Detecting spins by their fluorescence with a microwave photon counter.

Quantum emitters respond to resonant illumination by radiating part of the absorbed energy. A component of this radiation field is phase coherent with the driving tone, whereas another component is incoherent and consists of spontaneously emitted photons, forming the fluorescence signal1. Atoms, molecules and colour centres are routinely detected by their fluorescence at optical frequencies, with important applications in quantum technology2,3 and microscopy4-7. By contrast, electron spins are usually detected by the phase-coherent echoes that they emit in response to microwave driving pulses8. The incoherent part of their radiation-a stream of microwave photons spontaneously emitted upon individual spin relaxation events-has not been observed so far because of the low spin radiative decay rate and of the lack of single microwave photon detectors (SMPDs). Here using superconducting quantum devices, we demonstrate the detection of a small ensemble of donor spins in silicon by their fluorescence at microwave frequencies and millikelvin temperatures. We enhance their radiative decay rate by coupling them to a high-quality-factor and small-mode-volume superconducting resonator9, and we connect the device output to a newly developed SMPD10 based on a superconducting qubit. In addition, we show that the SMPD can be used to detect spin echoes and that standard spin characterization measurements (Rabi nutation and spectroscopy) can be achieved with both echo and fluorescence detection. We discuss the potential of SMPD detection as a method for magnetic resonance spectroscopy of small numbers of spins.

Quantum dynamics of simultaneously measured non-commuting observables.

In quantum mechanics, measurements cause wavefunction collapse that yields precise outcomes, whereas for non-commuting observables such as position and momentum Heisenberg's uncertainty principle limits the intrinsic precision of a state. Although theoretical work has demonstrated that it should be possible to perform simultaneous non-commuting measurements and has revealed the limits on measurement outcomes, only recently has the dynamics of the quantum state been discussed. To realize this unexplored regime, we simultaneously apply two continuous quantum non-demolition probes of non-commuting observables to a superconducting qubit. We implement multiple readout channels by coupling the qubit to multiple modes of a cavity. To control the measurement observables, we implement a 'single quadrature' measurement by driving the qubit and applying cavity sidebands with a relative phase that sets the observable. Here, we use this approach to show that the uncertainty principle governs the dynamics of the wavefunction by enforcing a lower bound on the measurement-induced disturbance. Consequently, as we transition from measuring identical to measuring non-commuting observables, the dynamics make a smooth transition from standard wavefunction collapse to localized persistent diffusion and then to isotropic persistent diffusion. Although the evolution of the state differs markedly from that of a conventional measurement, information about both non-commuting observables is extracted by keeping track of the time ordering of the measurement record, enabling quantum state tomography without alternating measurements. Our work creates novel capabilities for quantum control, including rapid state purification, adaptive measurement, measurement-based state steering and continuous quantum error correction. As physical systems often interact continuously with their environment via non-commuting degrees of freedom, our work offers a way to study how notions of contemporary quantum foundations arise in such settings.

Experimental demonstration of continuous quantum error correction.

The storage and processing of quantum information are susceptible to external noise, resulting in computational errors. A powerful method to suppress these effects is quantum error correction. Typically, quantum error correction is executed in discrete rounds, using entangling gates and projective measurement on ancillary qubits to complete each round of error correction. Here we use direct parity measurements to implement a continuous quantum bit-flip correction code in a resource-efficient manner, eliminating entangling gates, ancillary qubits, and their associated errors. An FPGA controller actively corrects errors as they are detected, achieving an average bit-flip detection efficiency of up to 91%. Furthermore, the protocol increases the relaxation time of the protected logical qubit by a factor of 2.7 over the relaxation times of the bare comprising qubits. Our results showcase resource-efficient stabilizer measurements in a multi-qubit architecture and demonstrate how continuous error correction codes can address challenges in realizing a fault-tolerant system.

Twenty-three-millisecond electron spin coherence of erbium ions in a natural-abundance crystal.

Erbium ions embedded in crystals have unique properties for quantum information processing, because of their optical transition at 1.5 µm and of the large magnetic moment of their effective spin-1/2 electronic ground state. Most applications of erbium require, however, long electron spin coherence times, and this has so far been missing. Here, by selecting a host matrix with a low nuclear-spin density (CaWO4) and by quenching the spectral diffusion due to residual paramagnetic impurities at millikelvin temperatures, we obtain a 23-ms coherence time on the Er3+ electron spin transition. This is the longest Hahn echo electron spin coherence time measured in a material with a natural abundance of nuclear spins and on a magnetically sensitive transition. Our results establish Er3+:CaWO4 as a potential platform for quantum networks.