Thesis defence

An estimation theoretic approach to quantum realizability problems

This thesis seeks to develop a general method for solving so-called quantum realizability problems, which are questions of the following form under which conditions does there exists a quantum state exhibiting a given collection of properties? The approach adopted by this thesis is to utilize mathematical techniques previously developed for the related problem of property estimation which is concerned with learning or estimating the properties of an unknown quantum state. Our primary result is to recognize a correspondence between (i) property values which are realized by some quantum state, and (ii) property values which are occasionally produced as estimates of a generic quantum state. In Chapter 3, we review the concepts of stability and norm minimization from geometric invariant theory and non-commutative optimization theory for the purposes of characterizing the flow of a quantum state under the action of a reductive group.

In particular, we discover that most properties of quantum states are related to the gradient of this flow, also known as the moment map. Afterwards, Chapter 4 demonstrates how to estimate the value of the moment map of a quantum state by performing a covariant quantum measurement on a large number of identical copies of the quantum state. These measurement schemes for estimating the moment map of a quantum state arise naturally from the decomposition of a large tensor-power representation into its irreducible sub-representations.

Then, in Chapter 5, we prove an exact correspondence between the realizability of a moment map value on one hand and the asymptotic likelihood it is produced as an estimate on the other hand. In particular, by composing these estimation schemes, we derive necessary and sufficient conditions for the existence of a quantum state jointly realizing any finite collection of moment maps. Finally, in Chapter 6 we apply these techniques to the quantum marginals problem which aims to characterize precisely the relationships between the marginal density operators describing the various subsystems of composite quantum state. We make progress toward an analytic solution to the quantum marginals problem by deriving a complete hierarchy of necessary inequality constraints.

Developing a Large-Scale, Programmable Trapped Ion Quantum Simulator with In Situ Mid-Circuit Measurement and Reset

Quantum simulators are a valuable resource for studying complex many-body systems. With their ability to provide near-term advantages, analog quantum simulators show great promise. During the course of my PhD, my aim was to construct a large-scale trapped-ion based analog quantum simulator with several objectives in mind: controllability, minimal external decoherence, an expandable toolkit for quantum simulations, enhanced stability through robust design practices, and pushing the boundaries of error correction.

One of my key achievements is the demonstration of high-fidelity preservation of an “asset” ion qubit while simultaneously resetting or measuring a neighboring “process” qubit located a few microns away. My results show that I achieve a probability of accidental measurement of the asset qubit below 1×10−3 while resetting the process qubit. Similarly, when applying a detection beam on the same neighboring qubit to achieve fast detection times, the probability remains below 4 × 10−3 at a distance of 6 μm. These low probabilities correspond to the preservation of the quantum state of the asset qubit with fidelities above 99.9% for state reset and 99.6% for state measurement.

Additionally, I successfully conduct a dissipative many-body cooling experiment based on reservoir engineering by leveraging site-selective mid-circuit resets. I propose and optimize a protocol utilizing reservoir engineering to efficiently cool the spin state of a subsystem coupled to a reservoir with controlled dissipation. Through analog quantum simulation of this protocol, I am able to demonstrate the lowering of energy within the subsystem.

Furthermore, I thoroughly discuss the design, fabrication, and assembly of a large-scale trapped ion quantum simulator called the Blade trap as part of my PhD work. I highlight the specific design considerations taken to isolate the trapped ions from external disturbances that could introduce errors. Comprehensive testing procedures are presented to evaluate the performance and stability of the Blade trap, which are crucial for assessing the effectiveness of the design. An important milestone I achieve is reaching a base pressure below 9E-13 mbar, demonstrating the successful implementation of techniques to maintain an extremely low-pressure environment ideal for quantum simulation.

Measuring Quantum Correlations of Polarization, Spatial Mode, and Energy-Time Entangled Photon Pairs

Optical quantum technologies have found applications in all facets of quantum information. Single photons are actively being researched for quantum computation, communication, and sensing, due to their robustness against decoherence stemming from their minimal interaction with the environment. For communication and networking applications, specifically, photons are lauded for their speed and coherence over long distances. While clear benefits arise from the lack of photon-environment interaction, measurement and control of all photonic degrees of freedom is made challenging. Each degree of freedom, be it polarization, space, time, or frequency, comes with its own advantages and drawbacks. The potential that single photons bring to future quantum technologies may only be realized by full control over each of these properties of light.

Ablation Loading and Qudit Measurements with Barium Ions

Barium is one of the best ions for performing quantum information in a trapped-ion system. Its long-lived metastable D5/2 state allows for some interesting quantum operations, including the current best state preparation and measurement fidelity in qubits. This metastable state also opens up the possibility of implementing higher dimensional qudits instead of qubits. However, installing a barium metal source in a vacuum chamber has shown to be somewhat of a challenge. Here, we present a loading technique which uses a barium chloride source instead, making it much easier to install. Laser ablation with a high-energy pulsed laser is used to generate neutral atoms, and a two-step photoionization technique is used to selectively load different isotopes of barium in our ion trap. The process of laser ablation and the plume of atoms it generates are characterized, informing us on how to best load ions. Loading is achieved, and selectivity of our method is demonstrated, giving us a reliable way to load ba138 and ba137 ions. The quadrupole transition into the metastable D5/2 state is investigated, with all of the individual transitions successfully found and characterized for ba138 and ba137. Coherent operations are performed on these transitions, allowing us to use them to define a 13-level qudit, on which we perform a state preparation and measurement experiment. The main error source in operations using this transition is identified to be magnetic field noise, and so we present attempts at mitigating this noise. An ac-line noise compensation method is used, which marginally improved the coherence time of the quadrupole transitions, and an additional method of using permanent magnets is proposed for future work. These efforts will help to make trapping barium more reliable, making it an even more attractive option for trapped ion systems. The state preparation and measurement results using the quadrupole transition to the long-lived metastable D52 state establish barium as an interesting platform for performing high-dimensional qudit quantum computing.

Control and Readout of High-Dimensional Trapped Ion Qudits

The trapped ion platform is one of the quantum computing platforms that is at the forefront for realizing large-scale quantum information processing, which is crucial for practically actualizing the advantages of quantum algorithms. Scaling up the trapped ion quantum computing architecture remains a challenge. We explore an alternative avenue in a trapped ion system for increasing the computational Hilbert space other than trapping more ions, which is by increasing the qudit dimension of an ion. Our ion of choice is 137Ba+, which has a rich energy level structure for high-dimensional qudit encoding. Utilizing the additional energy states found in 137Ba+ also comes with non-trivial complexities that require careful considerations, which we have solved and report in this work. We report on a single-shot state measurement protocol which allows qudit encoding in 137Ba+ of up to 25 levels, and demonstrate state preparation and measurement of up to 13 levels, which is unprecedented in a trapped ion system. This PhD defense presentation also covers some other interesting topics within the thesis, which include our experimental setup, barium ion loading via laser ablation, and detailed studies of some experimental observations that may not be intuitively clear.

Wigner negativity on the sphere

The rise of quantum information theory has largely vindicated the long-held belief that Wigner negativity is an indicator of genuine nonclassicality in quantum systems.  This thesis explores its manifestation in spin-j systems using the spherical Wigner function.  Common symmetric multi-qubit states are studied and compared.  Spin coherent states are shown to never have vanishing Wigner negativity.  Pure states that maximize negativity are determined and analyzed using the Majorana stellar representation.  The relationship between negativity and state mixedness is discussed, and polytopes characterizing unitary orbits of lower-bounded Wigner functions are studied.  Results throughout are contrasted with similar works on symmetric state entanglement and other forms of phase-space nonclassicality.

Single-photon detectors for satellite-based quantum communications

Nigar Sultana

Two-photon and Three-photon Parametric Interactions in Superconducting Microwave Circuits

Sandbo Chang

Aspects of particle detector model in quantum field theory with boundary conditions

Erickson Tjoa

Quantum Algorithmic Techniques for Fault-tolerant Quantum Computers

Maria Kieferova