Classical simulations of time-dependent quantum systems are widely used in quantum control research. In particular, these simulations are commonly used to host iterative optimal controlalgorithms. This is convenient for algorithms which are too onerous to run in the loop with current-day quantum hardware, as well as for researchers without consistent access to said hardware. However, if the model used to represent the system is not selected carefully, an optimised control protocol may be rendered futile when applied to hardware. We present a series of models, ordered in a hierarchy of progressive approximation, which appear in quantum control literature. Significant model deviations are highlighted, with a focus on simulated dynamics under simple single-qubit protocols. The validity of each model is characterised experimentally by designing and benchmarking control protocols for an IBMQ cloud quantum device. This result demonstrates an error amplification exceeding 100%, induced by the application of a first-order perturbative approximation. Finally, an evaluation of simulated control dynamics reveals that despite the substantial variance in numerical predictions across the proposed models, the complexity of discovering local optimal control protocols appears invariant for a simple control scheme. The set of findings presented heavily encourage practitioners of this field to ensure that their system models do not contain assumptions that markedly decrease applicability to hardware in experimentally relevant control parameter regimes.
Kitaev’s toric code is an exactly solvable model with Z2-topological order, which has potential applications in quantum computation and error correction. However, a direct experimentalrealization remains an open challenge. Here, we propose a building block for Z2 lattice gauge theories coupled to dynamical matter and demonstrate how it allows for an implementation of the toric-code ground state and its topological excitations. This is achieved by introducing separate matter excitations on individual plaquettes, whose motion induce the required plaquette terms. The proposed building block is realized in the second-order coupling regime and is well suited for implementations with superconducting qubits. Furthermore, we propose a pathway to prepare topologically non-trivial initial states during which a large gap on the order of the underlying coupling strength is present. This is verified by both analytical arguments and numerical studies. Moreover, we outline experimental signatures of the ground-state wavefunction and introduce a minimal braiding protocol. Detecting a π-phase shift between Ramsey fringes in this protocol reveals the anyonic excitations of the toric-code Hamiltonian in a system with only three triangular plaquettes. Our work paves the way for realizing non-Abelian anyons in analog quantum simulators.
Quantum mechanics postulates that measuring the qubit’s wave function results in its collapse, with the recorded discrete outcome designating the particular eigenstate the qubitcollapsed into. We show this picture breaks down when the qubit is strongly driven during measurement. More specifically, for a fast evolving qubit the measurement returns the time-averaged expectation value of the measurement operator, erasing information about the initial state of the qubit, while completely suppressing the measurement back-action. We call this regime `quantum rifling‘, as the fast spinning of the Bloch vector protects it from deflection into either of its two eigenstates. We study this phenomenon with two superconducting qubits coupled to the same probe field and demonstrate that quantum rifling allows us to measure either one of the two qubits on demand while protecting the state of the other from measurement back-action. Our results allow for the implementation of selective read out multiplexing of several qubits, contributing to efficient scaling up of quantum processors for future quantum technologies.
Random numbers are required for a variety of applications from secure communications to Monte-Carlo simulation. Yet randomness is an asymptotic property and no output string generatedby 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.
We present a technique to measure the transfer function of a control line using a qubit as a vector network analyzer. Our method requires coupling the line under test to the the longitudinalcomponent of the Hamiltonian of the qubit and the ability to induce Rabi oscillations through simultaneous driving of the transversal component. We used this technique to characterize the ‚flux‘ control of a superconducting Transmon qubit in the range of 8 to 400\,MHz. Our method can be used for the qubit ‚flux‘ line calibration to increase the fidelity of entangling gates for the quantum processor. The qubit can be also used as a microscopic probe of the electro-magnetic fields on a chip.
Three-dimensional (3D) superconducting microwave cavities with large mode volumes typically have high quality factors (>106). This is due to a reduced sensitivity to surface dielectriclosses, which is the limiting source of dissipation in two-dimensional transmission line resonators. In recent years, 3D microwave cavities have been extensively used for coupling and interacting with superconducting quantum bits (qubits), providing a versatile platform for quantum information processing and hybrid quantum systems. A current issue that has arisen is that 3D superconducting cavities do not permit magnetic field control of qubits embedded in these cavities. In contrast, microwave cavities made of normal metals can be transparent to magnetic fields, but experience a much lower quality factor (∼104), which negates many of the advantages of the 3D architecture. In an attempt to create a device that bridges a gap between these two types of cavities, having magnetic field control and high quality factor, we have created a hybrid 3D cavity. This new cavity is primarily composed of aluminium but also contains a small copper insert. We measured the internal quality factor of the hybrid cavity to be 102000, which is an order of magnitude improvement over all previously tested copper cavities. An added benefit to that our hybrid cavity possesses is that it also provides an improved thermal link to the sample that superconducting cavities alone cannot provide. In order to demonstrate precise magnetic control within the cavity, we performed spectroscopy of three superconducting qubits placed in the cavity, where individual control of each qubit’s frequency was exerted with small wire coils attached to the cavity. A large improvement in quality factor and magnetic field control makes this 3D hybrid cavity an attractive new platform for circuit quantum electrodynamics experiments.
Quantum physics cannot be reconciled with the classical philosophy of noncontextual realism. Realism demands that system properties exist independently of whether they are measured,while noncontextuality demands that the results of measurements do not depend on what other measurements are performed in conjunction with them. The Bell-Kochen-Specker theorem states that noncontextual realism cannot reproduce the measurement statistics of a single three-level quantum system (qutrit). Noncontextual realistic models may thus be tested using a single qutrit without relying on the notion of quantum entanglement in contrast to Bell inequality tests. It is challenging to refute such models experimentally, since imperfections may introduce loopholes that enable a realist interpretation. Using a superconducting qutrit with deterministic, binary-outcome readouts, we violate a noncontextuality inequality while addressing the detection, individual-existence and compatibility loopholes. Noncontextuality tests have been carried out in a range of different physical systems and dimensionalities, including neutrons, trapped ions and single photons, but no experiment addressing all three loopholes has been performed in the qutrit scenario where entanglement cannot play a role. Demonstrating state-dependent contextuality of a solid-state system is also an important conceptual ingredient for universal quantum computation in surface-code architectures, currently the most promising route to scalable quantum computing.
The ability to determine whether a multi-level quantum system is in a certain state while preserving quantum coherence between all orthorgonal states is necessary to realize binary-outcomecompatible measurements which are, in turn, a prerequisite for testing the contextuality of quantum mechanics. In this paper, we use a three-level superconducting system (a qutrit) coupled to a microwave cavity to explore different regimes of quantum measurement. In particular, we engineer the dispersive shifts of the cavity frequency to be identical for the first and second excited states of the qutrit which allows us to realize a strong projective binary-outcome measurement onto its ground state with a fidelity of 94.3%. Complemented with standard microwave control and low-noise parametric amplification, this scheme can be used to create sets of compatible measurements to reveal the contextual nature of superconducting circuits.
Non-linearity of the current-phase relationship of a Josephson junction is the key resource for a Josephson parametric amplifier (JPA), the only device in which the quantum limit hasso far been achieved at microwave frequencies. A standard approach to describe JPA takes into account only the lowest order (cubic) non-linearity resulting in a Duffing-like oscillator equation of motion or in a Kerr-type non-linearity term in the Hamiltonian. In this paper we derive the quantum expression for the gain of JPA including all orders of the Josephson junction non-linearity in the linear response regime. We then analyse gain saturation effect for stronger signals within semi-classical approach. Our results reveal non-linear effects of higher orders and their implications for operation of a JPA.
Photon-mediated interactions between atoms are of fundamental importance in quantum optics, quantum simulations and quantum information processing. The exchange of real and virtualphotons between atoms gives rise to non-trivial interactions the strength of which decreases rapidly with distance in three dimensions. Here we study much stronger photon mediated interactions using two superconducting qubits in an open onedimensional transmission line. Making use of the unique possibility to tune these qubits by more than a quarter of their transition frequency we observe both coherent exchange interactions at an effective separation of 3λ/4 and the creation of super- and sub-radiant states at a separation of one photon wavelength λ. This system is highly suitable for exploring collective atom/photon interactions and applications in quantum communication technology.