Abstract: Weak measurement has provided new insight into the nature of quantum measurement, by demonstrating the ability to extract average state information without fully projecting the system. For single-qubit measurements, this partial projection has been demonstrated with violations of the Leggett–Garg inequality. Here we investigate the effects of weak measurement on a maximally entangled Bell state through application of the Hybrid Bell–Leggett–Garg inequality (BLGI) on a linear chain of four transmon qubits. By correlating the results of weak ancilla measurements with subsequent projective readout, we achieve a violation of the BLGI with 27 s.d.s. of certainty.

A precise measurement of dephasing over a range of time scales is critical for improving quantum gates beyond the error correction threshold. We present a metrological tool based on randomized benchmarking capable of greatly increasing the precision of Ramsey and spin-echo sequences by the repeated but incoherent addition of phase noise. We find our superconducting-quantum-interference-device-based qubit is not limited by 1/f flux noise at short time scales but instead observe a telegraph noise mechanism that is not amenable to study with standard measurement techniques.

One of the key challenges in quantum information is coherently manipulating the quantum state. However, it is an outstanding question whether control can be realized with low error. Only gates from the Clifford group - containing π, π/2, and Hadamard gates - have been characterized with high accuracy. Here, we show how the Platonic solids enable implementing and characterizing larger gate sets. We find that all gates can be implemented with low error. The results fundamentally imply arbitrary manipulation of the quantum state can be realized with high precision, providing practical possibilities for designing efficient quantum algorithms.