Recent development of mixed-state encoding (MSE) allows pure-state logical information to be encoded by a bosonic (continuous-variable) system in mixed physical state. Despite interest due to its counterintuitiveness, the utility of the current MSE scheme is limited due to several operational drawbacks, namely redundant information carrier, probabilistic initialization, and requirement of discrete-variable measurement. In this work, we present a simplified MSE that does not suffer from any of these drawbacks. Specifically, our protocol encodes each qubit by only one mixed-state bosonic mode and the logical basis can be deterministically initialized from thermal equilibrium. All logical operations of this encoding can be performed with continuous-variable interaction and measurement only. Without the necessity of ground-state cooling, our proposal could broaden the set of candidate systems for implementing quantum computers and reduce the reliance on demanding refrigerating facility for current quantum computing architectures. Additionally, our protocol can enhance the noise tolerance of logical qubit even if the system can be efficiently cooled.
Recent development of mixed-state encoding (MSE) allows pure-state logical information to be encoded by a bosonic (continuous-variable) system in mixed physical state. Despite interest due to its counterintuitiveness, the utility of the current MSE scheme is limited due to several operational drawbacks, namely redundant information carrier, probabilistic initialization, and requirement of discrete-variable measurement. In this work, we present a simplified MSE that does not suffer from any of these drawbacks. Specifically, our protocol encodes each qubit by only one mixed-state bosonic mode and the logical basis can be deterministically initialized from thermal equilibrium. All logical operations of this encoding can be performed with continuous-variable interaction and measurement only. Without the necessity of ground-state cooling, our proposal could broaden the set of candidate systems for implementing quantum computers and reduce the reliance on demanding refrigerating facility for current quantum computing architectures. Additionally, our protocol can enhance the noise tolerance of logical qubit even if the system can be efficiently cooled.
One limitation of the quantum computing capability of a continuous-variable system is determined by our ability to cool it to the ground state, because pure logical states, in which we accurately encode quantum information, are conventionally pure physical states that are constructed from the ground state. In this work, we present an alternative quantum computing formalism that encodes logical quantum information in mixed physical states. We introduce a class of mixed-state protocols that are based on a parity encoding, and propose an implementation of the universal logic gates by using realistic hybrid interactions. When compared with the conventional pure-state protocols, our formalism could relax the necessity, and hence the systemic requirements, of cooling. Additionally, the mixed-state protocols are inherently resilient to a wider class of noise processes and reduce the fundamental energy consumption in initialization. Our work broadens the range of candidates for continuous-variable quantum computers.
Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal quantum computation with a fixed set of operations but arbitrary encoding. By storing a qubit in the parity of two or four qumodes, all computing processes can be implemented by basis state preparations, continuous-variable exponential-swap operations, and swap tests. Our formalism inherits the advantages that the quantum information is decoupled from collective noise, and logical qubits with different encodings can be brought to interact without decoding. We also propose a possible implementation of the required operations by using interactions that are available in a variety of continuous-variable systems. Our work separates the "hardware" problem of engineering quantum-computing-universal interactions, from the "software" problem of designing encodings for specific purposes. The development of quantum computer architecture could hence be simplified.
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.
Since the early days of quantum information science, diverse strategies have been proposed to encode qubits and implement quantum gates across various physical platforms. Modes and bosonic states offer a flexible framework for quantum information processing, from single-photon optics to superconducting circuits, combining massless and massive particles. Universal gate sets have been established for specific encodings—such as those based on Fock states or the field’s quadratures. However, a general framework clarifying how different bosonic resources—such as mode structure, particle-number statistics, Gaussian and non-Gaussian states and operations—combine to enable universality and potential quantum advantage irrespectively of the encoding remains lacking. A main difficulty lies in the coexistence of distinct paradigms that appear to combine loosely in bosonic quantum information: discrete-variable schemes—where information is encoded in qubits or effective finite-dimensional systems—and continuous-variable schemes—which rely on infinite-dimensional Hilbert spaces associated with the field’s quadratures. Despite the success of each approach, they remain seemingly incompatible in many aspects—in particular in terms of physical resource analysis for universality—due to their underlying mathematical differences. In this work, we apply a superselection-rule-compliant framework for bosonic quantum information that unifies these paradigms. This representation explicitly incorporates the phase reference and enforces total particle number conservation, allowing for a consistent treatment of bosonic quantum information protocols and resources across both discrete and continuous regimes. We derive necessary and sufficient conditions expressed in terms of Gaussian and non-Gaussian resources for universality that apply to any encoding, without resorting to specific mappings. Our results show that continuous variable encodings are not fundamentally distinct from discrete ones, but rather emerge as subspaces within a general bosonic structure. Importantly, in such a widely studied framework, non-Gaussian properties of bosonic states and operations can be washed out, providing evidence that the continuous variables regime is not the most suitable to fully assess the quantum properties of bosons.
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.
We present a fault-tolerant quantum computing architecture based on a code concatenation of the parity code. In addition to the recently explored concatenation with bosonic (i.e. continuous-variable) qubits, we propose and study a concatenation with discrete-variable stabilizer codes. The parity code can be understood as a low-density-parity-check (LDPC) code tailored specifically to obtain any desired logical connectivity from nearest neighbor physical interactions. On the bosonic side, the proposed scheme enables codes with better encoding rate compared to the repetition code with the same code distances, while requiring only weight-3 and weight-4 stabilizers and nearest neighbor 2D square-lattice connectivity. On the discrete-variable side, the proposed scheme enables Calderbank-Shor-Steane (CSS) codes with less physical qubits overhead compared to the surface code but they do not form a quantum LDPC family.