Demonstration of Weight-Four Parity Measurements in the Surface Code Architecture

Abstract

We present parity measurements on a five-qubit lattice with connectivity amenable to the surface code quantum error correction architecture. Using all-microwave controls of superconducting qubits coupled via resonators, we encode the parities of four data qubit states in either the X-or the Z-basis. Given the connectivity of the lattice, we perform full characterization of the static Zinteractions within the set of five qubits, as well as dynamical Z-interactions brought along by single-and two-qubit microwave drives. The parity measurements are significantly improved by modifying the microwave two-qubit gates to dynamically remove non-ideal Z errors.The fragile nature of quantum information means that the success of large-scale quantum computing hinges upon the successful implementation of quantum error correction (QEC) on physical qubit systems. Typically QEC protocols function through encoding of physical qubit information onto larger subspaces, which are subsequently protected against particular quantum errors [1, 2]. Amongst the many proposed QEC codes, the topological surface code [3,4] has gathered a large amount of interest by experimental implementations [5,6] due to its use of short-range nearest-neighbor interactions between physical qubits and its relatively high error thresholds.Building up a physical quantum network with the complete functionality of the surface code brings along a number of experimental challenges, some of which have yet to be explored. However, in the particular case of superconducting qubits, recent advances in coherence times [7][8][9] and in the understanding of environmental constraints [10,11] have triggered important experimental demonstrations on increasingly larger systems, including correction of bit-flip errors on linear qubit arrays [6,12], the detection of arbitrary quantum errors [13], and state preservation via encoding in cavity coherent states [14]. With gate fidelities continuing to improve [15,16], it becomes critical to demonstrate the ability to perform these operations in systems with the degree of connectivity required by the surface code. Furthermore, exploring higher-order errors in such nontrivially arranged networks of qubits are necessary for outlining the proper route towards larger numbers of interconnected qubits for QEC.In this Letter we demonstrate a plaquette of the surface code QEC protocol with an interconnected network of five superconducting transmon qubits. This network consists of four data qubits each explicitly coupled to a single syndrome qubit, through which single-shot highfidelity readout is used to measure weight-four checks of both the bit-flip and phase-flip data qubit parity. The geometrical arrangement of the network permits a systematic calibration of crosstalk noise within the plaquette, and we specifically look for errors in non-participating, or "spectator" qubits, during two-qubit gates. To make The five specific qubits used for the plaquette experiment are highlighted and labeled as data qubits (Di, i ∈ [1, 4]) and syndrome ...

Approaching ultrastrong coupling in transmon circuit QED using a high-impedance resonator

“…First, the transmon has become a standard in efforts to build a quantum processor [23][24][25]. Implementing USC in this system therefore paves the way to exploiting USC features in quantum computation to decrease gate times [10] and perform quantum error correction [11].…”

Convergence of the multimode quantum Rabi model of circuit quantum electrodynamics

“…Akin to cavity QED is the field of circuit QED [5], where artificial atoms such as anharmonic superconducting LC circuits couple to the modes of a waveguide resonator or an open transmission line. Such systems allow the study of a wealth of quantum effects [6,7] and are one of the most promising platforms for the realization of quantum processors [8][9][10]. Despite experimental successes, "ad hoc" multimode extensions of the Rabi model suffer from divergences when considering the limit of infinite modes in a waveguide resonator [11,12].…”

Three-qubit direct dispersive parity measurement with tunable coupling qubits

“…5 we see how building on this intuition we can conceive a configuration that implements the sign flip described by Eqs. (47).The bare transmons composing the TCQ are coupled at the same location (or close to each other) to resonator 1 while at locations separated by approximately half a wavelength to resonator 2. This idea is somehow similar to what has been proposed in [38] for implementing a giant atom coupled at different locations of a transmission line, although in a different context compared to the problem we are tackling here and most of all considering a simple transmon, and not a TCQ.…”