Quantum information is vulnerable to environmental noise and experimental imperfections, hindering the reliability of practical quantum information processors. Therefore, quantum error correction (QEC) that can protect quantum information against noise is vital for universal and scalable quantum computation. Among many different experimental platforms, superconducting quantum circuits and bosonic encodings in superconducting microwave modes are appealing for their unprecedented potential in QEC. During the last few years, bosonic QEC is demonstrated to reach the break-even point, i.e. the lifetime of a logical qubit is enhanced to exceed that of any individual components composing the experimental system. Beyond that, universal gate sets and fault-tolerant operations on the bosonic codes are also realized, pushing quantum information processing towards the QEC era. In this article, we review the recent progress of the bosonic codes, including the Gottesman-Kitaev-Preskill codes, cat codes, and binomial codes, and discuss the opportunities of bosonic codes in various quantum applications, ranging from fault-tolerant quantum computation to quantum metrology. We also summarize the challenges associated with the bosonic codes and provide an outlook for the potential research directions in the long terms.
Quantum information is vulnerable to environmental noise and experimental imperfections, hindering the reliability of practical quantum information processors. Therefore, quantum error correction (QEC) that can protect quantum information against noise is vital for universal and scalable quantum computation. Among many different experimental platforms, superconducting quantum circuits and bosonic encodings in superconducting microwave modes are appealing for their unprecedented potential in QEC. During the last few years, bosonic QEC is demonstrated to reach the break-even point, i.e. the lifetime of a logical qubit is enhanced to exceed that of any individual components composing the experimental system. Beyond that, universal gate sets and fault-tolerant operations on the bosonic codes are also realized, pushing quantum information processing towards the QEC era. In this article, we review the recent progress of the bosonic codes, including the Gottesman-Kitaev-Preskill codes, cat codes, and binomial codes, and discuss the opportunities of bosonic codes in various quantum applications, ranging from fault-tolerant quantum computation to quantum metrology. We also summarize the challenges associated with the bosonic codes and provide an outlook for the potential research directions in the long terms.
Quantum error correction (QEC) has emerged as a cornerstone in the quest for scalable and fault-tolerant quantum technologies. While quantum systems promise exponential advantages over classical computation, their extreme susceptibility to noise and decoherence presents a formidable challenge. This review critically examines the trajectory of QEC from its theoretical foundations to recent experimental realizations. Foundational codes, including Shor’s and Steane’s constructions, laid the groundwork for the stabilizer formalism and the development of topological and bosonic codes. Over the past decade, experimental demonstrations have validated these concepts, with logical qubits surpassing the lifetimes of physical qubits on platforms such as superconducting circuits, trapped ions, and photonics. Emerging approaches, including low-density parity-check codes, hybrid mitigation–correction strategies, and artificial intelligence–driven decoders, further illustrate the field’s dynamism. By synthesizing theoretical progress, empirical validation, and cross-platform innovations, this review highlights both achievements and persistent challenges particularly the overhead of physical qubits, the speed of real-time decoding, and integration into full-stack architectures. The analysis concludes that while scalable fault-tolerant quantum computing remains a work in progress, recent breakthroughs mark a decisive transition from abstraction to practicality, establishing QEC as a central pillar in the development of quantum computation, communication, and sensing.
Quantum computing holds the promise of solving classically intractable problems. Enabling this requires scalable and hardware-efficient quantum processors with vanishing error rates. This perspective manuscript describes how bosonic codes, particularly grid state encodings, offer a pathway to scalable fault-tolerant quantum computing in superconducting circuits. By leveraging the large Hilbert space of bosonic modes, quantum error correction can operate at the single physical unit level, therefore reducing drastically the hardware requirements to bring fault-tolerant quantum computing to scale. Going beyond the well-known Gottesman-Kitaev-Preskill (GKP) code, we discuss how using multiple bosonic modes to encode a single qubit offers increased protection against control errors and enhances its overall error-correcting capabilities. Given recent successful demonstrations of critical components of this architecture, we argue that it offers the shortest path to achieving fault tolerance in gate-based quantum computing processors with a MHz logical clock rate.
Recently, the achievement, entitled “lifetime enhancement for a logic qubit by bosonic encoding error correction”, has been selected as one of “The Ten Major Advances in Chinese Science 2023”. Here, we will introduce briefly the importance of this work. It is known that quantum states are fragile due to decoherence induced by environment. Error will happen on a qubit, resulting in continuously changes of the parameters for this qubit, such as amplitude and phase parameters. The aim of quantum error correction is to amend those errors by using various quantum error correction codes, in which a logic qubit can be represented by several physical qubits. It should be noted that the quantum error correction can be realized by correcting a discrete set of errors, such as bit-flip error, phase-flip error or both of them. On the other hand, types of errors occurred depend on specific platforms of quantum computation. For example, photon loss is more inclined to occur in photonic systems. In this case, the approach of bosonic encoding of quantum error correction is more efficient. The work “lifetime enhancement for a logic qubit by bosonic encoding error correction” is for such a scenario. The challenge of quantum error correction is that operation itself is not perfect which may incur new errors. So it is actually difficult to demonstrate that we can benefit from quantum error correction. The achievement of lifetime enhancement by bosonic encoding error correction succeeds in beating this break-even point. The experiments are performed by circuit quantum electrodynamics on a superconducting processor with a qubit and a coupled resonate cavity. The logic qubit is realized by the bosonic mode of the cavity, while the superconducting qubit plays the role of the ancillary qubit in error correction. The initial states are prepared by the superconducting qubit, and are transferred to the logic qubit in the cavity. Then the error correction can be performed based on detection of photon loss by the superconducting qubit. The results show that the lifetime of the logic qubit increases from 694 μs to 805 μs with 16% enhancement. Besides high quality devices, the success of this experiment depends on the feedback control to detect and correct the error of photon loss in a short time. The result of beating the break-even point of bosonic encoding error correction is for one logic qubit. In the near future, it is hopeful to implement logic gates, such as single-qubit rotation gate and two-qubit gate, on a couple of logic qubits by bosonic encoding. The importance of the results will depend on whether higher fidelity can be achieved compared with those of gates with physical qubits. In this way, the advantage of the logic qubits for quantum computation is presented. It will be significant that the approach of bosonic encoding with a superconducting processor is scalable to hundreds of logic qubits, which may take a few years to realize. Our aim is to realize a fault-tolerant universal quantum computer based on a large quantity of high-precision logic qubits. The work “lifetime enhancement for a logic qubit by bosonic encoding error correction” is an important step toward this aim.
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.
Protecting quantum information through quantum error correction (QEC) is a cornerstone of future fault-tolerant quantum computation. However, current QEC-protected logical qubits have only achieved coherence times about twice those of their best physical constituents. Here, we show that the primary barrier to higher QEC gains is ancilla-induced operational errors rather than intrinsic cavity coherence. To overcome this bottleneck, we introduce error-detectable universal control of bosonic modes, wherein ancilla relaxation events are detected and the corresponding trajectories discarded, thereby suppressing operational errors on logical qubits. For binomial codes, we demonstrate universal gates with fidelities exceeding 99.6% and QEC gains of 8.33× beyond break-even. Our results establish that gains beyond 10× are achievable with state-of-the-art devices, establishing a path toward fault-tolerant bosonic quantum computing.
Bosonic quantum error correction (QEC) offers a hardware-efficient route to fault-tolerant quantum computing. To date, however, superconducting circuit implementations of bosonic codes have utilized centimeter-scale 3D microwave cavities controlled by fixed-frequency transmon qubits, with logical lifetimes limited by transmon bit-flip errors. Here, we realize bosonic QEC in a fully planar architecture by pairing a heavy fluxonium, whose 451±70μs bit-flip lifetime exceeds that of any control qubit in previous demonstrations, with an on-chip Archimedean spiral resonator several orders of magnitude smaller in mode volume than prior 3D cavities. We prepare finite-energy Gottesman-Kitaev-Preskill (GKP) states and stabilize them using measurement-free error correction with rapid fluxonium reset, extending the logical lifetime by a factor of 1.59±0.05. These results provide the first demonstration of resonator control using a weakly coupled fluxonium and, with it, the first realization of standalone bosonic QEC in a fully planar superconducting circuit architecture.