arXiv subjects

Aadithya Ganeshram

Publications and source records attributed to Aadithya Ganeshram.

3 recordsLinked to original sources

arXiv2025

Walking through Hilbert Space with Quantum Computers

Computations of chemical systems' equilibrium properties and non-equilibrium dynamics have been suspected of being a "killer app" for quantum computers. This review highlights the recent advancements of quantum algorithms tackling complex sampling tasks in the key areas of computational chemistry: ground state, thermal state properties, and quantum dynamics calculations. We review a broad range of quantum algorithms, from hybrid quantum-classical to fully quantum, focusing on the traditional Monte Carlo family, including Markov chain Monte Carlo, variational Monte Carlo, projector Monte Carlo, path integral Monte Carlo, etc. We also cover other relevant techniques involving complex sampling tasks, such as quantum-selected configuration interaction, minimally entangled typical thermal states, entanglement forging, and Monte Carlo-flavored Lindbladian dynamics. We provide a comprehensive overview of these algorithms' classical and quantum counterparts, detailing their theoretical frameworks and discussing the potentials and challenges in achieving quantum computational advantages.

quant-ph↗

arXiv2023

Growth reduction of similarity transformed electronic Hamiltonians in qubit space

Accurately solving the electronic structure problem through the variational quantum eigensolver (VQE) is hindered by the available quantum resources of current and near-term devices. One approach to relieving the circuit depth requirements for VQE is to "pre-process" the electronic Hamiltonian by a similarity transformation incorporating some degree of electronic correlation, with the remaining correlation left to be addressed by the circuit ansatz. This often comes at the price of a substantial increase in the number of terms to measure in the similarity transformed Hamiltonian. In this work, we propose an efficient approach to sampling elements from the complete Pauli group for $N$ qubits which minimize the onset of new terms in the transformed Hamiltonian, while facilitating substantial energy lowering. We benchmark the growth-mitigating generator selection technique for ground state energy estimations applied to models of the H$_4$, N$_2$ and H$_2$O molecular systems. It is found that utilizing a selection procedure which obtains the growth-minimizing generator from the set of operators with maximal energy gradient is the most competitive approach to reducing the onset of Hamiltonian terms while achieving systematic energy lowering of the reference state.

quant-ph↗

arXiv2022

Deterministic improvements of quantum measurements with grouping of compatible operators, non-local transformations, and covariance estimates

Obtaining the expectation value of an observable on a quantum computer is a crucial step in the variational quantum algorithms. For complicated observables such as molecular electronic Hamiltonians, a common strategy is to present the observable as a linear combination of measurable fragments. The main problem of this approach is a large number of measurements required for accurate sampling of the observable's expectation value. We consider several partitioning schemes based on grouping of commuting multi-qubit Pauli products with the goal of minimizing the number of measurements. Three main directions are explored: 1) grouping commuting operators using the greedy approach, 2) involving non-local unitary transformations for measuring, and 3) taking advantage of compatibility of some Pauli products with several measurable groups. The last direction gives rise to a general framework that not only provides improvements over previous methods but also connects measurement grouping approaches with recent advances in techniques of shadow tomography. Following this direction, we develop two new measurement schemes that achieve a severalfold reduction in the number of measurements for a set of model molecules compared to previous state-of-the-art methods.

quant-ph↗