Theoretical aspects of ultra-cold fermions in the presence of artificial spin-orbit coupling

Main purpose of this thesis is to present a discussion of the effects of artificial spin-orbit coupling and Zeeman fields in fermionic ultra-cold atoms. Part of the work described here is inspired by the experimental realization of artificial spin-orbit coupling (SOC) in the fermionic isotope $^{40}$K using a Raman technique, which was done by NIST group recently. The first aspect investigated is the formation of two-body bound states of fermions when artificial spin-orbit coupling and artificial Zeeman fields are present. These bound-states are analyzed for two-hyperfine-state fermions in free space and in a harmonically confining potential. The second aspect explored is the study of spectroscopic and thermodynamic properties of three-hyperfine-state fermions. These properties are investigated as a function of spin-orbit coupling and Zeeman fields for non-interacting atoms, but when atom-atom interactions are also included, the many-body system consisting of three-hyperfine-state fermions can exhibit exotic superfluid phases.Ph.D

Preparing quantum many-body scar states on quantum computers

Quantum many-body scar states are highly excited eigenstates of many-body systems that exhibit atypical entanglement and correlation properties relative to typical eigenstates at the same energy density. Scar states also give rise to infinitely long-lived coherent dynamics when the system is prepared in a special initial state having finite overlap with them. Many models with exact scar states have been constructed, but the fate of scarred eigenstates and dynamics when these models are perturbed is difficult to study with classical computational techniques. In this work, we propose state preparation protocols that enable the use of quantum computers to study this question. We present protocols both for individual scar states in a particular model, as well as superpositions of them that give rise to coherent dynamics. For superpositions of scar states, we present both a system-size-linear depth unitary and a finite-depth nonunitary state preparation protocol, the latter of which uses measurement and postselection to reduce the circuit depth. For individual scarred eigenstates, we formulate an exact state preparation approach based on matrix product states that yields quasipolynomial-depth circuits, as well as a variational approach with a polynomial-depth ansatz circuit. We also provide proof of principle state-preparation demonstrations on superconducting quantum hardware.Comment: 20 Pages, 15 Figures, 2 Tables. V2: corrected typo

Some aspects of noise in binary classification with quantum circuits

We formally study the effects of a restricted single-qubit noise model inspired by real quantum hardware, and corruption in quantum training data, on the performance of binary classification using quantum circuits. We find that, under the assumptions made in our noise model, that the measurement of a qubit is affected only by the noises on that qubit even in the presence of entanglement. Furthermore, when fitting a binary classifier using a quantum dataset for training, we show that noise in the data can work as a regularizer, implying potential benefits from the noise in certain cases for machine learning problems.Comment: 11 pages, 2 figure

Preparing quantum-many body scars on a quantum computer

Quantum many-body scar states are highly excited eigenstates of many-body systems that exhibit atypical entanglement and correlation properties relative to typical eigenstates at the same energy density. Scar states also give rise to infinitely long-lived coherent dynamics when the system is prepared in a special initial state having finite overlap with them. Many models with exact scar states have been constructed, but the fate of scarred eigenstates and dynamics when these models are perturbed is difficult to study with classical computational techniques. In this work, we propose state preparation protocols that enable the use of quantum computers to study this question. We present protocols both for individual scar states in a particular model, as well as superpositions of them that give rise to coherent dynamics. For superpositions of scar states, we present both a system-size-linear depth unitary and a finite-depth nonunitary state preparation protocol, the latter of which uses measurement and postselection to reduce the circuit depth. For individual scarred eigenstates, we formulate an exact state preparation approach based on matrix product states that yields quasipolynomial-depth circuits, as well as a variational approach with a polynomial-depth ansatz circuit. We also provide proof of principle state-preparation demonstrations on superconducting quantum hardware.This is a pre-print of the article Gustafson, Erik J., Andy CY Li, Abid Kahn, Joonho Kim, Doga Murat Kurkcuoglu, M. Sohaib Alam, Peter P. Orth, Armin Rahmani, and Thomas Iadecola. "Preparing quantum-many body scars on a quantum computer." arXiv preprint arXiv:2301.08226 (2023). DOI: 10.48550/arXiv.2301.08226, Copyright 2023 The Authors. Posted with permission

Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model

Quantum spin systems may offer the first opportunities for beyond-classical quantum computations of scientific interest. While general quantum simulation algorithms likely require error-corrected qubits, there may be applications of scientific interest prior to the practical implementation of quantum error correction. The variational quantum eigensolver (VQE) is a promising approach to find energy eigenvalues on noisy quantum computers. Lattice models are of broad interest for use on near-term quantum hardware due to the sparsity of the number of Hamiltonian terms and the possibility of matching the lattice geometry to the hardware geometry. Here, we consider the Kitaev spin model on a hardware-native square-octagon qubit connectivity map, and examine the possibility of efficiently probing its rich phase diagram with VQE approaches. By benchmarking different choices of variational ansatz states and classical optimizers, we illustrate the advantage of a mixed optimization approach using the Hamiltonian variational ansatz (HVA). We further demonstrate the implementation of an HVA circuit on Rigetti's Aspen-9 chip with error mitigation.This is a pre-print of the article Li, Andy CY, M. Sohaib Alam, Thomas Iadecola, Ammar Jahin, Doga Murat Kurkcuoglu, Richard Li, Peter P. Orth, A. Barış Özgüler, Gabriel N. Perdue, and Norm M. Tubman. "Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model." arXiv preprint arXiv:2108.13375 (2021). DOI: 10.48550/arXiv.2108.13375. Copyright 2022 The Authors. Posted with permission