[month] [year]

Utkarsh Azad – Computational Problems

Utkarsh Azad received his MS Dual Degree in Computational Natural Sciences (CNS). His research work was supervised by Prof. Harjinder Singh. Here’s a summary of  his research work on A Fine Grained Approach to Computational Problems on Noisy Intermediate Scale Quantum Hardware:

The current generation of quantum computers is widely referred to as noisy intermediate-scale quantum (NISQ) computers. These devices are predecessors of fault-tolerant quantum computers, which are speculated to perform calculations that will be intractable for even the most powerful classical supercomputers. However, unlike fault-tolerant hardware, the computational capabilities of the near-term hardware are primarily affected by their limited qubit count, restrictive hardware topology, and lack of error correction. A natural question arises whether there are any practical applications for these NISQ devices in performing calculations of independent interest. This dissertation focuses on employing NISQ hardware for solving computational problems more efficiently. We begin by posing this problem into a series of key research questions that are built on understanding the noises present in these devices and designing software to tailor algorithms to be more noise resilient. Our major contributions are then based on answering each of these questions individually. In the beginning, we give a didactic introduction to quantum computation and NISQ architecture along with the self-contained theory for hybrid quantum-classical algorithms. We also provide a comprehensive review of the potential areas for applications of these hybrid algorithms and the field of quantum error mitigation. We then present Aakash, a software simulator based on IBM Qiskit, that models a noisy quantum processor based on density matrix formalism. This simulator is currently being used as a backend for the QSim: Quantum Computer Simulator Toolkit, one of India’s first initiatives under the Quantum-Enabled Science & Technology (QuEST) program to address the common challenge of advancing the quantum computing research frontiers in India. Furthermore, we showcase formulations for applications related to combinatorial optimization and quantum chemistry that can be used to solve problems using variational quantum algorithms such as quantum approximate optimization algorithm (QAOA) and variational quantum eigensolver (VQE), respectively. We also perform noise analysis for these algorithms, characterizing how different types of noise-based errors affect their performance. Our simulation of QAOA provides insightful data about the effect of errors due to amplitude decay, decoherence, thermalization, and logic gate imprecision, which will help in designing specific quantum hardware for variational quantum algorithms that will allow us to approximately solve NP problems more efficiently. We further use a VQE-based method to calculate molecular energy derivatives on a quantum computer for both ground state energy and excited state energies up to the second order. Other than minimum energy configuration search for H2 molecule, estimation of molecular response properties such as dipole moment and polarizability, we also pursue transition state search for the reaction H2+H↔H+H2. Our variational method gives results in complete agreement with those obtained using full configuration interaction (FCI) values. We also present qLEET, an open-source library for exploring loss landscape, expressibility, entangling capability, and training trajectories of noisy parameterized quantum circuits. It supports quantum circuits and noise models built using popular quantum computing libraries such as Qiskit, Cirq and Pyquil while providing opportunities to design new hybrid algorithms by utilizing intuitive insights from the ansatz capability and structure of the loss landscape. Finally, we show how NISQ hardware can be designed and utilized in a more circuit-centric fashion by studying the dependence of the circuit size, circuit depth on the interaction and connection between different qubits present in quantum hardware. Throughout our work, we have not performed any quantum computations beyond the reach of the current capabilities of classical computers. Still, we do address many implementation challenges that must be overcome in such an endeavor, including circuit optimization, efficient compilation, and error mitigation. We conclude by providing an optimistic outlook towards the incremental utilization of quantum computers and explicitly stating how our work could help with it.