Bosonic quantum computing with near-term devices and beyond

TL;DR

This work investigates how bosonic (continuous-variable) codes and quantum LDPC codes can be harnessed to realize scalable, fault-tolerant quantum computing with near-term hardware. It develops decoding methods that leverage analog syndrome information to couple continuous-variable and discrete-variable error correction, and introduces noise-biased encodings such as dissipatively stabilized squeezed cat qubits. By bridging physical-layer encodings, architecture design in superconducting circuits, and homological code theory via fault complexes and hypergraph-product constructions, the thesis presents both practical decoding strategies (localized statistics decoding) and novel code families (quantum radial codes) with favorable resource overheads. The results inform feasible paths toward low-overhead, high-threshold quantum memories and processors, while outlining fundamental open problems in space-time decoding, lattice-surgery-inspired fault tolerance, and the broader homological framework for dynamic fault-tolerant protocols.

Abstract

(Abridged.) This thesis investigates scalable fault-tolerant quantum computation through the development of bosonic quantum codes, quantum LDPC codes, and decoding protocols that connect continuous-variable and discrete-variable error correction. We investigate superconducting microwave implementations of continuous-variable quantum computing, including the deterministic generation of cubic phase states, and introduce the dissipatively stabilized squeezed cat qubit, a noise-biased bosonic encoding with enhanced error suppression and faster gates. The performance of rotation-symmetric and GKP codes is analyzed under realistic noise and measurement models, revealing key trade-offs in measurement-based schemes. To integrate bosonic codes into larger architectures, we develop decoding methods that exploit analog syndrome information, enabling quasi-single-shot decoding in concatenated systems. On the discrete-variable side, we introduce localized statistics decoding, a highly parallelizable decoder for quantum LDPC codes, and propose quantum radial codes, a new family of single-shot LDPC codes with low overhead and strong circuit-level performance. Finally, we present fault complexes, a homological framework for analyzing faults in dynamic quantum error correction protocols. Extending the role of homology in static CSS codes, fault complexes provide a general language for the design and analysis of fault-tolerant schemes.

Figures (14)

• Figure 1: a Quantum circuit for the measurement of an observable $A$ with eigenvalues $\pm 1$ by an ancilla. The circuit performs a controlled-$A$ gate between the $n$ qubit system and an ancilla initially prepared in the state $\ket{+}$ and measures the ancilla in the $X$ basis. b Circuit for measuring $A = Z Z$ using $\CZ$ gates.
• Figure 2: The one-bit teleportation primitive. The left-hand side of the equality shows how to teleport an arbitrary phase gate $P(\varphi)$ onto the input state $\ket{\psi}$ by preparing the second qubit in the state $P(\varphi)\ket{+}$. The right-hand side shows an equivalent circuit that only requires preparation of the state $\ket{+}$ and instead requires measurement of the first qubit in the rotated basis $P(\varphi) X P^{\dagger}(\varphi)$.
• Figure 3: Illustration of measurement-based quantum computing. A five-qubit cluster state is shown, with qubits (nodes) entangled as indicated by edges. Measurement proceeds left to right, with measured qubits shown in blue. a The left-most qubit is initialized in the state $\ket{\psi}$; others are in $\ket{+}$. b Measuring the first qubit in the $X$ basis teleports $\ket{\psi}$ one node right, up to a Hadamard gate and a Pauli correction $X^{m_1}$. c Measuring the next qubit in the $X$ basis further teleports the state, resulting in $X^{m_2} Z^{m_1}\ket{\psi}$ on the third qubit.
• Figure 4: a Cluster state representation of the remote entanglement primitive. b The remote entanglement primitive from the gate-based view consists of a low-depth circuit and measurement of the central qubits in the $X$ basis. c Evolution of the unmeasured qubits in the Heisenberg picture.
• Figure 5: Pictorial representation of three different classical noise channels, from left to right, the erasure channel, the binary symmetric channel, and the additive white Gaussian noise channel.