07/12/2023
By Emery Doucet

The Kennedy College of Sciences, Department of Physics & Applied Physics invites you to attend a Ph.D. dissertation defense by Emery Doucet on “Entanglement Stabilization with Linear Dissipation.”

Degree: Doctoral
Date: Monday July 24 2023
Time: 1 p.m.
Location: Olney 204

Committee Chair:
Prof. Archana Kamal, Department of Physics & Applied Physics, University of Massachusetts Lowell

Committee Members:

  • Prof. Viktor Podolskiy, Department of Physics & Applied Physics, University of Massachusetts Lowell
  • Prof. Timothy Cook, Department of Physics & Applied Physics, University of Massachusetts Lowell

Abstract

Quantum information processing as a field has grown greatly in recent years, seeking to exploit the uniquely quantum properties of entangled states to provide theoretical and practical advantages in a number of applications ranging from computation to communication to metrology and more. A key problem which must be solved for most of these applications is that of efficiently preparing robust non-classical states with high fidelity. This thesis focuses on one particularly elegant method for solving this problem in multi-qubit systems, based around the exploitation of dissipation. Typically dissipation is an unwanted feature to be avoided, as it leads to decoherence which destroys the fragile correlations underlying the power of quantum computation. However, if it can be introduced in a controlled manner it can be harnessed as a resource instead. This is termed dissipation engineering, and its application to the problem of state preparation is dissipative state stabilization. By coupling a set of qubits to an engineered environment in a controlled way, it is possible to cause those qubits to relax to a desired target state and subsequently to remain in that state indefinitely. In this thesis a variety of dissipative stabilization protocols are presented alongside their underlying design rules and their performance.
The approach to dissipation engineering taken for all protocols presented herein is straightforward and accessible to current experiments in a variety of architectures. Specifically, it allows the implementation of any arbitrary dissipator described by a linear jump operator through highly-tunable parametric interactions between a set of target qubits and an auxiliary decaying degree of freedom.

We begin by showing how a straightforward application of this approach to the problem of Bell state stabilization can only work if one is prepared to stabilize a state with some inherent error, which necessarily leads to a trade-off between the stabilization fidelity and time. To bypass this issue, we study a number of possible variations. One variation is based around a combination of parametric and dispersive interactions which leads to conditional qubit-qubit interactions. We show that through the use of these interactions it is possible to construct stabilization protocols for two-qubit Bell and three-qubit GHZ states, which could allow unit fidelity stabilization in an idealized case with no decoherence. Unfortunately, these protocols pose difficulties for implementation on current or near-term experimental hardware, as they are sensitive to the presence of off-resonant terms which cannot be made sufficiently small as to allow high-fidelity stabilization. Instead, we show that by expanding each two-level qubit to a multilevel qudit it is possible to construct a protocol which can stabilize Bell states while facing no impediment to experimental implementation and promising better performance even in the ideal case. The protocol based on these ideas presented in this thesis was designed in parallel with an implementation performed by circuit-QED experimenters which was able to achieve the fastest and highest-fidelity Bell state stabilization shown to date. We present a number of extensions to this protocol as well, both for improving its performance in stabilizing Bell states and for extending it to stabilizing a more general entangled qudit state -- the absolutely maximally entangled state of two qudits with arbitrarily many levels.

An important consideration with any qubit state preparation protocol is its scalability for the preparation of states of large entangled states comprising many qubits. This thesis tackles this problem by first considering the conceptual question of what is meant by a ``scalable'' state preparation protocol in the context of dissipative state stabilization. Inspired by the well-studied notions of complexity in the quantum circuit model, we provide three criteria which any stabilization protocol must satisfy to be scalable. We then discuss a novel scalable protocol for N-qubit W state stabilization employing linear dissipation and parametric Hamiltonians whose resource usage and performance metrics all scale polynomially with N. We find that by employing a ``modular'' approach to dissipation engineering with a number of overlapping few-qubit dissipators provides an exponential improvement in the scaling of the stabilization time with the number of qubits over the more typical ``global'' approach with a single dissipator acting on all qubits.