Dheeraj Peddireddy

Variational Quantum Algorithms (VQAs) are a central class of hybrid quantum–classical methods for optimization on noisy intermediate-scale quantum (NISQ) hardware. Their scalability is constrained by the cost of gradient evaluation via the parameter-shift rule, whose complexity grows with both the number of circuit parameters and Pauli terms in the Hamiltonian, quickly dominating runtime for deep circuits or large qubit counts. We present TREV (Tensor-Ring Evaluated Variational algorithms), a Python library that accelerates VQA simulation through batched parameter evaluation within tensor-ring state representations . By amortizing contraction and sampling costs across multiple parameter shifts, TREV exploits GPU-parallel tensor contractions to achieve substantial runtime reduction with tunable memory–throughput trade-offs. Implemented in PyTorch, the framework supports both deterministic contraction-based and stochastic sampling-based evaluations. Benchmarks on Max-Cut, Traveling Salesperson Problem (TSP), and molecular ground-state energy estimation (H ₂ , H ₄ , LiH, BeH ₂ ) show comparable accuracy and up to 97% runtime reduction over sequential evaluation, while outperforming PennyLane, TensorCircuit, and Qiskit in runtime scalability. The chemistry benchmarks further demonstrate that TREV handles arbitrary Pauli Hamiltonians beyond QUBO formulations, broadening its applicability to quantum chemistry.

Bayesian optimization is a powerful framework for global search, using maximum a posteriori updates instead of simulated annealing. We cast it as a multi-armed bandit problem with a Gaussian process (GP) for the payoff function. Action selections rely on upper confidence bound (UCB) or expected improvement (EI). Prior works with GPs faced challenges for large iteration horizons ( T ) due to cubic scaling in posterior computation. To address this, we propose a simple thresholding: incorporating an action into the GP posterior only when its conditional entropy surpasses ϵ . Doing so permits us to precisely characterize the tradeoff 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 $\textbf{Reg}_T/T \rightarrow \mathcal{O}(\epsilon)$ as $T\rightarrow \infty$ . Experiments demonstrate state-of-the-art accuracy and complexity trade-offs for GP bandit algorithms in global optimization, highlighting the benefits of compressed GPs in bandit settings.

Variational quantum algorithms, especially quantum approximate optimization and the variational quantum eigensolver (VQE), have demonstrated 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 the 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.

In this article, we present a novel 3-D descriptor, improved dexel representation (IDR), which assists to input holistic information from an engineering computer-aided design (CAD) model to convolutional neural network (CNN) based manufacturing applications. The IDR carries the model’s position, size, and surface information, which not only provides high resolution to small-scale local (machining) features, but also has the potential to reconstruct the original CAD model. Data conversion algorithms between IDR and other CAD models (mesh and NURBS model) are efficient. CNNs with IDR input can largely improve the prediction accuracy compared to other 3-D descriptors, which reaches 98.8% in the modified machining-process-identifier dataset and 100% on the FeatureNet style 3-class dataset. IDR benefits both the manufacturing industry and other CAD-related deep learning applications in engineering fields.