Quantum data are 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 to actively protect against both. In the smallest error correction 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. Here 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. While increased physical qubit coherence times and shorter quantum error correction blocks are required to actively safeguard the quantum information, this demonstration is a critical step towards larger codes based on multiple parity measurements.
Scaling down the dimensions of thermoacoustic sound sources (thermophones) improves efficiency by means of reducing speaker heat capacity. Recent experiments with nanoscale thermophones have revealed properties which are not fully understood theoretically. We develop a Green's function formalism which quantitatively explains some observed discrepancies, e.g., the effect of a heat-absorbing substrate in the proximity of the sound source. We also find a generic ultimate limit for thermophone efficiency. We verify the theory with experiments and finite difference method simulations which deal with thermoacoustically operated suspended arrays of nanowires. The efficiency of our devices is measured to be 1 order of magnitude below the ultimate bound. At low frequencies this mainly results from the presence of a substrate. At high frequencies, on the other hand, the efficiency is limited by the heat capacity of the nanowires. Measured sound pressure level and efficiency are in good agreement with simulations. We discuss the feasibility of reaching the ultimate limit in practice.
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