Qubit-field quantum transduction provides numerous advantages to quantum computing, such as device-specific error-correcting codes, efficient scalability, and effective entanglement generation. An all-to-all connected bus of qubits implanted around the outside of a topological insulator, allowed to interact with the edge state, is a promising arena for transduction with flying fermionic qubits. Unruh--DeWitt detectors have allowed quantum information scientists to model entanglement properties of qubit-field interactions in many settings in a field known as Relativistic Quantum Information (RQI). Unruh--DeWitt detectors are useful tools to realize quantum Shannon theory, a subset of the theory of quantum communication, in condensed matter systems, aptly named Unruh--DeWitt quantum computers. These systems will provide quantitative measurements of communication in quantum materials that utilize coherent states for bosonic and fermionic fields. In this thesis, emphasis is placed on the well-studied theory of Tomonaga-Luttinger liquids, as the bosonization of a helical Luttinger liquid provides a pedagogical arena to construct RQI channels of fermionic systems. Multiple experimentally realizable systems are proposed, and design constraints are constructed to ensure maximum channel capacity. Furthermore, we elucidate the strength of these quantum channels using measurements from quantum Shannon theory such as coherent information, dephasing formalism, diamond distance and universality of Unruh--DeWitt quantum logic gates.
Qubit-field quantum transduction provides numerous advantages to quantum computing, such as device-specific error-correcting codes, efficient scalability, and effective entanglement generation. An all-to-all connected bus of qubits implanted around the outside of a topological insulator, allowed to interact with the edge state, is a promising arena for transduction with flying fermionic qubits. Unruh--DeWitt detectors have allowed quantum information scientists to model entanglement properties of qubit-field interactions in many settings in a field known as Relativistic Quantum Information (RQI). Unruh--DeWitt detectors are useful tools to realize quantum Shannon theory, a subset of the theory of quantum communication, in condensed matter systems, aptly named Unruh--DeWitt quantum computers. These systems will provide quantitative measurements of communication in quantum materials that utilize coherent states for bosonic and fermionic fields. In this thesis, emphasis is placed on the well-studied theory of Tomonaga-Luttinger liquids, as the bosonization of a helical Luttinger liquid provides a pedagogical arena to construct RQI channels of fermionic systems. Multiple experimentally realizable systems are proposed, and design constraints are constructed to ensure maximum channel capacity. Furthermore, we elucidate the strength of these quantum channels using measurements from quantum Shannon theory such as coherent information, dephasing formalism, diamond distance and universality of Unruh--DeWitt quantum logic gates.
A set of universal quantum gates is a vital part of the theory of quantum computing, but is absent in the developing theory of Relativistic Quantum Information (RQI). Yet, the Unruh--DeWitt (UDW) detector formalism can be elevated to unitary gates between qubits and quantum fields and has allowed RQI applications in quantum Shannon theory, such as mutual information, coherent information, and quantum capacity in field-mediated quantum channels. Recently, experimental realizations of UDW-style qubits have been proposed in two-dimensional quantum materials, but their value as a quantum technology, including quantum communication and computation, is not yet clear, especially since fields introduce many avenues for decoherence. We introduce controlled-unitary UDW logic gates between qubit and field that are comparable to the two-qubit CNOT gate. We then extend this formalism to demonstrate Quantum State Transfer (QST) (two CNOT gates) and SWAP (three CNOT gates) channels. We illustrate the performance of these quantum operation gates with the diamond distance, a measure of distinguishability between quantum channels. Distinguishability measures like diamond distance allow for a rigorous comparison between field-mediated transduction through UDW detectors and local quantum mechanical operations and so quantify the performance of UDW detectors in quantum technological applications. Using the controlled-unitary qubit-field interactions we define an exact form of the CNOT gate. With this technique we also define quantum field-mediated single qubit operations associated with the Hadamard H, the S, and T gates. Thus, UDW detectors in simple settings enable a collection of gates known to provide universal quantum computing.
This thesis collects my own and collaborative work I have been involved with finding localised systems in quantum field theory that are useful for quantum information. It draws from many well established physical theories such as quantum field theory in curved spacetimes, quantum optics and Gaussian state quantum information. The results are split between three chapters. For the first results, we set-up the basic framework for working with quantum fields confined to cavities. By considering the real Klein-Gordon field, we describe how to model the non-uniform motion of a rigid cavity through spacetime. We employ the use of Bogoliubov transformations to describe the effects of changing acceleration. The second set of results investigate how the Dirac field can be confined to a cavity for quantum information purposes. By again considering Bogoliubov transformations, we thoroughly investigate how the entanglement shared between two cavities is affected by non-uniform motion. It is shown that different types of Dirac field states are more robust against motion than others. The final results look at using our second notion of localisation, Unruh- DeWitt detectors. We investigate how allowing for a "non-point-like" spatial profile of the Unruh-DeWitt detector affects how it interacts with a quantum field around it. By engineering suitable detector-field interactions, we use techniques from symplectic geometry to compute the dynamics of a quantum state beyond commonly used perturbation theory. There is also a conclusions chapter at the end of the thesis which summarises the results presented and suggestions of possible new directions of research in relativistic quantum information are made.
Quantum computation and communication are important branches of quantum information science. However, noise in realistic quantum devices fundamentally limits the utility of these quantum technologies. A conventional approach towards large-scale and fault-tolerant quantum information processing is to use multi-qubit quantum error correction (QEC), that is, to encode a logical quantum bit (or a logical qubit) redundantly over many physical qubits such that the redundancy can be used to detect errors. The required resource overhead associated with the use of conventional multi-qubit QEC schemes, however, is too high for these schemes to be realized at scale with currently available quantum devices. Recently, bosonic (or continuous-variable) quantum error correction has risen as a promising hardware-efficient alternative to multi-qubit QEC schemes. In this thesis, I provide an overview of bosonic QEC and present my contributions to the field. Specifically, I present the benchmark and optimization results of various single-mode bosonic codes against practically relevant excitation loss errors. I also demonstrate that fault-tolerant bosonic QEC is possible by concatenating a single-mode bosonic code with a multi-qubit error-correcting code. Moreover, I discuss the fundamental aspects of bosonic QEC using the framework of quantum communication theory. In particular, I present improved bounds on important communication-theoretic quantities such as the quantum capacity of bosonic Gaussian channels. Furthermore, I provide explicit bosonic error correction schemes that nearly achieve the fundamental performance limit set by the quantum capacity. I conclude the thesis with discussions on the importance of non-Gaussian resources for continuous-variable quantum information processing.
Quantum computers are devices that can solve certain problems faster than ordinary, classical computers. The fundamental units of quantum information are qubits, superpositions of two states, a "zero" state and a "one" state. There are various approaches to construct such two-level systems, among others, using superconducting circuits, trapped ions or photons. A common feature of these physical systems is that their coherence times are relatively short compared to the length of useful computations. Superconducting qubits, for instance, are currently the most advanced solid-state qubits, but they decohere after around 100 microseconds, and any information stored in these qubits is lost. On the other hand, useful quantum computations may require quantum information to survive on time scales that are many orders of magnitude longer, as their runtimes can reach several hours or even days. Topological quantum computing is an approach to construct qubits that survive for the entire duration of such a long computation. Topological quantum computing comes in two flavors. The condensed matter approach is to build error-resilient qubits using exotic quasiparticles in topological materials, most prominently Majorana zero modes in topological superconductors. Even though no such qubit has been built to date, the hope is that their coherence times may be significantly longer than the coherence times of currently available solid-state qubits, but are still expected to be too short for large-scale quantum computing. The quantum information approach is to combine many error-prone qubits to build more robust logical qubits using topological error-correcting codes, e.g., surface codes. Even though the first approach is hardware-based and the second approach is software-based, they are deeply related. With Majorana-based qubits, the main logical operations are Majorana fermion parity measurements. By replacing Majorana-based qubits with surface-code patches and parity measurements with lattice-surgery operations, schemes for quantum computation with Majorana-based qubits or with surface codes can be identical. In this thesis, we explore how to construct a large-scale topological fault-tolerant quantum computer that can perform useful quantum computations. Here, topological refers to the nature of the quantum error-correcting code, while the underlying hardware may be based on non-topological qubits, but could also be composed of Majorana-based qubits. We provide a complete picture of such a large-scale device, breaking down large quantum computations into logical qubits and logical operations, describing how these logical operations are performed on the level of physical qubits and physical gates, and finally discussing how these physical qubits can be pieced together in a Majorana-based system using topological superconducting nanowires.
Processing information quantum mechanically is known to enable new communication and computational scenarios that cannot be accessed with conventional information technology (IT). We present here a new approach to scalable quantum computing---a "qubus computer"---which realizes qubit measurement and quantum gates through interacting qubits with a quantum communication bus mode. The qubits could be "static" matter qubits or "flying" optical qubits, but the scheme we focus on here is particularly suited to matter qubits. Universal two-qubit quantum gates may be effected by schemes which involve measurement of the bus mode, or by schemes where the bus disentangles automatically and no measurement is needed. This approach enables a parity gate between qubits, mediated by a bus, enabling near-deterministic Bell state measurement and entangling gates. Our approach is therefore the basis for very efficient, scalable QIP, and provides a natural method for distributing such processing, combining it with quantum communication.
Quantum computers promise to solve computational problems that are inaccessible to classical machines. The reliable execution of large-scale quantum algorithms requires robust operations in the presence of noise. Quantum error correction addresses this challenge by encoding quantum information redundantly across several physical qubits, such that errors can be detected and corrected during a computation. However, no single error-correcting code intrinsically supports an inherently robust, fault-tolerant implementation of all gates needed for universal quantum computing. Moreover, most modern approaches to both quantum error correction and the implementation of universal logical operations on encoded qubits rely on mid-circuit measurements and feed-forward control. These types of operations are technologically demanding, often slow, and prone to high error rates, and they limit the overall success probability of quantum algorithms. In this thesis, we develop fault-tolerant protocols and circuits for quantum error correction and universal logical computation, with an emphasis on implementations compatible with current hardware systems. We first focus on fault-tolerant quantum error correction on small codes. By comparing different protocols, we identify trade-offs between compact circuit constructions and their robustness to noise. We then assess their practical performance by comparing numerical simulations of noisy circuits with experimental data. Beyond the preservation of encoded information, we study how universal logic can be implemented in a fault-tolerant manner on encoded qubits. A central approach considered in this thesis is code switching, in which logical information is transferred between two distinct error-correcting codes that support complementary sets of inherently fault-tolerant logical gates. In combination, these codes give access to a complete universal fault-tolerant logical gate set. In this thesis, we determine conditions that allow us to construct fault-tolerant protocols for code switching. We adapt these protocols to the capabilities of current hardware, thereby enabling the first experimental realization of universal fault-tolerant logic by means of code switching. However, the overall performance of these schemes is limited by slow and noisy mid-circuit measurements. To address this bottleneck, we construct a suite of measurement-free fault-tolerant universal operations that do not require any measurements during the execution of an algorithm. In this framework, error correction and logical operations are implemented coherently as part of the quantum circuit, without mid-circuit measurements or in-sequence classical control. We introduce measurement-free code-switching schemes that can be scaled to arbitrary code distances through concatenation, and which thereby provide, in principle, arbitrarily strong error suppression. We further tailor our approach to the capabilities of current trapped-ion quantum processors. New circuit constructions support the first experimental implementation of a logical quantum algorithm without mid-circuit measurements, demonstrated through Grover's search on three encoded qubits. Together, the results of this thesis expand the toolbox for early fault-tolerant quantum computation. They show how protocols for quantum error correction and universal logical gates can be designed without mid-circuit measurements with realistic hardware constraints in mind, opening new pathways towards universal quantum logic.