Debanjan Konar, Dheeraj Peddireddy, Vaneet Aggarwal et al.
Quantum machine learning researchers often rely on incorporating Tensor Networks (TN) into Deep Neural Networks (DNN) and variational optimization. However, the standard optimization techniques used for training the contracted trainable weights of each model layer suffer from the correlations and entanglement structure between the model parameters on classical implementations. To address this issue, a multi-layer design of a Tensor Ring optimized variational Quantum learning classifier (Quan-TR) comprising cascading entangling gates replacing the fully connected (dense) layers of a TN is proposed, and it is referred to as Tensor Ring optimized Quantum-enhanced tensor neural Networks (TR-QNet). TR-QNet parameters are optimized through the stochastic gradient descent algorithm on qubit measurements. The proposed TR-QNet is assessed on three distinct datasets, namely Iris, MNIST, and CIFAR-10, to demonstrate the enhanced precision achieved for binary classification. On quantum simulations, the proposed TR-QNet achieves promising accuracy of $94.5\%$, $86.16\%$, and $83.54\%$ on the Iris, MNIST, and CIFAR-10 datasets, respectively. Benchmark studies have been conducted on state-of-the-art quantum and classical implementations of TN models to show the efficacy of the proposed TR-QNet. Moreover, the scalability of TR-QNet highlights its potential for exhibiting in deep learning applications on a large scale. The PyTorch implementation of TR-QNet is available on Github:https://github.com/konar1987/TR-QNet/
Variational Quantum algorithms, especially Quantum Approximate Optimization and Variational Quantum Eigensolver (VQE) have established their potential to provide computational advantage in the realm of combinatorial optimization. However, these algorithms suffer from classically intractable gradients limiting the scalability. This work addresses the scalability challenge for VQE by proposing a classical gradient computation method which utilizes the parameter shift rule but computes the expected values from the circuits using a tensor ring approximation. The parametrized gates from the circuit transform the tensor ring by contracting the matrix along the free edges of the tensor ring. While the single qubit gates do not alter the ring structure, the state transformations from the two qubit rotations are evaluated by truncating the singular values thereby preserving the structure of the tensor ring and reducing the computational complexity. This variation of the Matrix product state approximation grows linearly in number of qubits and the number of two qubit gates as opposed to the exponential growth in the classical simulations, allowing for a faster evaluation of the gradients on classical simulators.
Quantum circuit routing is a key step in compiling programs for noisy intermediate-scale quantum processors. Routes that appear efficient by standard overhead metrics can still lose fidelity when they pass through poorly calibrated couplers. We study a calibration-aware graph reinforcement-learning router that uses same-day IBM Heron r2 calibration data to choose hardware-edge SWAPs. We train the policy with proximal policy optimization and evaluate it with exact simulated fidelity across nine Munich Quantum Toolkit (MQT) Bench circuits and three calibration snapshots. Across these evaluations, pooled mean exact fidelity is $0.727$, compared with $0.440$ for SABRE-best20 and $0.481$ for target-aware SABRE. Fidelity gains come with higher routed two-qubit counts and are concentrated in the 5q and 8q circuit families; under the fixed tree action graph, all 10q families favor SABRE-best20. Overall, our results show that calibration-aware learned routing can improve fidelity beyond gate-count-driven compilation.
Adaptive Hamiltonian learning is central to calibrating and characterizing quantum devices. In an adaptive controller, choosing the next experiment is itself a computation. Bayesian design rules are recomputed after every posterior update, and that step can take seconds. Across hundreds of shots, those seconds become a significant wall-clock cost for adaptivity. We introduce SymQNet, an amortized reinforcement-learning approach for low-latency adaptive Hamiltonian learning. SymQNet learns a posterior-conditioned acquisition policy offline, then uses a fast policy forward pass online while retaining Bayesian posterior feedback. On transverse-field Ising benchmarks, SymQNet substantially reduces acquisition latency relative to bounded Fisher-information search and bounded two-step Bayesian active learning by disagreement (BALD). At five qubits, it reduces acquisition-only decision latency by $47.1\times$ and $72.6\times$ relative to these online baselines; at twelve qubits, full simulated steps take $1.02$ s for SymQNet versus $13.27$ s for bounded two-step BALD. Overall, we show that learned acquisition can make adaptive Hamiltonian learning practical for repeated low-latency workloads.
In recent times, Variational Quantum Circuits (VQC) have been widely adopted to different tasks in machine learning such as Combinatorial Optimization and Supervised Learning. With the growing interest, it is pertinent to study the boundaries of the classical simulation of VQCs to effectively benchmark the algorithms. Classically simulating VQCs can also provide the quantum algorithms with a better initialization reducing the amount of quantum resources needed to train the algorithm. This manuscript proposes an algorithm that compresses the quantum state within a circuit using a tensor ring representation which allows for the implementation of VQC based algorithms on a classical simulator at a fraction of the usual storage and computational complexity. Using the tensor ring approximation of the input quantum state, we propose a method that applies the parametrized unitary operations while retaining the low-rank structure of the tensor ring corresponding to the transformed quantum state, providing an exponential improvement of storage and computational time in the number of qubits and layers. This approximation is used to implement the tensor ring VQC for the task of supervised learning on Iris and MNIST datasets to demonstrate the comparable performance as that of the implementations from classical simulator using Matrix Product States.
Xingyu Fu, Fengfeng Zhou, Dheeraj Peddireddy et al.
In this work, we present a Boundary Oriented Graph Embedding (BOGE) approach for the Graph Neural Network (GNN) to serve as a general surrogate model for regressing physical fields and solving boundary value problems. Providing shortcuts for both boundary elements and local neighbor elements, the BOGE approach can embed structured mesh elements into the graph and performs an efficient regression on large-scale triangular-mesh-based FEA results, which cannot be realized by other machine-learning-based surrogate methods. Focusing on the cantilever beam problem, our BOGE approach cannot only fit the distribution of stress fields but also regresses the topological optimization results, which show its potential of realizing abstract decision-making design process. The BOGE approach with 3-layer DeepGCN model \textcolor{blue}{achieves the regression with MSE of 0.011706 (2.41\% MAPE) for stress field prediction and 0.002735 MSE (with 1.58\% elements having error larger than 0.01) for topological optimization.} The overall concept of the BOGE approach paves the way for a general and efficient deep-learning-based FEA simulator that will benefit both industry and design-related areas.
Amrit Singh Bedi, Dheeraj Peddireddy, Vaneet Aggarwal et al.
Bayesian optimization is a framework for global search via maximum a posteriori updates rather than simulated annealing, and has gained prominence for decision-making under uncertainty. In this work, we cast Bayesian optimization as a multi-armed bandit problem, where the payoff function is sampled from a Gaussian process (GP). Further, we focus on action selections via upper confidence bound (UCB) or expected improvement (EI) due to their prevalent use in practice. Prior works using GPs for bandits cannot allow the iteration horizon $T$ to be large, as the complexity of computing the posterior parameters scales cubically with the number of past observations. To circumvent this computational burden, we propose a simple statistical test: only incorporate an action into the GP posterior when its conditional entropy exceeds an $ε$ threshold. Doing so permits us to precisely characterize the trade-off between regret bounds of GP bandit algorithms and complexity of the posterior distributions depending on the compression parameter $ε$ for both discrete and continuous action sets. To best of our knowledge, this is the first result which allows us to obtain sublinear regret bounds while still maintaining sublinear growth rate of the complexity of the posterior which is linear in the existing literature. Moreover, a provably finite bound on the complexity could be achieved but the algorithm would result in $ε$-regret which means $\textbf{Reg}_T/T \rightarrow \mathcal{O}(ε)$ as $T\rightarrow \infty$. Experimentally, we observe state of the art accuracy and complexity trade-offs for GP bandit algorithms applied to global optimization, suggesting the merits of compressed GPs in bandit settings.