Heisenberg-limited single-mode quantum metrology in a superconducting circuit

Quantum metrology is one of the most promising near-term applications of quantum technology. Reaching a quantum advantage in metrology usually requires hard-to-prepare two-mode entangled states such as NOON states. Instead of exploring quantum entanglement in the two-mode interferometers, a single bosonic mode also promises a measurement precision beyond the shot-noise limit (SNL) by taking advantage of the infinite-dimensional Hilbert space of Fock states. In this talk, we demonstrate such a single-mode phase estimation that approaches the Heisenberg limit (HL) unconditionally in a superconducting circuit by preparing the superpositions of Fock states (|0>+|N>) up to N=12. We realize a 9.1 dB improvement over the SNL at N=12, which is only 1.7 dB away from the HL. Our experimental architecture can be combined with quantum error correction techniques to fight against decoherence, and thus promises quantum-enhanced sensing in practical applications.