Bosonic codes have seen a resurgence in interest for applications as varied as fault-tolerant quantum architectures, quantum enhanced sensing, and entanglement distribution. Cat codes have been proposed as low-level elements in larger architectures, and the theory of rotationally symmetric codes more generally has been significantly expanded in the recent literature. The fault-tolerant preparation and maintenance of cat-code states as a standalone quantum error correction scheme remains, however, limited by the need for robust state preparation and strong intermode interactions. In this work, we consider the teleportation-based correction circuit for cat-code quantum error correction. We show that the class of acceptable ancillary states is broader than is typically acknowledged, and exploit this to propose the use of many-component bridge states, which, though not themselves in the cat-code space, are nonetheless capable of syndrome extraction in the regime where nonlinear interactions are a limiting factor.
Bosonic codes have seen a resurgence in interest for applications as varied as fault-tolerant quantum architectures, quantum enhanced sensing, and entanglement distribution. Cat codes have been proposed as low-level elements in larger architectures, and the theory of rotationally symmetric codes more generally has been significantly expanded in the recent literature. The fault-tolerant preparation and maintenance of cat-code states as a standalone quantum error correction scheme remains, however, limited by the need for robust state preparation and strong intermode interactions. In this work, we consider the teleportation-based correction circuit for cat-code quantum error correction. We show that the class of acceptable ancillary states is broader than is typically acknowledged, and exploit this to propose the use of many-component bridge states, which, though not themselves in the cat-code space, are nonetheless capable of syndrome extraction in the regime where nonlinear interactions are a limiting factor.
Bosonic codes encode quantum information into a single infinite-dimensional physical system endowed with error correction capabilities. This reduces the need for complex management of many physical constituents compared with standard approaches employing multiple physical qubits. Recent discussions of bosonic codes centre around correcting only boson-loss errors, with phase errors either actively suppressed or deferred to subsequent layers of encoding with standard qubit codes. Rotationally symmetric bosonic (RSB) codes, which include the well-known cat and binomial codes, are capable of simultaneous correction of loss and phase errors, offering an alternate route that deals with arbitrary errors already at the base layer. Here, we investigate the robustness of such codes, moving away from the more idealistic past studies towards a circuit-level noise analysis closer to the practical situation where every physical component in the device is potentially faulty. We extend the concept of fault tolerance to the case of RSB codes, and then examine the performance of two known error correction circuits under circuit-level noise. Our analysis reveals a significantly more stringent noise threshold for fault-tolerant operation than found in past works; nevertheless, we show how, through waiting-time optimization and the use of squeezing, we can restore the noise requirements to a regime achievable with near-term quantum hardware. While our focus here is on cat codes for concreteness, a similar analysis applies for general RSB codes.
Reliable quantum computation requires fault-tolerant protocols to prevent errors from propagating during syndrome extraction in quantum error correction. We present a novel fault-tolerant syndrome extraction technique for CSS codes, which we refer to as the cut-cat state scheme. While each ancilla qubit interacts non-fault-tolerantly with a pair of data qubits, we introduce additional cat stabilizer measurements to identify and correct the resulting hook errors. Our approach maintains the key benefit of cat-based extraction, i.e., parallelized data qubit interactions, while reducing the number of simultaneous qubits required by more than half. Compared to flag-based state-of-the-art protocols, the cut-cat scheme offers a notable advantage in terms of two-qubit gate count as the code distance increases.
In quantum error correction, information is encoded in a high-dimensional system to protect it from the environment.A crucial step is to use natural, two-body operations with an ancilla to extract information about errors without causing backaction on the encoded information.Essentially, ancilla errors must not propagate to the encoded system and induce errors beyond those which can be corrected.The current schemes for achieving this fault tolerance to ancilla errors come at the cost of increased overhead requirements.An efficient way to extract error syndromes in a fault-tolerant manner is by using a single ancilla with a strongly biased noise channel.Typically, however, required elementary operations can become challenging when the noise is extremely biased.We propose to overcome this shortcoming by using a bosonic-cat ancilla in a parametrically driven nonlinear oscillator.Such a cat qubit experiences only bit-flip noise, while the phase flips are exponentially suppressed.To highlight the flexibility of this approach, we illustrate the syndrome extraction process in a variety of codes such as qubit-based toric, bosonic-cat, and Gottesman-Kitaev-Preskill codes.Our results open a path for realizing hardware-efficient, fault-tolerant error syndrome extraction.
Building reliable quantum computers requires protecting fragile quantum states from inevitable environmental noise and operational errors. While quantum error correction codes like the Steane [[7,1,3]] code provide elegant theoretical solutions, their practical success hinges critically on how we measure errors - a process called syndrome extraction. The challenge lies in the ancilla qubits used for measurement: when they fail, errors can cascade across the entire quantum system, destroying the very information we're trying to protect. We address this fundamental problem by implementing and comparing three sophisticated syndrome measurement strategies: Shor's cat-state approach, which distributes measurements across multiple entangled ancillas achieving 85-92% preparation success; Steane's encoded-ancilla method using complete error-corrected logical qubits reaching 97.8% syndrome fidelity; and a flexible unified framework that adapts strategies based on hardware capabilities. Through extensive simulations using IBM's Qiskit platform spanning randomized benchmarking and T-heavy circuits, we demonstrate that intelligent ancilla management improves error suppression by up to 2.4× compared to standard approaches. Our implementations achieve logical error rates as low as 5.1×10−5 under realistic noise conditions with physical error rates of 10−3, while maintaining near-unity logical fidelity (0.99997) even for deep circuits. The threshold analysis reveals robust performance across distance-3 to distance-13 codes with characteristic threshold curves showing exponential error suppression below the critical physical error rate. These results provide immediately deployable tools for near-term quantum devices and establish practical design principles for scaling toward fault-tolerant quantum computers.
The cat code is a promising encoding scheme for bosonic quantum error correction as it allows for correction against losses---the dominant error mechanism in most bosonic systems. However, it has remained unclear how the required syndrome measurement and recovery can be implemented in the optical regime. Here, we introduce a teleportation-based error-correction scheme for the cat code, using elements suitable for an optical setting. The scheme detects and corrects single-photon losses while restoring the amplitude of the cat states, thereby greatly suppressing the accumulation of errors in lossy channels.
Quantum computation promises to revolutionize information processing by exploiting superposition and entanglement, enabling applications such as quantum simulation, combinatorial optimization, and secure quantum communication. Beyond individual processors, the quantum internet aims to connect quantum nodes through entanglement distribution, enabling distributed computation. However, quantum states are fragile: environmental interactions, imperfect gate operations, and measurement errors can quickly degrade encoded information. Reliable quantum computation therefore requires carefully designed quantum error-correcting codes and fault-tolerant protocols. Unlike classical redundancy schemes, quantum error correction must preserve delicate phase relationships and relies on indirect error detection through syndrome extraction with ancillary qubits, enabling error identification without collapsing encoded states. Topological codes, in particular, emerged early as the preferred choice for many architectures due to their planar structure, local interactions, and natural support for fault-tolerant logical operations. Color codes, for instance, allow transversal implementation of all Clifford gates, whereas non-Clifford operations require magic-state injection. More recent constructions, including quantum low-density parity-check codes, offer higher encoding rates and reduced resource overhead, but require long-range qubit connectivity and more complex protocols. Despite experimental progress, several challenges remain. Many platforms exhibit biased noise, motivating codes that exploit channel asymmetry. Real-time decoding remains a critical bottleneck, as fault-tolerant computation requires low-latency processing of rapidly generated syndrome data. Fault-tolerant logical state initialization also remains resource-intensive and scales poorly with code distance. Addressing these challenges, this thesis develops a unified framework spanning theory and experiment. It provides precise performance analysis of quantum error-correcting codes in the low physical error-rate regime, introduces codes tailored to biased noise, develops fast low-complexity decoding algorithms for real-time operation, and presents modular and efficient protocols for fault-tolerant state preparation of CSS codes. The latter is demonstrated experimentally through the preparation of a logical zero state of the Golay code on the Quantinuum H2 trapped-ion quantum computer.