Quantum error correction will be a necessary component towards realizing scalable quantum computers with physical qubits. Theoretically, it is possible to perform arbitrarily long computationsif the error rate is below a threshold value. The two-dimensional surface code permits relatively high fault-tolerant thresholds at the ~1% level, and only requires a latticed network of qubits with nearest-neighbor interactions. Superconducting qubits have continued to steadily improve in coherence, gate, and readout fidelities, to become a leading candidate for implementation into larger quantum networks. Here we describe characterization experiments and calibration of a system of four superconducting qubits arranged in a planar lattice, amenable to the surface code. Insights into the particular qubit design and comparison between simulated parameters and experimentally determined parameters are given. Single- and two-qubit gate tune-up procedures are described and results for simultaneously benchmarking pairs of two-qubit gates are given. All controls are eventually used for an arbitrary error detection protocol described in separate work [Corcoles et al., Nature Communications, 6, 2015]
To build a fault-tolerant quantum computer, it is necessary to implement a quantum error correcting code. Such codes rely on the ability to extract information about the quantum errorsyndrome while not destroying the quantum information encoded in the system. Stabilizer codes are attractive solutions to this problem, as they are analogous to classical linear codes, have simple and easily computed encoding networks, and allow efficient syndrome extraction. In these codes, syndrome extraction is performed via multi-qubit stabilizer measurements, which are bit and phase parity checks up to local operations. Previously, stabilizer codes have been realized in nuclei, trapped-ions, and superconducting qubits. However these implementations lack the ability to perform fault-tolerant syndrome extraction which continues to be a challenge for all physical quantum computing systems. Here we experimentally demonstrate a key step towards this problem by using a two-by-two lattice of superconducting qubits to perform syndrome extraction and arbitrary error detection via simultaneous quantum non-demolition stabilizer measurements. This lattice represents a primitive tile for the surface code, which is a promising stabilizer code for scalable quantum computing. Furthermore, we successfully show the preservation of an entangled state in the presence of an arbitrary applied error through high-fidelity syndrome measurement. Our results bolster the promise of employing lattices of superconducting qubits for larger-scale fault-tolerant quantum computing.
Quantum error correction (QEC) is an essential step towards realising scalable quantum computers. Theoretically, it is possible to achieve arbitrarily long protection of quantum informationfrom corruption due to decoherence or imperfect controls, so long as the error rate is below a threshold value. The two-dimensional surface code (SC) is a fault-tolerant error correction protocol} that has garnered considerable attention for actual physical implementations, due to relatively high error thresholds ~1%, and restriction to planar lattices with nearest-neighbour interactions. Here we show a necessary element for SC error correction: high-fidelity parity detection of two code qubits via measurement of a third syndrome qubit. The experiment is performed on a sub-section of the SC lattice with three superconducting transmon qubits, in which two independent outer code qubits are joined to a central syndrome qubit via two linking bus resonators. With all-microwave high-fidelity single- and two-qubit nearest-neighbour entangling gates, we demonstrate entanglement distributed across the entire sub-section by generating a three-qubit Greenberger-Horne-Zeilinger (GHZ) state with fidelity ~94%. Then, via high-fidelity measurement of the syndrome qubit, we deterministically entangle the otherwise un-coupled outer code qubits, in either an even or odd parity Bell state, conditioned on the syndrome state. Finally, to fully characterize this parity readout, we develop a new measurement tomography protocol to obtain a fidelity metric (90% and 91%). Our results reveal a straightforward path for expanding superconducting circuits towards larger networks for the SC and eventually a primitive logical qubit implementation.
We demonstrate the ability to control the spontaneous emission from a superconducting qubit coupled to a cavity. The time domain profile of the emitted photon is shaped into a symmetrictruncated exponential. The experiment is enabled by a qubit coupled to a cavity, with a coupling strength that can be tuned in tens of nanoseconds while maintaining a constant dressed state emission frequency. Symmetrization of the photonic wave packet will enable use of photons as flying qubits for transfering the quantum state between atoms in distant cavities.