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The performance of superconducting qubits has improved by several orders of magnitude in the past decade. These circuits benefit from the robustness of superconductivity and the Josephson effect, and at present they have not encountered any hard physical limits. However, building an error-corrected information processor with many such qubits will require solving specific architecture problems that constitute a new field of research. For the first time, physicists will have to master quantum error correction to design and operate complex active systems that are dissipative in nature, yet remain coherent indefinitely. We offer a view on some directions for the field and speculate on its future.

In quantum physics, measurements can fundamentally yield discrete and random results. Emblematic of this feature is Bohr’s 1913 proposal of quantum jumps between two discrete energy levels of an atom 1 . Experimentally, quantum jumps were first observed in an atomic ion driven by a weak deterministic force while under strong continuous energy measurement 2 – 4 . The times at which the discontinuous jump transitions occur are reputed to be fundamentally unpredictable. Despite the non-deterministic character of quantum physics, is it possible to know if a quantum jump is about to occur? Here we answer this question affirmatively: we experimentally demonstrate that the jump from the ground state to an excited state of a superconducting artificial three-level atom can be tracked as it follows a predictable ‘flight’, by monitoring the population of an auxiliary energy level coupled to the ground state. The experimental results demonstrate that the evolution of each completed jump is continuous, coherent and deterministic. We exploit these features, using real-time monitoring and feedback, to catch and reverse quantum jumps mid-flight—thus deterministically preventing their completion. Our findings, which agree with theoretical predictions essentially without adjustable parameters, support the modern quantum trajectory theory 5 – 9 and should provide new ground for the exploration of real-time intervention techniques in the control of quantum systems, such as the early detection of error syndromes in quantum error correction. Experiment overturns Bohr’s view of quantum jumps, demonstrating that they possess a degree of predictability and when completed are continuous, coherent and even deterministic.

Quantum superpositions of macroscopically distinct classical states—so-called Schrödinger cat states—are a resource for quantum metrology, quantum communication and quantum computation. In particular, the superpositions of two opposite-phase coherent states in an oscillator encode a qubit protected against phase-flip errors 1 , 2 . However, several challenges have to be overcome for this concept to become a practical way to encode and manipulate error-protected quantum information. The protection must be maintained by stabilizing these highly excited states and, at the same time, the system has to be compatible with fast gates on the encoded qubit and a quantum non-demolition readout of the encoded information. Here we experimentally demonstrate a method for the generation and stabilization of Schrödinger cat states based on the interplay between Kerr nonlinearity and single-mode squeezing 1 , 3 in a superconducting microwave resonator 4 . We show an increase in the transverse relaxation time of the stabilized, error-protected qubit of more than one order of magnitude compared with the single-photon Fock-state encoding. We perform all single-qubit gate operations on timescales more than sixty times faster than the shortest coherence time and demonstrate single-shot readout of the protected qubit under stabilization. Our results showcase the combination of fast quantum control and robustness against errors, which is intrinsic to stabilized macroscopic states, as well as the potential of these states as resources in quantum information processing 5 – 8 . A qubit generated and stabilized in a superconducting microwave resonator by encoding it into Schrödinger cat states produced by Kerr nonlinearity and single-mode squeezing shows intrinsic robustness to phase-flip errors.

Model bias is an inherent limitation of the current dominant approach to optimal quantum control, which relies on a system simulation for optimization of control policies. To overcome this limitation, we propose a circuit-based approach for training a reinforcement learning agent on quantum control tasks in a model-free way. Given a continuously parametrized control circuit, the agent learns its parameters through trial-and-error interaction with the quantum system, using measurement outcomes as the only source of information about the quantum state. Focusing on control of a harmonic oscillator coupled to an ancilla qubit, we show how to reward the learning agent with measurements of experimentally available observables. We train the agent to prepare various nonclassical states via both unitary control and control with adaptive measurement-based quantum feedback, and to execute logical gates on encoded qubits. The agent does not rely on averaging for state tomography or fidelity estimation, and significantly outperforms widely used model-free methods in terms of sample efficiency. Our numerical work is of immediate relevance to superconducting circuits and trapped ions platforms where such training can be implemented in experiment, allowing complete elimination of model bias and the adaptation of quantum control policies to the specific system in which they are deployed.

A quantum-error-correction system is demonstrated in which natural errors due to energy loss are suppressed by encoding a logical state as a superposition of Schrödinger-cat states, which results in the system reaching the ‘break-even’ point, at which the lifetime of a qubit exceeds the lifetime of the constituents of the system. Extended quantum error correction Although quantum error correction is a crucial ingredient when building a fully-fledged quantum computer, experimental demonstrations of this concept have so far been incomplete proof-of-principles. Here, Nissim Ofek et al . take another important step towards practical quantum error correction. Encoding a logical state in superpositions of Schrödinger-cat states, the authors demonstrate that they can extend the lifetime of a superconducting qubit beyond the lifetime of any of its constituents. Although the scheme is not fully fault-tolerant, it demonstrates all of the crucial ingredients of quantum error correction. Because the scheme is hardware efficient, it might become the method of choice when correcting errors in superconducting qubits. Quantum error correction (QEC) can overcome the errors experienced by qubits 1 and is therefore an essential component of a future quantum computer. To implement QEC, a qubit is redundantly encoded in a higher-dimensional space using quantum states with carefully tailored symmetry properties. Projective measurements of these parity-type observables provide error syndrome information, with which errors can be corrected via simple operations 2 . The ‘break-even’ point of QEC—at which the lifetime of a qubit exceeds the lifetime of the constituents of the system—has so far remained out of reach 3 . Although previous works have demonstrated elements of QEC 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , they primarily illustrate the signatures or scaling properties of QEC codes rather than test the capacity of the system to preserve a qubit over time. Here we demonstrate a QEC system that reaches the break-even point by suppressing the natural errors due to energy loss for a qubit logically encoded in superpositions of Schrödinger-cat states 17 of a superconducting resonator 18 , 19 , 20 , 21 . We implement a full QEC protocol by using real-time feedback to encode, monitor naturally occurring errors, decode and correct. As measured by full process tomography, without any post-selection, the corrected qubit lifetime is 320 microseconds, which is longer than the lifetime of any of the parts of the system: 20 times longer than the lifetime of the transmon, about 2.2 times longer than the lifetime of an uncorrected logical encoding and about 1.1 longer than the lifetime of the best physical qubit (the |0〉 f and |1〉 f Fock states of the resonator). Our results illustrate the benefit of using hardware-efficient qubit encodings rather than traditional QEC schemes. Furthermore, they advance the field of experimental error correction from confirming basic concepts to exploring the metrics that drive system performance and the challenges in realizing a fault-tolerant system.

In contrast to a single quantum bit, an oscillator can store multiple excitations and coherences provided one has the ability to generate and manipulate complex multiphoton states. We demonstrate multiphoton control by using a superconducting transmon qubit coupled to a waveguide cavity resonator with a highly ideal off-resonant coupling. This dispersive interaction is much greater than decoherence rates and higher-order nonlinearities to allow simultaneous manipulation of hundreds of photons. With a tool set of conditional qubit-photon logic, we mapped an arbitrary qubit state to a superposition of coherent states, known as a \"cat state.\" We created cat states as large as 111 photons and extended this protocol to create superpositions of up to four coherent states. This control creates a powerful interface between discrete and continuous variable quantum computation and could enable applications in metrology and quantum information processing.

The accuracy of logical operations on quantum bits (qubits) must be improved for quantum computers to outperform classical ones in useful tasks. One method to achieve this is quantum error correction (QEC), which prevents noise in the underlying system from causing logical errors. This approach derives from the reasonable assumption that noise is local, that is, it does not act in a coordinated way on different parts of the physical system. Therefore, if a logical qubit is encoded non-locally, we can—for a limited time—detect and correct noise-induced evolution before it corrupts the encoded information 1 . In 2001, Gottesman, Kitaev and Preskill (GKP) proposed a hardware-efficient instance of such a non-local qubit: a superposition of position eigenstates that forms grid states of a single oscillator 2 . However, the implementation of measurements that reveal this noise-induced evolution of the oscillator while preserving the encoded information 3 – 7 has proved to be experimentally challenging, and the only realization reported so far relied on post-selection 8 , 9 , which is incompatible with QEC. Here we experimentally prepare square and hexagonal GKP code states through a feedback protocol that incorporates non-destructive measurements that are implemented with a superconducting microwave cavity having the role of the oscillator. We demonstrate QEC of an encoded qubit with suppression of all logical errors, in quantitative agreement with a theoretical estimate based on the measured imperfections of the experiment. Our protocol is applicable to other continuous-variable systems and, in contrast to previous implementations of QEC 10 – 14 , can mitigate all logical errors generated by a wide variety of noise processes and facilitate fault-tolerant quantum computation. Quantum error correction of Gottesman–Kitaev–Preskill code states is realized experimentally in a superconducting quantum device.

An entangled Bell state of two superconducting quantum bits can be stabilized for an arbitrary time using an autonomous feedback scheme, that is, one that does not require a complicated external error-correcting feedback loop. Harnessing dissipation in entangled quantum states Entangled states are a key resource in fundamental quantum physics, quantum cryptography and quantum computation. It has been generally assumed that the creation of such states requires the avoidance of contact with a dissipative environment, and minimization of decoherence. Some studies have shown, however, that dissipative interactions can be used to preserve coherence, and in this issue of Nature two groups demonstrate this principle for continuously driven physical systems. Lin et al . use engineered dissipation to deterministically produce and stabilize entanglement between two trapped-ion qubits, independent of their initial state. Shankar et al . use an autonomous feedback scheme to counteract decoherence and demonstrate the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time. This approach may be applied to a broad range of experimental systems to achieve desired quantum dynamics or steady states. Quantum error correction codes are designed to protect an arbitrary state of a multi-qubit register from decoherence-induced errors 1 , but their implementation is an outstanding challenge in the development of large-scale quantum computers. The first step is to stabilize a non-equilibrium state of a simple quantum system, such as a quantum bit (qubit) or a cavity mode, in the presence of decoherence. This has recently been accomplished using measurement-based feedback schemes 2 , 3 , 4 , 5 . The next step is to prepare and stabilize a state of a composite system 6 , 7 , 8 . Here we demonstrate the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time. Our result is achieved using an autonomous feedback scheme that combines continuous drives along with a specifically engineered coupling between the two-qubit register and a dissipative reservoir. Similar autonomous feedback techniques have been used for qubit reset 9 , single-qubit state stabilization 10 , and the creation 11 and stabilization 6 of states of multipartite quantum systems. Unlike conventional, measurement-based schemes, the autonomous approach uses engineered dissipation to counteract decoherence 12 , 13 , 14 , 15 , obviating the need for a complicated external feedback loop to correct errors. Instead, the feedback loop is built into the Hamiltonian such that the steady state of the system in the presence of drives and dissipation is a Bell state, an essential building block for quantum information processing. Such autonomous schemes, which are broadly applicable to a variety of physical systems, as demonstrated by the accompanying paper on trapped ion qubits 16 , will be an essential tool for the implementation of quantum error correction.

Circulators and directional amplifiers are crucial nonreciprocal signal routing and processing components involved in microwave read-out chains for a variety of applications. They are particularly important in the field of superconducting quantum information, where the devices also need to have minimal photon losses to preserve the quantum coherence of signals. Conventional commercial implementations of each device suffer from losses and are built from very different physical principles, which has led to separate strategies for the construction of their quantum-limited versions. However, as recently theoretically, by establishing simultaneous pairwise conversion and/or gain processes between three modes of a Josephson-junction-based superconducting microwave circuit, it is possible to endow the circuit with the functions of either a phase-preserving directional amplifier or a circulator. Here, we experimentally demonstrate these two modes of operation of the same circuit. Furthermore, in the directional amplifier mode, we show that the noise performance is comparable to standard nondirectional superconducting amplifiers, while in the circulator mode, we show that the sense of circulation is fully reversible. Our device is far simpler in both modes of operation than previous proposals and implementations, requiring only three microwave pumps. It offers the advantage of flexibility, as it can dynamically switch between modes of operation as its pump conditions are changed. Moreover, by demonstrating that a single three-wave process yields nonreciprocal devices with reconfigurable functions, our work breaks the ground for the development of future, more complex directional circuits, and has excellent prospects for on-chip integration.

A quantum computer has the potential to efficiently solve problems that are intractable for classical computers. However, constructing a large-scale quantum processor is challenging because of the errors and noise that are inherent in real-world quantum systems. One approach to addressing this challenge is to utilize modularity—a strategy used frequently in nature and engineering to build complex systems robustly. Such an approach manages complexity and uncertainty by assembling small, specialized components into a larger architecture. These considerations have motivated the development of a quantum modular architecture, in which separate quantum systems are connected into a quantum network via communication channels 1 , 2 . In this architecture, an essential tool for universal quantum computation is the teleportation of an entangling quantum gate 3 – 5 , but such teleportation has hitherto not been realized as a deterministic operation. Here we experimentally demonstrate the teleportation of a controlled-NOT (CNOT) gate, which we make deterministic by using real-time adaptive control. In addition, we take a crucial step towards implementing robust, error-correctable modules by enacting the gate between two logical qubits, encoding quantum information redundantly in the states of superconducting cavities 6 . By using such an error-correctable encoding, our teleported gate achieves a process fidelity of 79 per cent. Teleported gates have implications for fault-tolerant quantum computation 3 , and when realized within a network can have broad applications in quantum communication, metrology and simulations 1 , 2 , 7 . Our results illustrate a compelling approach for implementing multi-qubit operations on logical qubits and, if integrated with quantum error-correction protocols, indicate a promising path towards fault-tolerant quantum computation using a modular architecture. A teleported controlled-NOT gate is realized experimentally between two logical qubits implemented as superconducting cavity quantum memories, thus demonstrating an important tool for universal computation in a quantum modular architecture.