arXiv subjects

Tzu-Chieh Wei

Publications and source records attributed to Tzu-Chieh Wei.

At least 73 records · Page 4Linked to original sources

arXiv2021

Application of Quantum Machine Learning using the Quantum Kernel Algorithm on High Energy Physics Analysis at the LHC

Quantum machine learning could possibly become a valuable alternative to classical machine learning for applications in High Energy Physics by offering computational speed-ups. In this study, we employ a support vector machine with a quantum kernel estimator (QSVM-Kernel method) to a recent LHC flagship physics analysis: $t\bar{t}H$ (Higgs boson production in association with a top quark pair). In our quantum simulation study using up to 20 qubits and up to 50000 events, the QSVM-Kernel method performs as well as its classical counterparts in three different platforms from Google Tensorflow Quantum, IBM Quantum and Amazon Braket. Additionally, using 15 qubits and 100 events, the application of the QSVM-Kernel method on the IBM superconducting quantum hardware approaches the performance of a noiseless quantum simulator. Our study confirms that the QSVM-Kernel method can use the large dimensionality of the quantum Hilbert space to replace the classical feature space in realistic physics datasets.

quant-ph↗

arXiv2021

Application of Quantum Machine Learning using the Quantum Variational Classifier Method to High Energy Physics Analysis at the LHC on IBM Quantum Computer Simulator and Hardware with 10 qubits

One of the major objectives of the experimental programs at the LHC is the discovery of new physics. This requires the identification of rare signals in immense backgrounds. Using machine learning algorithms greatly enhances our ability to achieve this objective. With the progress of quantum technologies, quantum machine learning could become a powerful tool for data analysis in high energy physics. In this study, using IBM gate-model quantum computing systems, we employ the quantum variational classifier method in two recent LHC flagship physics analyses: $t\bar{t}H$ (Higgs boson production in association with a top quark pair) and $H\rightarrowμ^{+}μ^{-}$ (Higgs boson decays to two muons, probing the Higgs boson couplings to second-generation fermions). We have obtained early results with 10 qubits on the IBM quantum simulator and the IBM quantum hardware. With small training samples of 100 events on the quantum simulator, the quantum variational classifier method performs similarly to classical algorithms such as SVM (support vector machine) and BDT (boosted decision tree), which are often employed in LHC physics analyses. On the quantum hardware, the quantum variational classifier method has shown promising discrimination power, comparable to that on the quantum simulator. This study demonstrates that quantum machine learning has the ability to differentiate between signal and background in realistic physics datasets. We foresee the usage of quantum machine learning in future high-luminosity LHC physics analyses, including measurements of the Higgs boson self-couplings and searches for dark matter.

quant-ph↗

arXiv2021

A Unified Framework for Quantum Supervised Learning

Quantum machine learning is an emerging field that combines machine learning with advances in quantum technologies. Many works have suggested great possibilities of using near-term quantum hardware in supervised learning. Motivated by these developments, we present an embedding-based framework for supervised learning with trainable quantum circuits. We introduce both explicit and implicit approaches. The aim of these approaches is to map data from different classes to separated locations in the Hilbert space via the quantum feature map. We will show that the implicit approach is a generalization of a recently introduced strategy, so-called \textit{quantum metric learning}. In particular, with the implicit approach, the number of separated classes (or their labels) in supervised learning problems can be arbitrarily high with respect to the number of given qubits, which surpasses the capacity of some current quantum machine learning models. Compared to the explicit method, this implicit approach exhibits certain advantages over small training sizes. Furthermore, we establish an intrinsic connection between the explicit approach and other quantum supervised learning models. Combined with the implicit approach, this connection provides a unified framework for quantum supervised learning. The utility of our framework is demonstrated by performing both noise-free and noisy numerical simulations. Moreover, we have conducted classification testing with both implicit and explicit approaches using several IBM Q devices.

quant-ph↗

arXiv2021

Quantum Zeno approach for molecular energies with maximum commuting initialHamiltonians

We propose to use a quantum adiabatic and simulated-annealing framework to compute theground state of small molecules. The initial Hamiltonian of our algorithms is taken to be themaximum commuting Hamiltonian that consists of a maximal set of commuting terms in the fullHamiltonian of molecules in the Pauli basis. We consider two variants. In the first method, weperform the adiabatic evolution on the obtained time- or path-dependent Hamiltonian with theinitial state as the ground state of the maximum commuting Hamiltonian. However, this methoddoes suffer from the usual problems of adiabatic quantum computation due to degeneracy andenergy-level crossings along the Hamiltonian path. This problem is mitigated by a Zeno method,i.e., via a series of eigenstate projections used in the quantum simulated annealing, with the path-dependent Hamiltonian augmented by a sum of Pauli X terms, whose contribution vanishes at thebeginning and the end of the path. In addition to the ground state, the low lying excited states canbe obtained using this quantum Zeno approach with equal accuracy to that of the ground state.

quant-ph↗

arXiv2021

Hybrid Quantum-Classical Graph Convolutional Network

The high energy physics (HEP) community has a long history of dealing with large-scale datasets. To manage such voluminous data, classical machine learning and deep learning techniques have been employed to accelerate physics discovery. Recent advances in quantum machine learning (QML) have indicated the potential of applying these techniques in HEP. However, there are only limited results in QML applications currently available. In particular, the challenge of processing sparse data, common in HEP datasets, has not been extensively studied in QML models. This research provides a hybrid quantum-classical graph convolutional network (QGCNN) for learning HEP data. The proposed framework demonstrates an advantage over classical multilayer perceptron and convolutional neural networks in the aspect of number of parameters. Moreover, in terms of testing accuracy, the QGCNN shows comparable performance to a quantum convolutional neural network on the same HEP dataset while requiring less than $50\%$ of the parameters. Based on numerical simulation results, studying the application of graph convolutional operations and other QML models may prove promising in advancing HEP research and other scientific fields.

cs.LG↗

arXiv2020

Quantum Convolutional Neural Networks for High Energy Physics Data Analysis

This work presents a quantum convolutional neural network (QCNN) for the classification of high energy physics events. The proposed model is tested using a simulated dataset from the Deep Underground Neutrino Experiment. The proposed architecture demonstrates the quantum advantage of learning faster than the classical convolutional neural networks (CNNs) under a similar number of parameters. In addition to faster convergence, the QCNN achieves greater test accuracy compared to CNNs. Based on experimental results, it is a promising direction to study the application of QCNN and other quantum machine learning models in high energy physics and additional scientific fields.

cs.LG↗

arXiv2020

Unsupervised learning of topological phase transitions using Calinski-Harabaz index

Machine learning methods have been recently applied to learning phases of matter and transitions between them. Of particular interest is the topological phase transition, such as in the XY model, which can be difficult for unsupervised learning such as the principal component analysis. Recently, authors of [Nature Physics \textbf{15},790 (2019)] employed the diffusion-map method for identifying topological order and were able to determine the BKT phase transition of the XY model, specifically via the intersection of the average cluster distance $\bar{D}$ and the within cluster dispersion $\barσ$ (when the different clusters vary from separation to mixing together). However, sometimes it is not easy to find the intersection if $\bar{D}$ or $\barσ$ does not change too much due to topological constraint. In this paper, we propose to use the Calinski-Harabaz ($ch$) index, defined roughly as the ratio $\bar D/\bar σ$, to determine the critical points, at which the $ch$ index reaches a maximum or minimum value, or jump sharply. We examine the $ch$ index in several statistical models, including ones that contain a BKT phase transition. For the Ising model, the peaks of the quantity $ch$ or its components are consistent with the position of the specific heat maximum. For the XY model both on the square lattices and honeycomb lattices, our results of the $ch$ index show the convergence of the peaks over a range of the parameters $\varepsilon/\varepsilon_0$ in the Gaussian kernel. We also examine the generalized XY model with $q=2$ and $q=8$ and at the value away from the pure XY limit. Our method is thus useful to both topological and non-topological phase transitions and can achieve accuracy as good as supervised learning methods previously used in these models, and may be used for searching phases from experimental data.

cond-mat.stat-mech↗

arXiv2020

The AKLT models on the singly decorated diamond lattice and two degree-4 planar lattices are gapped

Recently various 2D AKLT models have been shown to be gapped, including the one on the hexagonal lattice. Here we report on a non-trivial 3D AKLT model which consists of spin-2 entities on the diamond lattice sites and one single spin-1 entity between every neighboring spin-2 site. Although the nonzero gap problem for the uniformly spin-2 AKLT models on the diamond and square lattices is still open, we are able to establish the existence of the gap for two planar lattices, which we call the inscribed square lattice and the triangle-octagon lattice, respectively. So far, these latter two models are the only two uniformly spin-2 AKLT models that have a provable nonzero gap above the ground state. We also discuss some attempts in proving the gap existence on both the square and kagome lattices. In addition, we show that if one can solve a finite-size problem of a weighted AKLT Hamiltonian and if the gap is larger than certain threshold, then the model on the square lattice is gapped in the thermodynamic limit. The threshold of the gap scales inversely with the linear size of the finite-size problem.

cond-mat.str-el↗

arXiv2020

Quantum algorithm for spectral projection by measuring an ancilla iteratively

We propose a quantum algorithm for projecting a quantum system to eigenstates of any Hermitian operator, provided one can access the associated control-unitary evolution for the ancilla and the system, as well as the measurement of the controlling ancillary qubit. Such a Hadamard-test like primitive is iterated so as to achieve the spectral projection, and the distribution of the projected eigenstates obeys the Born rule. This algorithm can be used as a subroutine in the quantum annealing procedure by measurement to drive the system to the ground state of a final Hamiltonian, and we simulate this for quantum many-body spin chains.

quant-ph↗

arXiv2019

Demonstrating the AKLT spectral gap on 2D degree-3 lattices

We establish that the spin-3/2 AKLT model on the honeycomb has a nonzero spectral gap. We use the relation between the anticommutator of two projectors and their sum, and apply it to related AKLT projectors that occupy plaquettes or other extended regions. We analytically reduce the complexity in the resulting eigenvalue problem and use a Lanczos numerical method to show that the required inequality for the nonzero spectral gap holds. This approach is also successfuly applied to several other spin-3/2 AKLT models on degree-3 semiregular tilings, such as the square octagon, star and cross lattices, where the complexity is low enough that exact diagonalization can be used instead of the Lanczos method. In addition, we also close the previously open cases in the singly decorated honeycomb and square lattices.

cond-mat.stat-mech↗

arXiv2019

AKLT models on decorated square lattices are gapped

The nonzero spectral gap of the original two-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) models has remained unproven for more than three decades. Recently, Abdul-Rahman et al. [arXiv:1901.09297] provided an elegant approach and proved analytically the existence of a nonzero spectral gap for the AKLT models on the decorated honeycomb lattice (for the number $n$ of spin-1 decorated sites on each original edge no less than 3). We perform calculations for the decorated square lattice and show that the corresponding AKLT models are gapped if $n\ge 4$. Combining both results, we also show that a family of decorated hybrid AKLT models, whose underlying lattice is of mixed vertex degrees 3 and 4, are also gapped for $n\ge 4$. We develop a numerical approach that extends beyond what was accessible previously. Our numerical results further improve the nonzero gap to $n\ge 2$, including the establishment of the gap for $n=2$ in the decorated triangular and cubic lattices. The latter case is interesting, as this shows the AKLT states on the decorated cubic lattices are not Néel ordered, in contrast to the state on the undecorated cubic lattice.

quant-ph↗

arXiv2019

Geometric Entanglement and Quantum Phase Transition in Generalized Cluster-XY models

In this work, we investigate quantum phase transition (QPT) in a generic family of spin chains using the ground-state energy, the energy gap, and the geometric measure of entanglement (GE). In many of prior works, GE per site was used. Here, we also consider GE per block with each block size being two. This can be regarded as a coarse grain of GE per site. We introduce a useful parameterization for the family of spin chains that includes the XY models with n-site interaction, the GHZ-cluster model and a cluster-antiferromagnetic model, the last of which exhibits QPT between a symmetry-protected topological (SPT) phase and a symmetry-breaking antiferromagnetic phase. As the models are exactly solvable, their ground-state wavefunctions can be obtained and thus their GE can be studied. It turns out that the overlap of the ground states with translationally invariant product states can be exactly calculated and hence the GE can be obtained via further parameter optimization. The QPTs exhibited in these models are detected by the energy gap and singular behavior of geometric entanglement. In particular, the XzY model exhibits transitions from the nontrivial SPT phase to a trivial paramagnetic phase. Moreover, the halfway XY model exhibits a first-order transition across the Barouch-McCoy circle, on which it was only a crossover in the standard XY model.

quant-ph↗

arXiv2019

Machine learning of phase transitions in the percolation and XY models

In this paper, we apply machine learning methods to study phase transitions in certain statistical mechanical models on the two dimensional lattices, whose transitions involve non-local or topological properties, including site and bond percolations, the XY model and the generalized XY model. We find that using just one hidden layer in a fully-connected neural network, the percolation transition can be learned and the data collapse by using the average output layer gives correct estimate of the critical exponent $ν$. We also study the Berezinskii-Kosterlitz-Thouless transition, which involves binding and unbinding of topological defects---vortices and anti-vortices, in the classical XY model. The generalized XY model contains richer phases, such as the nematic phase, the paramagnetic and the quasi-long-range ferromagnetic phases, and we also apply machine learning method to it. We obtain a consistent phase diagram from the network trained with only data along the temperature axis at two particular parameter $Δ$ values, where $Δ$ is the relative weight of pure XY coupling. Besides using the spin configurations (either angles or spin components) as the input information in a convolutional neural network, we devise a feature engineering approach using the histograms of the spin orientations in order to train the network to learn the three phases in the generalized XY model and demonstrate that it indeed works. The trained network by using system size $L\times L$ can be used to the phase diagram for other sizes ($L'\times L'$, where $L'\ne L$) without any further training.

cond-mat.stat-mech↗

arXiv2019

Detector Tomography on IBM 5-qubit Quantum Computers and Mitigation of Imperfect Measurement

We use quantum detector tomography to characterize the qubit readout in terms of measurement POVMs on IBM Quantum Computers IBM Q 5 Tenerife and IBM Q 5 Yorktown. Our results suggest that the characterized detector model deviates from the ideal projectors by a few percent. Further improvement on this characterization can be made by adopting two- or more-qubit detector models instead of independent single-qubit detectors for all the qubits in one device. An unexpected behavior was seen in the physical qubit labelled as qubit 3 of IBM Q 5 Tenerife, which can be a consequence of detector crosstalk or qubit operations influencing each other and requires further investigation. This peculiar behavior is consistent with characterization from the more sophisticated approach of the gate set tomography. We also discuss how the characterized detectors' POVM, despite deviation from the ideal projectors, can be used to estimate the ideal detection distribution.

quant-ph↗

arXiv2018

Phase transitions of a 2D deformed-AKLT model

We study spin-2 deformed-AKLT models on the square lattice, specifically a two-parameter family of $O(2)$-symmetric ground-state wavefunctions as defined by Niggemann, Klümper, and Zittartz, who found previously that the phase diagram consists of a Néel-ordered phase and a disordered phase which contains the AKLT point. Using tensor-network methods, we not only confirm the Néel phase but also find an XY phase with quasi-long-range order and a region adjacent to it, within the AKLT phase, with very large correlation length, and investigate the consequences of a perfectly factorizable point at the corner of that phase.

cond-mat.str-el↗

arXiv2018

Global and short-range entanglement properties in excited, many-body localized spin chains

We explore the use of short-range entanglement measures, such as concurrence and negativity, and global entanglement measures such as geometric entanglement, as indicators of many-body localization (MBL) in the spectra of disordered spin systems. From the perspective of entanglement monogamy, the two types of entanglement behave oppositely in the thermalized and MBL phases. In a recent work, the concurrence of subsystems, a measure of local entanglement, was used in a study of many-body localization in a one-dimensional spin-$1/2$ system (Bera and Lakshminarayan, 2016). We show numerically that the negativity displays notably similar behavior for this system, with the advantage that it can also be extended to systems of higher local dimension. We then demonstrate this extension in practice by using it to predict the existence of an MBL phase in a disordered a spin-1 system. In terms of global entanglement, the geometric entanglement of both spin-$1/2$ and spin-1 systems is also shown to behave as a complementary indicator of the MBL phenomenon.

quant-ph↗

arXiv2018

Unwinding Short-Range Entanglement

Symmetry-Protected Topological (SPT) phases are gapped phases of quantum matter protected by global symmetries that cannot be adiabatically deformed to a trivial phase without breaking symmetry. In this work, we show that, for several SPT phases that are short range entangled (SRE), enlarging symmetries may effectively achieve the consequences of explicitly breaking symmetries. In other words, we demonstrate that non-trivial SPT phases can be unwound to trivial ones by symmetry extension- through a path where the Hilbert space is enlarged and the Hamiltonian is invariant under an extended symmetry group applying the idea of Wang, Wen and Witten in arXiv:1705.06728. We show examples of both bosonic and fermionic SPT phases in 1+1 dimensions, including Haldane's bosonic spin chain and layers of Kitaev's fermionic Majorana chains. By adding degrees of freedom into the boundary/bulk, we can lift the zero mode degeneracy, or unwind the whole system. Furthermore, based on properties of Schur cover, we sketch a general picture of unwinding applicable to any 1+1 D bosonic SPT phase protected by on-site finite symmetry. Altogether we show that SRE states can be unwound by symmetry breaking, inversion and symmetry extension.

quant-ph↗

arXiv2018

Universal quantum computing using $(\mathbb{Z}_d)^3$ symmetry-protected topologically ordered states

Measurement-based quantum computation describes a scheme where entanglement of resource states is utilized to simulate arbitrary quantum gates via local measurements. Recent works suggest that symmetry-protected topologically non-trivial, short-ranged entanged states are promising candidates for such a resource. Miller and Miyake [NPJ Quantum Information 2, 16036 (2016)] recently constructed a particular $\mathbb{Z}_2 \times \mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry-protected topological state on the Union-Jack lattice and established its quantum computational universality. However, they suggested that the same construction on the triangular lattice might not lead to a universal resource. Instead of qubits, we generalize the construction to qudits and show that the resulting $(d-1)$ qudit nontrivial $\mathbb{Z}_d \times \mathbb{Z}_d \times \mathbb{Z}_d$ symmetry-protected topological states are universal on the triangular lattice, for $d$ being a prime number greater than 2. The same construction also holds for other 3-colorable lattices, including the Union-Jack lattice.

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