Deterministic teleportation of a quantum gate between two logical qubits.

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 channels1,2. In this architecture, an essential tool for universal quantum computation is the teleportation of an entangling quantum gate3-5, 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 cavities6. 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 computation3, and when realized within a network can have broad applications in quantum communication, metrology and simulations1,2,7. 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.

Extending the lifetime of a quantum bit with error correction in superconducting circuits.

Quantum error correction (QEC) can overcome the errors experienced by qubits 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. 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. Although previous works have demonstrated elements of QEC, 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 of a superconducting resonator. 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.

Path-Independent Quantum Gates with Noisy Ancilla.

Ancilla systems are often indispensable to universal control of a nearly isolated quantum system. However, ancilla systems are typically more vulnerable to environmental noise, which limits the performance of such ancilla-assisted quantum control. To address this challenge of ancilla-induced decoherence, we propose a general framework that integrates quantum control and quantum error correction, so that we can achieve robust quantum gates resilient to ancilla noise. We introduce the path independence criterion for fault-tolerant quantum gates against ancilla errors. As an example, a path-independent gate is provided for superconducting circuits with a hardware-efficient design.

High-contrast qubit interactions using multimode cavity QED.

We introduce a new multimode cavity QED architecture for superconducting circuits that can be used to implement photonic memories, more efficient Purcell filters, and quantum simulations of photonic materials. We show that qubit interactions mediated by multimode cavities can have exponentially improved contrast for two qubit gates without sacrificing gate speed. Using two qubits coupled via a three-mode cavity system we spectroscopically observe multimode strong couplings up to 102 MHz and demonstrate suppressed interactions off resonance of 10 kHz when the qubits are ≈600 MHz detuned from the cavity resonance. We study Landau-Zener transitions in our multimode systems and demonstrate quasiadiabatic loading of single photons into the multimode cavity in 25 ns. We introduce an adiabatic gate protocol to realize a controlled-Z gate between the qubits in 95 ns and create a Bell state with 94.7% fidelity. This corresponds to an on/off ratio (gate contrast) of 1000.

Implementing a universal gate set on a logical qubit encoded in an oscillator.

A logical qubit is a two-dimensional subspace of a higher dimensional system, chosen such that it is possible to detect and correct the occurrence of certain errors. Manipulation of the encoded information generally requires arbitrary and precise control over the entire system. Whether based on multiple physical qubits or larger dimensional modes such as oscillators, the individual elements in realistic devices will always have residual interactions, which must be accounted for when designing logical operations. Here we demonstrate a holistic control strategy which exploits accurate knowledge of the Hamiltonian to manipulate a coupled oscillator-transmon system. We use this approach to realize high-fidelity (98.5%, inferred), decoherence-limited operations on a logical qubit encoded in a superconducting cavity resonator using four-component cat states. Our results show the power of applying numerical techniques to control linear oscillators and pave the way for utilizing their large Hilbert space as a resource in quantum information processing.A logical qubit is a two-dimensional subspace of a higher dimensional system, whose manipulation requires precise control over the whole system. Here the authors demonstrate a control strategy which exploits precise knowledge of the Hamiltonian to manipulate a coupled oscillator-transmon system.

A Schrödinger cat living in two boxes.

Quantum superpositions of distinct coherent states in a single-mode harmonic oscillator, known as "cat states," have been an elegant demonstration of Schrödinger's famous cat paradox. Here, we realize a two-mode cat state of electromagnetic fields in two microwave cavities bridged by a superconducting artificial atom, which can also be viewed as an entangled pair of single-cavity cat states. We present full quantum state tomography of this complex cat state over a Hilbert space exceeding 100 dimensions via quantum nondemolition measurements of the joint photon number parity. The ability to manipulate such multicavity quantum states paves the way for logical operations between redundantly encoded qubits for fault-tolerant quantum computation and communication.