Two-Qubit Spectroscopy of Spatiotemporally Correlated Quantum Noise in Superconducting Qubits

Abstract

Noise that exhibits significant temporal and spatial correlations across multiple qubits can be especially harmful to both fault-tolerant quantum computation and quantum-enhanced metrology. However, a complete spectral characterization of the noise environment of even a two-qubit system has not been reported thus far. We propose and experimentally demonstrate a protocol for two-qubit dephasing noise spectroscopy based on continuous-control modulation. By combining ideas from spin-locking relaxometry with a statistically motivated robust estimation approach, our protocol allows for the simultaneous reconstruction of all the single-qubit and two-qubit cross-correlation spectra, including access to their distinctive nonclassical features. Only single-qubit control manipulations and state-tomography measurements are employed, with no need for entangled-state preparation or readout of two-qubit observables. While our experimental demonstration uses two superconducting qubits coupled to a shared, colored engineered noise source, our methodology is portable to a variety of dephasing-dominated qubit architectures. By pushing quantum noise spectroscopy beyond the single-qubit setting, our work heralds the characterization of spatiotemporal correlations in both engineered and naturally occurring noise environments.

Multi-level quantum noise spectroscopy

“…The level separation between dressed states is the Rabi frequency Ω (0, 1) , and it is determined predominantly (although not exactly, as we describe below) by the effective driving strength λ (0, 1) A drive ≡ A drive 34 , 35 . These dressed states form the usual spin-locking basis of a conventional, driven two-level sensor 16 , 32 , 33 .…”

“…First, although the splitting energy ℏ Ω ( j −1, j ) between the j th pair of dressed states (the j th spin-locked states) is predominantly determined by the effective driving energy ℏ ( λ ( j −1, j ) A drive ), they are not universally equivalent. For an ideal two-level system within the rotating wave approximation, the Rabi frequency is indeed proportional to the effective driving field via the standard Rabi formula 16 , 32 , 33 . However, this is not generally the case in a multi-level setting due to additional level repulsion from adjacent dressed states 36 .…”

“…In the limit where λ ( j −1, j ) A drive is small compared to the sensor anharmonicities, Eqs. ( 4 ) and ( 5 ) reduce to which conform to the standard spin-locking noise spectroscopy protocol for a two-level sensor 16 , 32 , 33 . However, as the effective drive strength λ ( j −1, j ) A drive increases, the contribution of peripheral bare states— other than and —to the formation of the spin-locked states and increases.…”

“…As a result, in the large λ ( j −1, j ) A drive limit, the multi-level dressing transduces the frequency fluctuations of more than two levels to the longitudinal relaxation within the j th spin locking frame. Also, this multi-level effect contributes to the emergence of non-zero transverse relaxation , terms which would otherwise be absent within a two-level approximation 16 , 32 , 33 .…”

“…Among existing QNS protocols, the spin-locking approach has been shown to be applicable to both classical and non-classical noise spectra. It is also experimentally advantageous, using a relatively straightforward relaxometry analysis to extract a spectral decomposition of the environmental noise affecting single qubits 16 , 32 , and it has recently been extended to measure the cross-spectra of spatially correlated noise in multi-qubit systems 33 . As with many contemporary QNS protocols, the spin-locking approach presumes a two-level-system approximation.…”