Random numbers are required for a variety of applications from secure communications to MonteCarlo simulation. Yet randomness is an asymptotic property and no output string generated by a physical device can be strictly proven to be random. We report an experimental realization of a quantum random number generator (QRNG) with randomness certified by quantum contextuality and the Kochen-Specker theorem. The certification is not performed in a device-independent way but through a rigorous theoretical proof of each outcome being value-indefinite even in the presence of experimental imperfections. The analysis of the generated data confirms the incomputable nature of our QRNG.While we can consider a mathematical abstraction of a true random number generator and examine its properties, in the physical world we are confined to performing finite statistical tests on the output strings. By applying sets of such tests (like NIST [1] or diehard [2]) we can verify with arbitrarily high probability that the generator is NOT random (if it has failed at least one test), but cannot prove its randomness in the opposite case. As an example, one may construct a pseudo-random number generator which passes all above-mentioned tests while the produced sequence is deterministic and even computable [3]. The impossibility of a rigorous proof of randomness for a finite string generated by a physical device motivates the consideration of more fundamental arguments to support a RNG's randomness. From this point of view, no classical RNG may be truly random as it is deterministic by the laws of classical mechanics, and may in principle be predicted. A natural foundation to build a RNG would be quantum theory, as it is intrinsically random.However, although quantum mechanics obeys probabilistic rules, the possibility of separating intrinsic randomness from apparent randomness arising from a lack of control or from experimental noise is still under debate [4]. Moreover, while quantum mechanics for a two-level system is described by the same intrinsically-probabilistic measurement rules, one may not strictly prove valueindefiniteness, and hence indeterminism, of its results [5].These considerations led to the next advance in quantum number generation: the protocols certified by violation of certain Bell-type inequalities [6][7][8]. More specifically, through violation of the CHSH inequality one may certify that the observed outputs are not entirely predetermined and write a lower bound on the generating process entropy. Unfortunately, this approach does not allow one to close the gap between this lower bound and true randomness. In addition, the Bell-type certification schemes can be regarded as random expanders rather than generators due to the requirement of "a small private random seed" to operate [6,9,10]. Finally, the random number generators certified by Bell inequalities utilize no-signaling assumption and is, therefore, inherently a non-local device which is challenging to use for practical applications.To address this problem, a diff...

Superposition, entanglement and non-locality constitute fundamental features of quantum physics. The fact that quantum physics does not follow the principle of local causality1–3 can be experimentally demonstrated in Bell tests4 performed on pairs of spatially separated, entangled quantum systems. Although Bell tests, which are widely regarded as a litmus test of quantum physics, have been explored using a broad range of quantum systems over the past 50 years, only relatively recently have experiments free of so-called loopholes5 succeeded. Such experiments have been performed with spins in nitrogen–vacancy centres6, optical photons7–9 and neutral atoms10. Here we demonstrate a loophole-free violation of Bell’s inequality with superconducting circuits, which are a prime contender for realizing quantum computing technology11. To evaluate a Clauser–Horne–Shimony–Holt-type Bell inequality4, we deterministically entangle a pair of qubits12 and perform fast and high-fidelity measurements13 along randomly chosen bases on the qubits connected through a cryogenic link14 spanning a distance of 30 metres. Evaluating more than 1 million experimental trials, we find an average S value of 2.0747 ± 0.0033, violating Bell’s inequality with a P value smaller than 10−108. Our work demonstrates that non-locality is a viable new resource in quantum information technology realized with superconducting circuits with potential applications in quantum communication, quantum computing and fundamental physics15.

We propose and experimentally realize a technique to measure the transfer function of a control line in the frequency domain using a qubit as a vector network analyzer. Our method requires coupling the line under test to the longitudinal component of the Hamiltonian of the qubit and the ability to induce Rabi oscillations through simultaneous driving of the transversal component. The method can be used to increase the fidelity of entangling gates in a quantum processor. We have demonstrated that by characterizing the 'flux' control line of a superconducting Transmon qubit in the range from 1 to 450 MHz and using this characterization to improve the fidelity of an entangling CPHASE gate between two Transmon qubits.