abstract
Quantum machine learning (QML) is one of the most promising applications of quantum computation. However, it is still unclear whether quantum advantages exist when the data is of a classical nature and the search for practical, real-world applications of QML remains active. In this work, we apply the well-studied quantum support vector machine (QSVM), a powerful QML model, to a binary classification task which classifies peptides as either hemolytic or non-hemolytic. Using three peptide datasets, we apply and contrast the performance of the QSVM, numerous classical SVMs, and the best published results on the same peptide classification task, out of which the QSVM performs best. The contributions of this work include (i) the first application of the QSVM to this specific peptide classification task, (ii) an explicit demonstration of QSVMs outperforming the best published results attained with classical machine learning models on this classification task and (iii) empirical results showing that the QSVM is capable of outperforming many (and possibly all) classical SVMs on this classification task. This foundational work paves the way to verifiable quantum advantages in the field of computational biology and facilitates safer therapeutic development.
Sotelo, R., Giusto, E., Nakamura, Y., & Wang, J.
"The 2nd Workshop on Quantum in Consumer Technology At IEEE Quantum Week"
IEEE Consumer Electronics Magazine, 13(5), 1-2, 2024; https://doi.org/10.1109/MCE.2024.3407740
Abstract
The 2nd Workshop on Quantum in Consumer Technology, held during the IEEE Quantum Week 2023, continued to explore the integration and application of quantum technologies in consumer electronics. Organized by the Quantum in Consumer Technology Technical Committee (QCT TC) of the IEEE Consumer Technology Society (CTSoc), this year's workshop featured two insightful panels discussing the cutting-edge advancements and applications of quantum technologies that aim to revolutionize consumer products and services.
Quantum Convolutional Neural Network (QCNN) has achieved significant success in solving various complex problems, such as quantum many-body physics and image recognition. In comparison to the classical Convolutional Neural Network (CNN) model, the QCNN model requires excellent numerical performance or efficient computational resources to showcase its potential quantum advantages, particularly in classical data processing tasks. In this paper, we propose a computationally resource-efficient QCNN model referred to as RE-QCNN. Specifically, through a comprehensive analysis of the complexity associated with the forward and backward propagation processes in the quantum convolutional layer, our results demonstrate a significant reduction in computational resources required for this layer compared to the classical CNN model. Furthermore, our model is numerically benchmarked on recognizing images from the MNIST and Fashion-MNIST datasets, achieving high accuracy in these multi-class classification tasks.
Quantum Federated Learning (QFL) enables collaborative training of a Quantum Machine Learning (QML) model among multiple clients possessing quantum computing capabilities, without the need to share their respective local data. However, the limited availability of quantum computing resources poses a challenge for each client to acquire quantum computing capabilities. This raises a natural question: Can quantum computing capabilities be deployed on the server instead? In this paper, we propose a QFL framework specifically designed for classical clients, referred to as CCQFL, in response to this question. In each iteration, the collaborative training of the QML model is assisted by the shadow tomography technique, eliminating the need for quantum computing capabilities of clients. Specifically, the server constructs a classical representation of the QML model and transmits it to the clients. The clients encode their local data onto observables and use this classical representation to calculate local gradients. These local gradients are then utilized to update the parameters of the QML model. We evaluate the effectiveness of our framework through extensive numerical simulations using handwritten digit images from the MNIST dataset. Our framework provides valuable insights into QFL, particularly in scenarios where quantum computing resources are scarce.
Y Wu, JB Wang, Y Li
"Quantum Computing for Option Portfolio Analysis"
arXiv:2406.00486 (2024)
Abstract
In this paper, we introduce an efficient and end-to-end quantum algorithm tailored for computing the Value-at-Risk (VaR) and conditional Value-at-Risk (CVar) for a portfolio of European options. Our focus is on leveraging quantum computation to overcome the challenges posed by high dimensionality in VaR and CVaR estimation. While our innovative quantum algorithm is designed primarily for estimating portfolio VaR and CVaR for European options, we also investigate the feasibility of applying a similar quantum approach to price American options. Our analysis reveals a quantum 'no-go' theorem within the current algorithm, highlighting its limitation in pricing American options. Our results indicate the necessity of investigating alternative strategies to resolve the complementarity challenge in pricing American options in future research.
GALLERY
Preview
Congratulations, Josh!
Preview
Congratulations, Dr. Yusen!
Preview
Preview
Tavis at IEEE Quantum Week 2024
Preview
Online conversation on Quantum Entanglement and Computing
Preview
Jingbo at "Quantum Australia 2024" with Andrea Morello and Derek Muller
Preview
Quantum meets logistics 2024
Preview
QUISA meeting 2024
Preview
Minister Dawson, VC Chakma, DVCR Nowak visiting QUISA in 2023
Preview
Quantum games workshop 2024
GALLERY
Preview
Congratulations, Josh!
Preview
Congratulations, Dr. Yusen!
Preview
Preview
Tavis at IEEE Quantum Week 2024
Preview
Online conversation on Quantum Entanglement and Computing
Preview
Jingbo at "Quantum Australia 2024" with Andrea Morello and Derek Muller
Preview
Quantum meets logistics 2024
Preview
QUISA meeting 2024
Preview
Minister Dawson, VC Chakma, DVCR Nowak visiting QUISA in 2023
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