Single-qubit gates on superconducting quantum processors are typically implemented using microwave pulses applied through dedicated control lines. However, these microwave pulses may also drive other qubits due to crosstalk arising from capacitive coupling and wavefunction overlap in systems with closely spaced transition frequencies. Crosstalk and frequency crowding increase errors during simultaneous single-qubit operations relative to isolated gates, thus forming a major bottleneck for scaling superconducting quantum processors. In this work, we combine model-based qubit frequency optimization with pulse shaping to demonstrate crosstalk error mitigation in single-qubit gates on a 49-qubit superconducting quantum processor. We introduce and experimentally verify an analytical model of simultaneous single-qubit gate error caused by microwave crosstalk that depends on a given pulse shape. By employing a model-based optimization strategy of qubit frequencies, we minimize the crosstalk-induced error across the processor and achieve a mean simultaneous single-qubit gate fidelity of 99.96

Achieving high-fidelity single-qubit gates, two-qubit gates, and qubit readout is critical for building scalable, error-corrected quantum computers. However, device parameters that enhance one operation often degrade the others, making simultaneous optimization challenging. Here, we demonstrate that careful tuning of qubit-coupler coupling strengths in a superconducting circuit with two transmon qubits coupled via a tunable coupler enables high-fidelity single- and two-qubit gates, without compromising readout performance. Furthermore, we introduce a new calibration protocol for diabatic controlled-Z gates, phased-averaged leakage error amplification (PALEA), which enables efficient suppression of coherent gate errors and leakage to noncomputational states. Using PALEA in combination with careful tuning of qubit-coupler coupling strengths, we achieve a 40 h-averaged CZ gate fidelity of 99.93 %, simultaneous single-qubit gate fidelities of 99.98 %, and readout fidelities over 99.94 % in a single device. Our results demonstrate a viable path toward scaling up superconducting quantum processors while maintaining consistently high gate and readout fidelities.

In this work we introduce a superconducting quantum processor architecture that uses a transmission-line resonator to implement effective all-to-all connectivity between six transmon qubits. This architecture can be used as a test-bed for algorithms that benefit from high connectivity. We show that the central resonator can be used as a computational element, which offers the flexibility to encode a qubit for quantum computation or to utilize its bosonic modes which further enables quantum simulation of bosonic systems. To operate the quantum processing unit (QPU), we develop and benchmark the qubit-resonator conditional Z gate and the qubit-resonator MOVE operation. The latter allows for transferring a quantum state between one of the peripheral qubits and the computational resonator. We benchmark the QPU performance and achieve a genuinely multi-qubit entangled Greenberger-Horne-Zeilinger (GHZ) state over all six qubits with a readout-error mitigated fidelity of 0.86.

Modeling composite systems of spins or electrons coupled to bosonic modes is of significant interest for many fields of applied quantum physics and chemistry. A quantum simulation can allow for the solution of quantum problems beyond classical numerical methods. However, implementing this on existing noisy quantum computers can be challenging due to the mapping between qubits and bosonic degrees of freedom, often requiring a large number of qubits or deep quantum circuits. In this work, we discuss quantum algorithms to solve composite systems by augmenting conventional superconducting qubits with microwave resonators used as computational elements. This enables direct representation of bosonic modes by resonators. We derive efficient algorithms for typical models and propose a device connectivity that allows for feasible scaling of simulations with linear overhead. We also show how the dissipation of resonators can be a useful parameter for modeling continuous bosonic baths. Experimental results demonstrating these methods were obtained on the IQM Resonance cloud platform, based on high-fidelity gates and tunable couplers. These results present the first digital quantum simulation including a computational resonator on a commercial quantum platform.

Achieving industrial quantum advantage is unlikely without the use of quantum error correction (QEC). Other QEC codes beyond surface code are being experimentally studied, such as color codes and quantum low-density parity check codes, that could benefit from new quantum processing unit (QPU) architectures. We introduce the six-qubit star lattice architecture that offers parallelism and effective local all-to-all connectivity and thus enables hardware-efficient implementation of certain QEC codes. As a first demonstration of this new architecture, we encode two logical qubits in a six-qubit superconducting QPU with a star topology using the ⟦4,2,2⟧ code and characterize the logical states with the classical shadow framework. Logical lifetime and logical error rate are measured over repeated quantum error detection cycles for various logical states including a logical Bell state. We measure logical state fidelities above 96% for every cardinal logical state, find logical lifetimes above the best physical element, and logical error-per-cycle values ranging from 0.25(2)% to 0.91(3)%. In future, such star units can be tiled into a lattice to enable QEC codes with high-weight and overlapping stabilizers for improved encoding rates.

Security of modern classical data encryption often relies on computationally hard problems, which can be trivialized with the advent of quantum computers. A potential remedy for this is quantum communication which takes advantage of the laws of quantum physics to provide secure exchange of information. Here, quantum key distribution (QKD) represents a powerful tool, allowing for unconditionally secure quantum communication between remote parties. At the same time, microwave quantum communication is set to play an important role in future quantum networks because of its natural frequency compatibility with superconducting quantum processors and modern near-distance communication standards. To this end, we present an experimental realization of a continuous-variable QKD protocol based on propagating displaced squeezed microwave states. We use superconducting parametric devices for generation and single-shot quadrature detection of these states. We demonstrate unconditional security in our experimental microwave QKD setting. We show that security performance can be improved by adding finite trusted noise to the preparation side. Our results indicate feasibility of secure microwave quantum communication with the currently available technology in both open-air (up to $\sim$ 80 m) and cryogenic (over 1000 m) conditions.

Understanding the non-deterministic behavior of deterministic nonlinear systems has been an implicit dream since Lorenz named it the "butterfly effect". A prominent example is the hysteresis and bistability of the Duffing oscillator, which in the classical description is attributed to the coexistence of two steady states in a double-well potential. However, this interpretation fails in the quantum-mechanical perspective, where a single unique steady state is allowed in the whole parameter space. Here, we measure the non-equilibrium dynamics of a superconducting Duffing oscillator and reconcile the classical and quantum descriptions in a unified picture of quantum metastability. We demonstrate that the two classically regarded steady states are in fact metastable states. They have a remarkably long lifetime in the classical hysteresis regime but must eventually relax into a single unique steady state allowed by quantum mechanics. By engineering the lifetime of the metastable states sufficiently large, we observe a first-order dissipative phase transition, which mimics a sudden change of the mean field in a 11-site Bose-Hubbard lattice. We also reveal the two distinct phases of the transition by quantum state tomography, namely a coherent-state phase and a squeezed-state phase separated by a critical point. Our results reveal a smooth quantum state evolution behind a sudden dissipative phase transition, and they form an essential step towards understanding hysteresis and instability in non-equilibrium systems.

Quantum state tomography of weak microwave signals is an important part of many protocols in the field of quantum information processing with superconducting circuits. This step typically relies on an accurate $\textit{in-situ}$ estimation of signal losses in the experimental set-up and requires a careful photon number calibration. Here, we present an improved method for the microwave loss estimation inside of a closed cryogenic system. Our approach is based on Planck's law and makes use of independent temperature sweeps of individual parts of the cryogenic set-up. Using this technique, we can experimentally resolve changes in microwave losses of less than 0.1 dB in the cryogenic environment. We discuss potential applications of this approach for precise characterization of quantum-limited superconducting amplifiers and in other prominent experimental settings.

The field of propagating quantum microwaves is a relatively new area of research that is receiving increased attention due to its promising technological applications, both in communication and sensing. While formally similar to quantum optics, some key elements required by the aim of having a controllable quantum microwave interface are still on an early stage of development. Here, we argue where and why a fully operative toolbox for propagating quantum microwaves will be needed, pointing to novel directions of research along the way: from microwave quantum key distribution to quantum radar, bath-system learning, or direct dark matter detection. The article therefore functions both as a review of the state-of-the-art, and as an illustration of the wide reach of applications the future of quantum microwaves will open.

One of the cornerstones of quantum communication is the unconditionally secure distribution of classical keys between remote parties. This key feature of quantum technology is based on the quantum properties of propagating electromagnetic waves, such as entanglement, or the no-cloning theorem. However, these quantum resources are known to be susceptible to noise and losses, which are omnipresent in open-air communication scenarios. In this work, we theoretically investigate the perspectives of continuous-variable open-air quantum key distribution at microwave frequencies. In particular, we present a model describing the coupling of propagating microwaves with a noisy environment. Using a protocol based on displaced squeezed states, we demonstrate that continuous-variable quantum key distribution with propagating microwaves can be unconditionally secure at room temperature up to distances of around 200 meters. Moreover, we show that microwaves can potentially outperform conventional quantum key distribution at telecom wavelength at imperfect weather conditions.

Microwave technology plays a central role in current wireless communications, standing among them mobile communication and local area networks (LANs). The microwave range shows relevant advantages with respect to other frequencies in open-air transmission, such as low absorption losses and low energy consumption, and it is additionally the natural working frequency in superconducting quantum technologies. Entanglement distribution between separate parties is at the core of secure quantum communications. Therefore, understanding its limitations in realistic open-air settings, specially in the rather unexplored microwave regime, is crucial for transforming microwave quantum communications into a mainstream technology. Here, we investigate the feasibility of an open-air entanglement distribution scheme with microwave two-mode squeezed states. First, we study the reach of direct entanglement transmission in open-air, obtaining a maximum distance of approximately 500 meters in a realistic setting with state-of-the-art experimental parameters. Afterwards, we adapt entanglement distillation and entanglement swapping protocols to microwave technology in order to reduce environmental entanglement degradation. While entanglement distillation helps to increase quantum correlations in the short-distance low-squeezing regime by up to $46\%$, entanglement swapping increases the reach by $14\%$. Then, we compute the fidelity of a continuous-variable quantum teleportation protocol using open-air-distributed entanglement as a resource. Finally, we adapt the machinery to explore the limitations of quantum communication between satellites, where the thermal noise impact is substantially reduced and diffraction losses are dominant.

We describe a unified quantum approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. We also generalize the method to a chain of resonators with time delays, and reveal several transport properties similar to a photonic crystal. It is shown that both the quantum and classical analyses provide consistent results, and they together reveal different decay and decoherence mechanisms in a general microwave resonator. These results form a solid basis for understanding the scattering spectrums of networks of microwave resonators, and pave the way for applying superconducting microwave resonators in complex circuits.

We propose a tunable coupler consisting of N fixed-frequency qubits, which can tune and even amplify the effective interaction between two superconducting quantum circuits. The tuning range of the interaction is proportional to N, with a minimum value of zero and a maximum that can exceed the physical coupling rates between the coupler and the circuits. The effective coupling rate is determined by the collective magnetic quantum number of the qubit ensemble, which takes only discrete values and is free from collective decay and decoherence. Using single-photon pi-pulses, the coupling rate can be switched between arbitrary choices of the initial and final values within the dynamic range in a single step without going through intermediate values. A cascade of the couplers for amplifying small interactions or weak signals is also discussed. These results should not only stimulate interest in exploring the collective effects in quantum information processing, but also enable development of applications in tuning and amplifying the interactions in a general cavity-QED system.

We describe a unified classical approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. To fill the gap between experiment and theory, we also consider the influences of small circuit asymmetry and the finite length of the feedlines, and describe a procedure to correct their influences in typical experiments. We show that, similar to the transmission coefficient of a hanger-type resonator, the reflection coefficient of a necklace- or cross-type resonator also contains a so-called reference point that can be used to characterize the internal quality factor of the resonator. Our results provide a comprehensive understanding of superconducting microwave resonators from the design concepts to the characterization details.

We have fabricated and studied a system of two tunable and coupled nonlinear superconducting resonators. The nonlinearity is introduced by galvanically coupled dc superconducting quantum interference devices. We simulate the system response by means of a circuit model, which includes an additional signal path introduced by the electromagnetic environment. Furthermore, we present two methods allowing us to experimentally determine the nonlinearity. First, we fit the measured frequency and flux dependence of the transmission data to simulations based on the equivalent circuit model. Second, we fit the power dependence of the transmission data to a model that is predicted by the nonlinear equation of motion describing the system. Our results show that we are able to tune the nonlinearity of the resonators by almost two orders of magnitude via an external coil and two on-chip antennas. The studied system represents a basic building block for larger systems, allowing for quantum simulations of bosonic many-body systems with a larger number of lattice sites.

The field of quantum communication promises to provide efficient and unconditionally secure ways to exchange information, particularly, in the form of quantum states. Meanwhile, recent breakthroughs in quantum computation with superconducting circuits trigger a demand for quantum communication channels between spatially separated superconducting processors operating at microwave frequencies. In pursuit of this goal, we demonstrate the unconditional quantum teleportation of propagating coherent microwave states by exploiting two-mode squeezing and analog feedforward over a macroscopic distance of d = 0.42 m. We achieve a teleportation fidelity of F = 0.689 ± 0.004, exceeding the asymptotic no-cloning threshold. Thus, the quantum nature of the teleported states is preserved, opening the avenue toward unconditional security in microwave quantum communication.

Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms where a considerable amount of ancilla qubits and gates are often needed to form a Hilbert space large enough for high-precision results. Qubit recycling reduces the number of ancilla qubits to one but imposes the requirement of repeated measurements and feedforward within the coherence time of the qubits. Moreover, recycling only applies to certain cases where QFT can be carried out in a semi-classical way. Here, we report a novel approach based on two harmonic resonators which form a high-dimensional Hilbert space for the realization of QFT. By employing the all-resonant and perfect state-transfer methods, we develop a protocol that transfers an unknown multi-qubit state to one resonator. QFT is performed by the free evolution of the two resonators with a cross-Kerr interaction. Then, the fully-quantum result can be localized in the second resonator by a projective measurement. Qualitative analysis shows that a 2^10-dimensional QFT can be realized in current superconducting quantum circuits which paves the way for implementing various quantum algorithms in the noisy intermediate-scale quantum (NISQ) era.