Fig. 1

Experimental layout. The schematic shows a transmon qubit (in blue) comprised of a capacitor and a SQUID loop with two nearly identical junctions. The qubit charging and total Josephson energies are E_C = 299 MHz and E_JΣ = 26.2 GHz. The qubit is coupled via a gate capacitor C_g to a coplanar waveguide resonator (CPW, in green) with a resonance frequency ω_r around 2π × 5.12 GHz. The magnetic flux Φ through the transmon’s SQUID loop is controlled by a dc-current flowing through a flux-bias line (in red). An arbitrary waveform generator (AWG) and a microwave analog signal generator are employed to create a Ramsey sequence of two π/2 microwave pulses at a carrier frequency ω_d = 2π × 7.246 GHz separated by a time delay τ. The sequence drives the transmon into a superposition of ground and excited states where the state amplitudes depend on the accumulated phase ϕ = [ω_d−ω₀₁(Φ)]τ. The qubit state is read out nondestructively using a probe pulse sent to the CPW resonator; the reflected signal is downconverted (not shown in the figure), digitized, and analyzed by a computer. Next, the computer updates a flux distribution function \({\cal P}({\mathrm{\Phi }})\) stored in its memory, determines the next optimal Ramsey delay time, and feeds it back into the AWG. a Qubit transition frequency ω₀₁(Φ) as a function of magnetic flux Φ (parabolic curve). The bottom inset shows the CPW resonator’s spectrum. The red circles indicate the bias point of our transmon sensor: we operate far away from the ‘sweet spot’ in a regime where the transmon’s frequency ω₀₁(Φ) is an approximately linear function of the flux Φ within the entire flux range ΔΦ. For the fluxes around the point considered here, the frequency ω_r of the readout CPW resonator remains approximately constant. b A pre-measured sample-specific Ramsey interference fringes pattern defines the “passport” function of our sensor. This can be regarded as a non-normalized probability function P _p (τ, Φ) to observe the qubit in the excited state after a Ramsey sequence with a delay τ for a specific value of the magnetic flux Φ. The largest flux value used to obtain the Ramsey interference fringes pattern Φ = 0.1394 Φ₀ corresponds to a frequency detuning Δω = ω_d−ω₀₁(Φ) = 2π × 15.8 MHz between the drive and the qubit transition frequencies. The flux range of the “passport” ΔΦ~2.5 × 10⁻³ Φ₀ corresponds to a range 2π × 13.8 MHz in frequency detuning