Entangled microwave photons form a fundamental resource for quantum information processing and sensing with continuous variables. We use a low-loss Josephson metamaterial comprising superconducting, nonlinear, asymmetric inductive elements to generate frequency-entangled photons from vacuum fluctuations at a rate of 2 giga entangled bits per second spanning over the 4-GHz bandwidth. The device is operated as a traveling-wave parametric amplifier under Kerr-relieving biasing conditions. Furthermore, we demonstrate single-mode squeezing in such devices—$3.1\pm 0.7\mathrm{dB}$ below the zero-point level at half of modulation frequency.

Quantum state preparation is a vital routine in many quantum algorithms, including solution of linear systems of equations, Monte Carlo simulations, quantum sampling, and machine learning. However, to date, there is no established framework of encoding classical data into gate-based quantum devices. In this work, we propose a method for the encoding of vectors obtained by sampling analytical functions into quantum circuits that features polynomial runtime with respect to the number of qubits and provides >99.9% accuracy, which is better than a state-of-the-art two-qubit gate fidelity. We employ hardware-efficient variational quantum circuits, which are simulated using tensor networks, and matrix product state representation of vectors. In order to tune variational gates, we utilize Riemannian optimization incorporating auto-gradient calculation. Besides, we propose a ‘cut once, measure twice’ method, which allows us to avoid barren plateaus during gates’ update, benchmarking it up to 100-qubit circuits. Remarkably, any vectors that feature low-rank structure—not limited by analytical functions—can be encoded using the presented approach. Our method can be easily implemented on modern quantum hardware, and facilitates the use of the hybrid-quantum computing architectures.

The detection of microwave fields at single-photon power levels is a much-sought-after technology, with practical applications in nanoelectronics and quantum information science. Here we demonstrate a simple yet powerful criticality-enhanced method of microwave photon detection by operating a magnetic-field-tunable Kerr Josephson parametric amplifier at the border of a first-order phase transition and close to the critical point. We obtain an efficiency of 73% and a dark-count rate of 167 kHz, corresponding to a responsivity of $1.3\times {10}^{17}{\mathrm{W}}^{-1}$ and noise-equivalent power of 3.28 $\mathrm{zW}/\sqrt{\mathrm{Hz}}$. We verify the single-photon operation by extracting the Poissonian statistics of a coherent probe signal.

We present a lumped-element Josephson parametric amplifier (JPA) fabricated using a straightforward e-beam lithography process. Our strongly coupled flux-pumped JPA achieves a gain of 20 dB with a bandwidth of 95 MHz around 5 GHz, while the center frequency is tunable by more than 1 GHz, with the additional possibility for rapid tuning by varying the pump frequency alone. Analytical calculations based on the input-output theory reproduce our measurement results closely.

Quantum correlations are a vital resource in advanced information processing based on quantum phenomena. Remarkably, the vacuum state of a quantum field may act as a key element for the generation of multipartite quantum entanglement. In this work, generation of genuine tripartite entangled state and its control is achieved by the use of the phase difference between two continuous pump tones. Control of the subspaces of the covariance matrix for tripartite bisqueezed state is demonstrated. Furthermore, by optimizing the phase relationships in a three‐tone pumping scheme genuine quadripartite entanglement of a generalized H‐graph state (‐graph) is explored. This scheme provides a comprehensive control toolbox for the entanglement structure and allows to demonstrate, for first time to the authors' knowledge, genuine quadripartite entanglement of microwave modes. All experimental results are verified with numerical simulations of the nonlinear quantum Langevin equation. It is envisioned that quantum resources facilitated by multi‐pump configurations offer enhanced prospects for quantum data processing using parametric microwave cavities.

Running quantum algorithms often involves implementing complex quantum circuits with such a large number of multi-qubit gates that the challenge of tackling practical applications appears daunting. In this article, we propose a novel approach called Tensor Quantum Programming, which leverages tensor networks (TNs) for hybrid quantum computing. Our key insight is that the primary challenge of algorithms based on TNs lies in their high ranks (bond dimensions). Quantum computing offers a potential solution to this challenge, as an ideal quantum computer can represent tensors with arbitrarily high ranks in contrast to classical counterparts, which indicates the way towards quantum advantage. While tensor-based vector-encoding and state-readout are known procedures, the matrix-encoding required for performing matrix-vector multiplications directly on quantum devices is much less studied. We introduce an algorithm that encodes matrix product operators into quantum circuits with a depth that scales linearly with the number of qubits. We demonstrate the algorithm’s performance for matrices commonly encountered in differential equations, optimization problems, and quantum chemistry, for systems involving up to 50 qubits.