Quantum data is susceptible to decoherence induced by the environment and to errors in the hardware processing it. A future fault-tolerant quantum computer will use quantum error correction (QEC) to actively protect against both. In the smallest QEC
codes, the information in one logical qubit is encoded in a two-dimensional subspace of a larger Hilbert space of multiple physical qubits. For each code, a set of non-demolition multi-qubit measurements, termed stabilizers, can discretize and signal physical qubit errors without collapsing the encoded information. Experimental demonstrations of QEC to date, using nuclear magnetic resonance, trapped ions, photons, superconducting qubits, and NV centers in diamond, have circumvented stabilizers at the cost of decoding at the end of a QEC cycle. This decoding leaves the quantum information vulnerable to physical qubit errors until re-encoding, violating a basic requirement for fault tolerance. Using a five-qubit superconducting processor, we realize the two parity measurements comprising the stabilizers of the three-qubit repetition code protecting one logical qubit from physical bit-flip errors. We construct these stabilizers as parallelized indirect measurements using ancillary qubits, and evidence their non-demolition character by generating three-qubit entanglement from superposition states. We demonstrate stabilizer-based quantum error detection (QED) by subjecting a logical qubit to coherent and incoherent bit-flip errors on its constituent physical qubits. While increased physical qubit coherence times and shorter QED blocks are required to actively safeguard quantum information, this demonstration is a critical step toward larger codes based on multiple parity measurements.
We demonstrate the active suppression of transmon qubit dephasing induced by dispersive measurement, using parametric amplification and analog feedback. By real-time processing of the homodyne record, the feedback controller reverts the stochastic qu
antum phase kick imparted by the measurement on the qubit. The feedback operation matches a model of quantum trajectories with measurement efficiency $tilde{eta} approx 0.5$, consistent with the result obtained by postselection. We overcome the bandwidth limitations of the amplification chain by numerically optimizing the signal processing in the feedback loop and provide a theoretical model explaining the optimization result.
We realize indirect partial measurement of a transmon qubit in circuit quantum electrodynamics by interaction with an ancilla qubit and projective ancilla measurement with a dedicated readout resonator. Accurate control of the interaction and ancilla
measurement basis allows tailoring the measurement strength and operator. The tradeoff between measurement strength and qubit back-action is characterized through the distortion of a qubit Rabi oscillation imposed by ancilla measurement in different bases. Combining partial and projective qubit measurements, we provide the solid-state demonstration of the correspondence between a non-classical weak value and the violation of a Leggett-Garg inequality.
We experimentally demonstrate single-spin magnetometry with multi-pulse sensing sequences. The use of multi-pulse sequences can greatly increase the sensing time per measurement shot, resulting in enhanced ac magnetic field sensitivity. We theoretica
lly derive and experimentally verify the optimal number of sensing cycles, for which the effects of decoherence and increased sensing time are balanced. We perform these experiments for oscillating magnetic fields with fixed phase as well as for fields with random phase. Finally, by varying the phase and frequency of the ac magnetic field, we measure the full frequency-filtering characteristics of different multi-pulse schemes and discuss their use in magnetometry applications.
