Session X32: Quantum Machine Learning III

Live

We introduce the bQCNN, a variation of the quantum convolutional neural network (QCNN) in which outcomes from mid-circuit measurements of subsets of qubits inform subsequent quantum gate operations. This leads to a classical branching structure in which each branch contains its own set of trainable parameterized entangling gates, resulting in significantly more parameters as compared to a standard QCNN circuit of the same depth. We demonstrate classification tasks in which the bQCNN significantly outperforms a comparable QCNN of the same circuit depth. Using results from noisy simulations, we discuss the advantages that mid-circuit-measurement based circuits can offer as variational ansätze in NISQ devices.   

Live

Nonlocality lies at the heart of many striking features of quantum states such as entanglement. The Greenberger-Horne-Zeilinger (GHZ) states and Cluster states are known as an important category of highly entangled quantum states. They play key roles in various quantum-based technologies and are particularly of interest in benchmarking noisy quantum hardwares. A novel quantum inspired generative model known as Born Machine which leverages on probabilistic nature of quantum physics has shown a great success in learning classical and quantum data over tensor network (TN) architecture. To this end, we investigate the training of the Born Machine for learning both local and nonlocal data encoded in GHZ and Cluster states over various tensor network architectures. Our result indicates that gradient-based training schemes over TN Born Machine fails to learn the nonlocal information of the coherent superposition (or parity) of the GHZ state. Finally, we adapt a gradient free training algorithm similar to Density Matrix Renormalization Group. This opens a new direction of adapting quantum inspired gradient free training schemes in learning highly entangled and other exotic quantum states.   

Live

Machine learning provides effective methods for identifying topological features [1]. We show that unsupervised manifold learning can successfully retrieve topological quantum phase transitions [1]. We have also developed [2] machine learning-inspired quantum state tomography based on neural-network representations of quantum states. We also consider conditional generative adversarial networks (CGANs) to QST [3]. We demonstrate [4] that artificial neural networks can simulate first-principles calculations of extended materials.

[1] Y. Che, C. Gneiting, T. Liu, F. Nori, Topological Quantum Phase Transitions Retrieved from Manifold Learning, Phys. Rev. B 102, 134213 (2020).
[2] A. Melkani, C. Gneiting, F. Nori, Eigenstate extraction with neural-network tomography, Phys. Rev. A 102, 022412 (2020).
[3] S. Ahmed, C.S. Munoz, F. Nori, A.F. Kockum, Quantum State Tomography with Conditional Generative Adversarial Networks, (2020). [arXiv]
[4] N. Yoshioka, W. Mizukami, F. Nori, Neural-Network Quantum States for the Electronic Structure of Real Solids, (2020). arXiv
[5] K. Bartkiewicz, et al., Experimental kernel-based quantum machine learning in finite feature space, Sci. Rep. 10, 12356 (2020).   

Live

Variational quantum circuits (VQCs) built upon noisy intermediate-scale quantum (NISQ) hardware, in conjunction with classical processing, constitute a promising architecture for quantum simulations, classical optimization, and machine learning. However, the required VQC depth to demonstrate a quantum advantage overclassical schemes is beyond the reach of available NISQ devices. Supervised learning assisted by an entangledsensor network (SLAEN) is a distinct paradigm that harnesses VQCs trained by classical machine learning algorithms to tailor multipartite entanglement shared by the sensors for solving practically useful data processing problems. Here, we report the first experimental demonstration of SLAEN and show an entanglement-enabled reduction in the error probability for classification of multidimensional radio-frequency signals. Our work paves a new route for quantum-enhanced data processing and its applications in the NISQ era.   

Live

A key open question in quantum computing is whether quantum algorithms can offer significant advantage over classical algorithms for tasks of practical interest. Probing classical computing limits in simulating quantum systems is one important route to address this question. We introduce a method to classically simulate quantum circuits made of several layers of parameterized gates, a key component of variational algorithms suitable for near-term quantum computers. Our approach is based on a neural-network parameterization of the many-qubit wave function, focusing on states relevant for the Quantum Approximate Optimization Algorithm (QAOA). We reach 54 qubits and QAOA depth of 4 without requiring large-scale computational resources. When possible, we compare obtained states with outputs of exact simulators and find good approximations for cost function values and state vectors. For larger qubit counts, our approach provides accurate QAOA simulations at previously unexplored regions of its parameter space, and to benchmark the next generation of experiments in the Noisy Intermediate-Scale Quantum era. (arXiv:2009.01760)   

Live

Robust control of a quantum system is fundamental to studying those systems or performing quantum simulation or computation. Reinforcement learning (RL) offers promising alternatives to existing methods for quantum control. We compare RL algorithms to gradient ascent pulse engineering (GRAPE) for both state-to-state transfer operations as well as the design of desired unitary operations on single- and two-qubit systems. GRAPE algorithms perform well when the system Hamiltonian is well-known, and when any uncertainties can be well parametrized a priori. On the other hand, RL algorithms, by treating the system’s dynamics as a black box and only receiving partial observations and reward signals from the system, have the potential to provide robust control of larger systems with more complex sources of error. The application of RL to Hamiltonian engineering of many-spin systems for quantum simulation and sensing is also considered.   

Live

Recent studies of the classification of entangled states have utilized aspects of machine learning such as neural networks. However, the number of features (or observables) taken as input into such systems required to provide correct inference often grow to the number required for full state tomography.

Here, we show a correspondence between linear support vector machines (SVMs) and entanglement witnesses, and use this correspondence to generate entanglement witnesses for bipartite and tripartite qubit (and qudit) target states.

An SVM allows for the construction of a hyperplane that clearly delineates between separable states and the target state; this hyperplane is essentially a weighted sum of observables (‘features’) whose weights are adjusted during the training of the SVM. In contrast to other methods such as deep neural nets, the training of an SVM is a convex optimization problem and results in an ‘optimal’ solution every time. We show that SVMs are flexible enough to allow us to rank features, and to reduce the number of features systematically while bounding the inference error. This programmatic approach will allow us to streamline the detection of entangled states in experiment.   

Live

As we enter the age of Artificial Intelligence (AI) and Noisy Intermediate-Scale Quantum Computing (NISQ), there has been an increased interest in applying machine learning models to quantum physics. Most applications of AI in quantum mechanics use supervised learning models such as Recurrent Neural Networks (RNN) to predict various quantum properties. However, these models are essentially performing curve fitting and have not learned the underlying dynamics found in a quantum system. In this talk, we describe the application of generative models using neural ODEs to quantum dynamics, which we show, can learn the underlying quantum dynamics and can extrapolate well beyond the training regime when performing reconstructions. Furthermore, random samples from the model satisfy the Heisenberg uncertainty principle. We apply our model to closed and open quantum system dynamics, showing that the model can distinguish between the dynamics of pure and mixed states. We demonstrate, for each hamiltonian it has trained on, the model learns an interpretable representation of the Hilbert space.   

Live

Recent work has shown that quantum annealing for machine learning, referred to as QAML, can perform comparably to state-of-the-art machine learning methods with a specific application to Higgs boson classification. We propose QAML-Z, a novel algorithm that iteratively zooms in on a region of the energy surface by mapping the problem to a continuous space and sequentially applying quantum annealing to an augmented set of weak classifiers. Results on a programmable quantum annealer show that QAML-Z matches classical deep neural network performance at small training set sizes and reduces the performance margin between QAML and classical deep neural networks by almost 50% at large training set sizes, as measured by area under the ROC curve. The significant improvement of quantum annealing algorithms for machine learning and the use of a discrete quantum algorithm on a continuous optimization problem both opens a new class of problems that can be solved by quantum annealers and suggests the approach in performance of near-term quantum machine learning towards classical benchmarks.   

Live

Using neural network architectures that employ quantum variational Monte Carlo methods has opened up a new method of studying quantum many body systems. We discuss previous work in using a deep convolutional neural network for studying a 1D SU(N) spin chain, and our use of Importance Sampling Gradient Optimization (ISGO) method to speed up the learning from the Variational Quantum Monte Carlo. We further discuss how symmetries of this spin-chain model play a role in the training and how they can be exploited to accelerate the training. Finally, we compare the neural network to other families of wavefunction ansatzes.   

Not Participating

The expected speedup of quantum algorithms on near-term quantum processors as well as the resource requirements for achieving quantum fault-tolerance relies on the fidelity of gate operations on available qubits. Traditionally, quantum control and mitigation protocols have been obtained via optimizing control trajectories by assuming simple a priori error models that impact the qubits, or the amplitude, frequency, and phase of the driving control fields. Although these models have been instrumental in achieving individual 1,2-qubit gates with average fidelities of 99-99.9%, however various sources of noise get mixed up and accumulated in running quantum circuits with larger numbers of qubits. Here we propose an "end-to-end" framework, which instead starts from direct experimental observations to obtain optimal quantum control trajectories that are sufficiently resilient to all sources of errors. We achieve this by combining existing quantum control and characterization techniques with the representation and learning power of modern deep learning algorithms. We demonstrate our framework to achieve high fidelity 1,2-qubit gates that are resilient to various sources of noise.   

Live

Learning underlying patterns with unsupervised generative models is a challenging task. Inspired by the probabilistic nature of quantum physics, Born Machines as generative models have shown great success in learning the joint probability distribution of a given dataset. Leveraging on the expressibility and training power of Projected Entangled Pair State (PEPS) networks, we study the capability of our Born Machine with PEPS structure in learning the underlying patterns in the classical Ising model and two dimensional Rydberg atom. Considering that PEPS models may not be easily extended to larger systems with higher bond dimensions, we also investigate the effect of more efficient tensor network contractions such as MPS snake-like and MPS-MPO as well as random contractions on the performance of Born Machine.
Our early results indicate that our PEPS model on the 2D Ising configurations significantly outperforms the MPS snake-like model. We also discuss that in the vicinity of the Ising critical point, the Energy and Magnetization profiles in sampled configurations of the PEPS model slightly deviate from the Monte Carlo samples. We argue that this is due to the emergence of long-range spin correlations close to the Ising critical point.   

Live

The use of advanced quantum neuron models for pattern recognition applications require fault tolerant quantum coomputing. Such models are challenging to implement on currently available quantum processors due to noise introduced by non-local operations. We propose an alternative quantum perceptron (QP) model that uses a reduced number of multi-qubit gates and is less susceptible to quantum errors than other existing models. We demonstrate the performance of the proposed model through an implemention of the QP on a few qubits using an actual quantum computer. The proposed QP uses an N-ary encoding of the binary input data characterizing the patterns. We develop various hybrid (quantum-classical) training procedures for simulating the learning process of the QP and test their efficiency. We also provide a comparative analysis of the required quantum error corrections for scalability.   

On Demand

Deep Learning (DL) has empowered computers with superior performance in modern Natural Language Processing (NLP) tasks, such as sentiment analysis and machine translation. Even for texts with long-range correlations such as sequences of characters in Wikipedia, DL can effectively express the power-law decay in the mutual information between two distant characters [1]. Despite empirical successes, its intrinsic non-linearity complicates the analysis of algorithmic behaviours. Which network architectures and how many parameters are essential to reproduce long-range correlations are important yet theoretically challenging questions to tackle. Here, we attempt to provide systematic answers through the mapping between DL and its matrix product state (MPS) counterpart [2]. By recasting DL as MPS, we show that the number of parameters required to achieve high performance in sentiment analysis, and to reproduce power-law decay in the mutual information in Wikipedia texts, can be efficiently extracted from the entanglement entropy in the dual MPS. Our work utilises tools in many-body quantum physics to resolve explainability issues of NLP, and more generally of sequence modelling.

[1] H. W. Lin, M. Tegmark, Entropy, 19, 299 (2017)
[2] Y. Levine et al. Phys. Rev. Lett, 122, 065301 (2019)   

On Demand

The principal limiting factor in scale-up of quantum computers is not the number of qubits, but the entangling gate infidelity. Current QPU bring-up relies on a large number of tailored routines to extract individual model parameters (characterization), and the huge effort required inevitably this leads to incomplete characterization, partial insight into the sources of error, and threfore slow progress in improving gate fidelities.

To rectify the situation, we provide a new integrated open-source tool-set for Control, Calibration and Characterization (C3) [1]. We present a methodology to combine these tools to find a quantitatively accurate system model, high-fidelity gates and an approximate error budget.

In this talk I shall present the overall concept, and insights into future directions. Follow-up talks by Nicolas Wittler and Federico Roy will expand some of the details and walk through an example of C3 usage.

[1] Wittler, N., Roy, F., Pack, K. ... & Machnes, S. (2020). An integrated tool-set for Control, Calibration and Characterization of quantum devices applied to superconducting qubits. arXiv:2009.09866