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Density matrix exponentiation (DME) is a general technique for using a quantum state ρ to enact the quantum operation e^{-iρθ} on a target system. It was first proposed in the context of quantum machine learning, but has since been shown to have broad applications in quantum metrology and computation. No experimental demonstration of DME has been performed thus far due to its demanding circuit depths and the need to efficiently generate multiple identical copies of ρ during the finite lifetime of the target system. In this work, we describe the first demonstration of the DME algorithm, which we accomplish using a superconducting quantum processor. Our demonstration relies on a 99.7% fidelity controlled-phase gate implemented using two tunable superconducting transmon qubits. We achieve a fidelity surpassing 90% at circuit depths exceeding 70 when comparing the output of the circuit executed on our quantum processor to a simulation assuming perfect operations and measurements.

The microscopic description of 1/f magnetic flux noise in superconducting circuits has remained an open question for several decades despite extensive experimental and theoretical investigation. Recent progress in superconducting devices for quantum information has highlighted the need to mitigate sources of qubit decoherence, driving a renewed interest in understanding the underlying noise mechanism(s). Though a consensus has emerged attributing flux noise to surface spins, their identity and interaction mechanisms remain unclear, prompting further study. Here, we apply weak in-plane magnetic fields to a capacitively shunted flux qubit (where the Zeeman splitting of surface spins lies below the device temperature) and study the flux-noise-limited qubit dephasing, revealing previously unexplored trends that may shed light on the dynamics behind the emergent 1/f noise. Notably, we observe an enhancement (suppression) of the spin-echo (Ramsey) pure-dephasing time in fields up to B=100  G. With direct noise spectroscopy, we further observe a transition from a 1/f to approximately Lorentzian frequency dependence below 10 Hz and a reduction of the noise above 1 MHz with increasing magnetic field. We suggest that these trends are qualitatively consistent with an increase of spin cluster sizes with magnetic field. These results should help to inform a complete microscopic theory of 1/f flux noise in superconducting circuits.

Superconducting qubits are a promising platform for building a larger-scale quantum processor capable of solving otherwise intractable problems. In order for the processor to reach practical viability, the gate errors need to be further suppressed and remain stable for extended periods of time. With recent advances in qubit control, both single- and two-qubit gate fidelities are now in many cases limited by the coherence times of the qubits. Here we experimentally employ closed-loop feedback to stabilize the frequency fluctuations of a superconducting transmon qubit, thereby increasing its coherence time by 26% and reducing the single-qubit error rate from (8.5 ± 2.1) × 10 -4 to (5.9 ± 0.7) × 10 -4 . Importantly, the resulting high-fidelity operation remains effective even away from the qubit flux-noise insensitive point, significantly increasing the frequency bandwidth over which the qubit can be operated with high fidelity. This approach is helpful in large qubit grids, where frequency crowding and parasitic interactions between the qubits limit their performance., (© 2022. The Author(s).)

Dielectrics with low loss at microwave frequencies are imperative for high-coherence solid-state quantum computing platforms. Here we study the dielectric loss of hexagonal boron nitride (hBN) thin films in the microwave regime by measuring the quality factor of parallel-plate capacitors (PPCs) made of NbSe 2 -hBN-NbSe 2 heterostructures integrated into superconducting circuits. The extracted microwave loss tangent of hBN is bounded to be at most in the mid-10 -6 range in the low-temperature, single-photon regime. We integrate hBN PPCs with aluminium Josephson junctions to realize transmon qubits with coherence times reaching 25 μs, consistent with the hBN loss tangent inferred from resonator measurements. The hBN PPC reduces the qubit feature size by approximately two orders of magnitude compared with conventional all-aluminium coplanar transmons. Our results establish hBN as a promising dielectric for building high-coherence quantum circuits with substantially reduced footprint and with a high energy participation that helps to reduce unwanted qubit cross-talk., (© 2022. The Author(s), under exclusive licence to Springer Nature Limited.)

System noise identification is crucial to the engineering of robust quantum systems. Although existing quantum noise spectroscopy (QNS) protocols measure an aggregate amount of noise affecting a quantum system, they generally cannot distinguish between the underlying processes that contribute to it. Here, we propose and experimentally validate a spin-locking-based QNS protocol that exploits the multi-level energy structure of a superconducting qubit to achieve two notable advances. First, our protocol extends the spectral range of weakly anharmonic qubit spectrometers beyond the present limitations set by their lack of strong anharmonicity. Second, the additional information gained from probing the higher-excited levels enables us to identify and distinguish contributions from different underlying noise mechanisms.

Models of light-matter interactions in quantum electrodynamics typically invoke the dipole approximation 1,2 , in which atoms are treated as point-like objects when compared to the wavelength of the electromagnetic modes with which they interact. However, when the ratio between the size of the atom and the mode wavelength is increased, the dipole approximation no longer holds and the atom is referred to as a 'giant atom' 2,3 . So far, experimental studies with solid-state devices in the giant-atom regime have been limited to superconducting qubits that couple to short-wavelength surface acoustic waves 4-10 , probing the properties of the atom at only a single frequency. Here we use an alternative architecture that realizes a giant atom by coupling small atoms to a waveguide at multiple, but well separated, discrete locations. This system enables tunable atom-waveguide couplings with large on-off ratios 3 and a coupling spectrum that can be engineered by the design of the device. We also demonstrate decoherence-free interactions between multiple giant atoms that are mediated by the quasi-continuous spectrum of modes in the waveguide-an effect that is not achievable using small atoms 11 . These features allow qubits in this architecture to switch between protected and emissive configurations in situ while retaining qubit-qubit interactions, opening up possibilities for high-fidelity quantum simulations and non-classical itinerant photon generation 12,13 .

The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal interaction. In the weak coupling regime, it reduces to the well-known Jaynes-Cummings model by applying a rotating wave approximation. The rotating wave approximation breaks down in the ultra-strong coupling regime, where the effective coupling strength g is comparable to the energy ω of the bosonic mode, and remarkable features in the system dynamics are revealed. Here we demonstrate an analog quantum simulation of an effective quantum Rabi model in the ultra-strong coupling regime, achieving a relative coupling ratio of g/ω ~ 0.6. The quantum hardware of the simulator is a superconducting circuit embedded in a cQED setup. We observe fast and periodic quantum state collapses and revivals of the initial qubit state, being the most distinct signature of the synthesized model.An analog quantum simulation scheme has been explored with a quantum hardware based on a superconducting circuit. Here the authors investigate the time evolution of the quantum Rabi model at ultra-strong coupling conditions, which is synthesized by slowing down the system dynamics in an effective frame.