Encoding a magic state with beyond break-even fidelity.

To run large-scale algorithms on a quantum computer, error-correcting codes must be able to perform a fundamental set of operations, called logic gates, while isolating the encoded information from noise1-8. We can complete a universal set of logic gates by producing special resources called magic states9-11. It is therefore important to produce high-fidelity magic states to conduct algorithms while introducing a minimal amount of noise to the computation. Here we propose and implement a scheme to prepare a magic state on a superconducting qubit array using error correction. We find that our scheme produces better magic states than those that can be prepared using the individual qubits of the device. This demonstrates a fundamental principle of fault-tolerant quantum computing12, namely, that we can use error correction to improve the quality of logic gates with noisy qubits. Moreover, we show that the yield of magic states can be increased using adaptive circuits, in which the circuit elements are changed depending on the outcome of mid-circuit measurements. This demonstrates an essential capability needed for many error-correction subroutines. We believe that our prototype will be invaluable in the future as it can reduce the number of physical qubits needed to produce high-fidelity magic states in large-scale quantum-computing architectures.

Quantifying error and leakage in an encoded Si/SiGe triple-dot qubit.

Quantum computation requires qubits that satisfy often-conflicting criteria, which include long-lasting coherence and scalable control1. One approach to creating a suitable qubit is to operate in an encoded subspace of several physical qubits. Although such encoded qubits may be particularly susceptible to leakage out of their computational subspace, they can be insensitive to certain noise processes2,3 and can also allow logical control with a single type of entangling interaction4 while maintaining favourable features of the underlying physical system. Here we demonstrate high-fidelity operation of an exchange-only qubit encoded in a subsystem of three coupled electron spins5 confined in gated, isotopically enhanced silicon quantum dots6. This encoding requires neither high-frequency electric nor magnetic fields for control, and instead relies exclusively on the exchange interaction4,5, which is highly local and can be modulated with a large on-off ratio using only fast voltage pulses. It is also compatible with very low and gradient-free magnetic field environments, which simplifies integration with superconducting materials. We developed and employed a modified blind randomized benchmarking protocol that determines both computational and leakage errors7,8, and found that unitary operations have an average total error of 0.35%, with half of that, 0.17%, coming from leakage driven by interactions with substrate nuclear spins. The combination of this proven performance with complete control via gate voltages makes the exchange-only qubit especially attractive for use in many-qubit systems.

Efficient measurement of quantum gate error by interleaved randomized benchmarking.

We describe a scalable experimental protocol for estimating the average error of individual quantum computational gates. This protocol consists of interleaving random Clifford gates between the gate of interest and provides an estimate as well as theoretical bounds for the average error of the gate under test, so long as the average noise variation over all Clifford gates is small. This technique takes into account both state preparation and measurement errors and is scalable in the number of qubits. We apply this protocol to a superconducting qubit system and find a bounded average error of 0.003 [0,0.016] for the single-qubit gates X(π/2) and Y(π/2). These bounded values provide better estimates of the average error than those extracted via quantum process tomography.

Universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits.

We use quantum process tomography to characterize a full universal set of all-microwave gates on two superconducting single-frequency single-junction transmon qubits. All extracted gate fidelities, including those for Clifford group generators, single-qubit π/4 and π/8 rotations, and a two-qubit controlled-not, exceed 95% (98%), without (with) subtracting state preparation and measurement errors. Furthermore, we introduce a process map representation in the Pauli basis which is visually efficient and informative. This high-fidelity gate set serves as a critical building block towards scalable architectures of superconducting qubits for error correction schemes and pushes up on the known limits of quantum gate characterization.

Entanglement of two superconducting qubits in a waveguide cavity via monochromatic two-photon excitation.

We report a system where fixed interactions between noncomputational levels make bright the otherwise forbidden two-photon |00}→|11} transition. The system is formed by hand selection and assembly of two discrete component transmon-style superconducting qubits inside a rectangular microwave cavity. The application of a monochromatic drive tuned to this transition induces two-photon Rabi-like oscillations between the ground and doubly excited states via the Bell basis. The system therefore allows all-microwave two-qubit universal control with the same techniques and hardware required for single qubit control. We report Ramsey-like and spin echo sequences with the generated Bell states, and measure a two-qubit gate fidelity of F(g)=90% (unconstrained) and 86% (maximum likelihood estimator).