Session T47: Machine Learning for Quantum Matter III

Tuning quantum dot arrays with rays

Current semiconductor-based quantum computing approaches rely upon achieving control of nanocircuits at the single-electron level and using them as quantum bits (qubits). Establishing a stable configuration of spins in quantum dot (QD) devices is accomplished by a combination of electrostatic confinement, bandgap engineering, and dynamical control via nearby electrical gates. However, with an increasing number of QD qubits, the relevant parameter space grows exponentially, making heuristic control unfeasible. In semiconductor quantum computing, devices now have tens of individual electrostatic and dynamical gate voltages that must be carefully set to isolate the system to the single-electron regime and to realize good qubit performance. Large-scale quantum processors hinge on fully autonomous tuning processes that can be parallelized for practical applications.  

Over the past decade, there has been a number of advances aimed at automation of the various aspect of tuning QD devices, from testing device functionality and bootstrapping to setting the device topology to charge tuning. While the initial attempts relied on the appealingly intuitive and relatively easy to implement conventional algorithms involving a combination of techniques from regression analysis, pattern matching, and quantum control theory, more recently researchers began to take advantage of the tools provided by the field of artificial intelligence. In this talk, I will discuss how the recently proposed ray-based classification framework [1] can be combined with an “action-based” algorithm to tune a bootstrapped QD device into a specific few-electron charge configuration. I will also consider extensions of the tuning problem to the multiple QD scenario. Our approach enables automation of the tuning process while significantly reducing the number of measurements required for autonomous control.   

Unsupervised learning of quantum phases with topological order

Machine learning methods are emerging as powerful tools for detecting quantum phase transitions from simulated or experimental data. Most successes in this regard, have been achieved in the context of phases with a local order parameter, which can be described by the Landau theory of symmetry breaking. However, it was shown that phases that do not have such local order parameters but depend on the underlying global topology are much more difficult to capture. While there have been recent successes with unsupervised learning of topological phase transitions of classical models or non-interacting quantum systems, it remains an open question whether machine learning methods can identify interacting quantum phases of topological nature without involved feature engineering. 

In this work, we present a unsupervised machine-learning procedure, combining machine-learning-aided variational wavefunction descriptions and clustering techniques, to identify quantum phases with topological order. In particular, we consider the Kitaev Toric code model, which hosts Z2 topological order. We demonstrate that our procedure can capture both the loss of topological order at finite temperature and the transition to a polarized phase that emerges when a sufficiently strong magnetic field is applied. Our work opens the door to identifying exotic topological quantum phases without prior knowledge of the phase.   

Machine-learning discovery of descriptors for Topological Semimetals

The accumulation of massive amounts of materials data motivates data-based machine learning(ML) approaches. 

However, an extensive database of materials relying on high-throughput density functional theory (DFT) can be unreliable for emergent properties. Much needed is an approach that can articulate and build on expert human researchers' insights. The tolerance factor introduced in Refs [1-2] articulates a chemical insight for identifying topological semimetals among square-net materials and presents an opportunity to develop such a human-machine synergy. Hence, we developed a supervised-unsupervised hybrid approach combining non-linear Gaussian Process (GP) regression [3] with supervised metric learning to discover descriptors for topological semimetals. Simultaneously, we curated a database containing 1279 square-net materials featuring different physical and chemical attributes and the binary label for the topological property associated with each material. Application of the GP model to the database rediscovers the tolerance factor and offers new theoretical insight. 

 

[1] Klemenz, et al, J. Am. Chem. Soc. 2020, 142, 13, 6350–6359 

[2] Klemenz, et al, Annual Review of Materials Research 2019 49:1, 185-206 

[3] D. Milios, et al, Advance in Neural Information Processing Systems, page 11, 2018    

Bragg glass signatures in the disordered charge density wave material PdxErTe3 from X-ray diffraction data using unsupervised machine learning

Vestigial nematic and Bragg glass are new phases that emerge when an incommensurate long-range ordered charge density wave (CDW) gets suppressed by a quenched disorder. Pd intercalated rare earth tritelluride (PdxRTe3) has emerged as a promising model system to systematically investigate these emergent phases when the bi-directional orthogonal CDW order of RTe3 interacts with a controlled amount of disorder (Pd intercalation). Using X-ray diffraction Temperature Clustering (X-TEC), an unsupervised and interpretable machine learning technique introduced in Ref. [1], we extract signatures of  Bragg glass and vestigial nematic phases in PdxErTe3 from a large volume of X-ray temperature series data spanning 20000 Brillouin zones, collected using the Pilatus 2M CdTe detector on Sector 6-ID-D at the Advanced Photon Source. In addition to identifying the two order parameters from the CDW peak intensities, X-TEC probes the temperature dependence of the CDW peak widths and the disorder induced asymmetry in the diffuse scattering. X-TEC-enabled extraction of these otherwise subtle signatures from the data helps us arrive at a phase diagram. Our results suggest that  Pd intercalation turns the long-range ordered CDW into the Bragg glass phase, providing first X-ray based detection of the Bragg glass phase.  

 

 

[1] Venderley et al, https://arxiv.org/abs/2008.03275    

Neural network-based approach to analytic continuation

While most quantum Monte Carlo methods provide Green's function of imaginary time, the dynamical quantities relevant to experiments need to be expressed in real frequency. The standard approach that allows one to obtain these functions is based on the MaxEnt method. Unfortunately, this is an ill-conditioned problem where small errors in the imaginary time Green's functions lead to large errors in the real frequency quantities. And since the Monte Carlo results always have some statistical errors, in order to obtain reliable results this procedure must be iteratively repeated multiple times and then averaged.

It has already been proposed to replace this procedure by using an artificial neural network to perform the analytic continuation [1-3]. Such a possibility follows from the universal approximation theorem, which states that any piecewise continuous function can be approximated to any degree of accuracy by a sufficiently large neural network. In these approaches, at the first stage a large number of spectral functions A(ω) are modeled in a physically meaningful way, usually as sums of random Gaussian or Lorentzian peaks. Then, corresponding imaginary time Green's functions G(τ) are calculated. Pairs [G(τ),A(ω)] are then used to train the network to be able to reconstruct A(ω) from a given G(τ). Here, we propose an alternative approach, where we train the network with the help of the actual Green's function generated in QMC, not the ones calculated from postulated A(ω). Then, it is more general in that there is no need to postulate the functional form of A(ω). An additional advantage is that this method can be easily applied also to other inverse problems, like the deconvolution of ARPES data.

1. Louis-François Arsenault et al., Inverse Problems 33, 115007 (2017)

2. R. Fournier, et al., Phys. Rev. Lett. 124, 056401 (2020)

3. Lukas Kades, et al., Phys. Rev. D 102, 096001 (2020)   

Machine learning discovery of new phases in programmable Rydberg quantum simulator snapshots

Machine learning has recently emerged as a promising approach for studying the complex and rich datasets produced by projective measurements of quantum simulators. In particular, data-centric approaches lend to the possibility of automatically discovering structure in the experimental dataset which may be missed by manual inspection. Here, we introduce a unsupervised-supervised hybrid machine learning approach, hybrid-correlation convolutional neural network (Hybrid-CCNN), and apply it to study experimental square-lattice Rydberg atom simulator snapshots to discover two new hidden phases. The initial unsupervised dimensionality reduction and clustering first revealed five distinct phase regions. We then refined these boundaries and identified each phase by training CCNNs with learnable spatial weighting and interpreting their learning. The characteristic spatial weightings and snippets of correlations specifically recognized in each phase captured the nature of quantum fluctuations in the striated phase and mapped out the phase space regions for two previously unknown phases, the rhombic and edge-ordered phases. Hence, we establish that machine learning approaches can enable discoveries of correlated and entangled quantum states hidden in large volumes of experimental snapshot data from finite size quantum simulators.   

Construction of Bayesian mixture model for efficient calculation of electron-hole interaction kernel in quantum dots

This work presents the development and implementation of the Bayesian mixture model for a computationally efficient calculation of electronically excited states in semiconductor quantum dots. In the Bayesian quasiparticle kernel method, the electron-hole interaction kernel is constructed iteratively from real-space sampling of the single-particle states in the quantum dot. For a given particle-hole excitation, the transition density matrix is expressed as a Gaussian Mixture Model and the mixing coefficients are obtained using an iterative Bayesian updating procedure. The quasiparticle kenel was constructed using 2nd-order many-body perturbation theory and was applied for the calculation of exciton binding energies and biexciton binding energies in PbS, CdS, PbSe, and CdSe quantum dots. The quality of the Bayesian quasiparticle kernel was independently tested by comparing the ionization potentials obtained from non-machine-learning based methods for these quantum dots. The results from these calculations highlight the application of Bayesian quasiparticle kernel method as a fast and accurate first-principles method for investigating excited states properties of large chemical systems.    

Autonomous identification of quantum dot device failure modes

Gate-defined quantum dots have appealing attributes as a quantum computing platform, however near-term devices possess a range of possible imperfections. Recent efforts have introduced synthetic noise into simulated data[1,2] and a framework to avoid failures when tuning up nonideal devices [2]. However, resolving certain failure modes requires targeted identification of specific nonidealities. By incorporating into a quantum dot simulator sources of physical imperfections that go beyond noise, we expand the framework proposed in Ref. [2] to identify common defects and enable autonomous targeted device recalibration. Among others, we’re developing systems to autonomously flag devices with unintended dots near the operating regime and for identifying high levels of telegraph noise. These autonomous systems will enable both high throughput screening of quantum dot devices as well as more reliable tuning to a regime suitable for qubit operations.

[1] J. Darulova, et al., Evaluation of synthetic and experimental training data in supervised machine learning applied to charge state detection of quantum dots, arxiv:2005.08131 (2020).

[2] J. Ziegler, et al., Towards Robust Autotuning of Noisy Quantum Dot Devices, arxiv:2108.00043 (2021).   

Machine learning for quantum spin dynamics in and out of equilibrium

We propose a new numerical framework based on machine learning (ML) potentials to enable large-scale adiabatic quantum Landau-Lifshitz-Gilbert (LLG) dynamics simulations of itinerant electron magnets. Such metallic spin systems are central to novel phenomena such as colossal magnetoresistance and spin-transfer torques. Our approach is similar in spirit to the Behler-Parrinello ML scheme that has become a cornerstone of large-scale molecular dynamics method with the accuracy of quantum calculation. Based on the principle of locality for electronic systems, the total electronic energy is partitioned into contributions from individual spins which depend only on the local environment. A neural network model is then trained from exact solutions on small systems to approximate the complex dependence of the local energy on the neighborhood spin configuration. We further develop a novel descriptor to ensure the spin rotation symmetry as well as the discrete lattice symmetry. Our work opens new avenues for using deep-learning models to simulate and understand large-scale dynamical phenomena in functional magnetic systems.   

Automated derivation of effective models for quantum impurity models

The theoretical description of quantum transport through nanodevices such as molecular junctions necessitates the formulation of models that are sufficiently complex to capture strong electronic interactions and orbital/chemical structure, but simple enough to be treated with methods like the Numerical Renormalisation Group (NRG). The sheer diversity of different molecules requires extremely flexible effective models, capable of faithfully representing the properties of such systems. To overcome these difficulties we introduce a Machine Learning algorithm that combines convex and non-convex optimization to automatically derive a symmetry-inspired effective impurity model, that is simple enough to be simulated using NRG. The resulting model can be used to carry out highly accurate conductance calculations, which we benchmark against brute-force calculations for the simplest systems. The methodology will allow an accurate treatment of larger strongly correlated systems, beyond present capabilities.   

Application of Variational Autoencoder to Detect Critical Points of Anisotropic Classical Model

The macroscopic properties of a physical system change at a phase transition. In most instances, the phase is identified using an order parameter consistent with the symmetry of the underlying Hamiltonian. We use recent advances in Machine Learning, in particular Autoencoders, to detect a phase transition just by identifying changes in the patterns of Quantum Monte Carlo data across the transition region, and without explicitly constructing any order parameter. We generalize previous studies on the application of variational autoencoders to the anisotropic two-dimensional Ising model. We identify the phase diagram for a wide range of anisotropic couplings and temperatures via a variational autoencoder without the explicit construction of an order parameter. Our phase diagram agrees with the one produced using the self-duality property of the model. Considering that the partition function of d + 1-dimensional anisotropic models can be mapped to that of the d-dimensional quantum spin models, this study provides numerical evidence that a variational autoencoder can be applied to analyze quantum systems.