P. C. de Groot

Observation of two-orbital spin-exchange interactions with ultracold SU( N )-symmetric fermions

Using the two stable electronic states of alkaline-earth atoms, an orbital spin-exchange interaction—the building block of orbital quantum magnetism—has been observed in a fermionic quantum gas.

Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits

Quantum computation requires quantum logic gates that use the interaction within pairs of quantum bits (qubits) to perform conditional operations. Superconducting qubits may offer an attractive route towards scalable quantum computing. In previous experiments on coupled superconducting qubits, conditional gate behaviour and entanglement were demonstrated. Here we demonstrate selective execution of the complete set of four different controlled-NOT (CNOT) quantum logic gates, by applying microwave pulses of appropriate frequency to a single pair of coupled flux qubits. All two-qubit computational basis states and their superpositions are used as input, while two independent single-shot SQUID detectors measure the output state, including qubit–qubit correlations. We determined the gate’s truth table by directly measuring the state transfer amplitudes and by acquiring the relevant quantum phase shift using a Ramsey-like interference experiment. The four conditional gates result from the symmetry of the qubits in the pair: either qubit can assume the role of control or target, and the gate action can be conditioned on either the 0-state or the 1-state. These gates are now sufficiently characterized to be used in quantum algorithms, and together form an efficient set of versatile building blocks.

Quantum non-demolition measurement of a superconducting two-level system

In quantum mechanics, the process of measurement is a subtle interplay between extraction of information and disturbance of the state of the quantum system. A quantum non-demolition (QND) measurement minimizes this disturbance by using a particular system—detector interaction that preserves the eigenstates of a suitable operator of the quantum system. This leads to an ideal projective measurement. We present experiments in which we carry out two consecutive measurements on a quantum two-level system, a superconducting flux qubit, by probing the hysteretic behaviour of a coupled nonlinear resonator. The large correlation between the results of the two measurements demonstrates the QND nature of the readout method. The fact that a QND measurement is possible for superconducting qubits strengthens the notion that these fabricated mesoscopic systems are to be regarded as fundamental quantum objects. Our results are also relevant for quantum-information processing for protocols such as state preparation and error correction.

Partial-Measurement Backaction and Nonclassical Weak Values in a Superconducting Circuit

We realize indirect partial measurement of a transmon qubit in circuit quantum electrodynamics by interaction with an ancilla qubit and projective ancilla measurement with a dedicated readout resonator. Accurate control of the interaction and ancilla measurement basis allows tailoring the measurement strength and operator. The tradeoff between measurement strength and qubit backaction is characterized through the distortion of a qubit Rabi oscillation imposed by ancilla measurement in different bases. Combining partial and projective qubit measurements, we provide the solid-state demonstration of the correspondence between a nonclassical weak value and the violation of a Leggett-Garg inequality.

Interqubit coupling mediated by a high-excitation-energy quantum object

We consider a system composed of two qubits and a high excitation energy quantum object used to mediate coupling between the qubits. We treat the entire system quantum mechanically and analyze the properties of the eigenvalues and eigenstates of the total Hamiltonian. After reproducing well known results concerning the leading term in the mediated coupling, we obtain an expression for the residual coupling between the qubits in the off state. We also analyze the entanglement between the three objects, i.e., the two qubits and the coupler, in the eigenstates of the total Hamiltonian. Although we focus on the application of our results to the recently realized parametric-coupling scheme with two qubits, we also discuss extensions of our results to harmonicoscillator couplers, couplers that are near resonance with the qubits and multiqubit systems. In particular, we find that certain errors that are absent for a two-qubit system arise when dealing with multiqubit systems.

Selective darkening of degenerate transitions demonstrated with two superconducting quantum bits

A new technique for controlling the quantum state of a superconducting qubit is now presented. Microwave pulses are applied in such a way that they excite only one of a pair of degenerate states. The concept enables construction of a controlled-NOT gate, a device important for quantum logic. Controlled manipulation of quantum states is central to studying natural and artificial quantum systems. If a quantum system consists of interacting subunits, the nature of the coupling may lead to quantum levels with degenerate energy differences. This degeneracy makes frequency-selective quantum operations impossible. For the prominent group of transversely coupled two-level systems, that is, qubits, we introduce a method to selectively suppress one transition of a degenerate pair while coherently exciting the other, effectively creating artificial selection rules. It requires driving two qubits simultaneously with the same frequency and specified relative amplitude and phase. We demonstrate our method on a pair of superconducting flux qubits1. It can directly be applied to the other superconducting qubits2,3,4,5,6, and to any other qubit type that allows for individual driving. Our results provide a single-pulse controlled-NOT gate for the class of transversely coupled qubits.

Speed limits for quantum gates in multiqubit systems

We use analytical and numerical calculations to obtain speed limits for various unitary quantum operations in multiqubit systems under typical experimental conditions. The operations that we consider include single-, two-, and three-qubit gates, as well as quantum-state transfer in a chain of qubits. We find in particular that simple methods for implementing two-qubit gates generally provide the fastest possible implementations of these gates. We also find that the three-qubit Toffoli gate time varies greatly depending on the type of interactions and the system’s geometry, taking only slightly longer than a two-qubit controlled-NOT (CNOT) gate for a triangle geometry. The speed limit for quantum-state transfer across a qubit chain is set by the maximum spin-wave speed in the chain.

Low-crosstalk bifurcation detectors for coupled flux qubits

We present experimental results on the crosstalk between two ac-operated dispersive bifurcation detectors, implemented in a circuit for high-fidelity readout of two strongly coupled flux qubits. Both phase-dependent and phase-independent contributions to the crosstalk are analyzed. For proper tuning of the phase the measured crosstalk is 0.1% and the correlation between the measurement outcomes is less than 0.05%. These results show that bifurcative readout provides a reliable and generic approach for multipartite correlation experiments.

Selective darkening of degenerate transitions for implementing quantum controlled-NOT gates

We present a theoretical analysis of the selective darkening method for implementing quantum controlled-NOT (CNOT) gates. This method, which we have recently proposed and demonstrated, consists of driving two transversely coupled quantum bits (qubits) with a driving field that is resonant with one of the two qubits. For specific relative amplitudes and phases of the driving field felt by the two qubits, one of the two transitions in the degenerate pair is darkened or, in other words, becomes forbidden by effective selection rules. In these driving conditions, the evolution of the two-qubit state realizes a CNOT gate. The gate speed is found to be limited only by the coupling energy J , which is the fundamental speed limit for any entangling gate. Numerical simulations show that at gate speeds corresponding to 0.48J and 0.07J , the gate fidelity is 99% and 99.99%, respectively, and increases further for lower gate speeds. In addition, the effect of higher-lying energy levels and weak anharmonicity is studied, as well as the scalability of the method to systems of multiple qubits. We conclude that in all these respects this method is competitive with existing schemes for creating entanglement, with the added advantages of being applicable for qubits operating at fixed frequencies (either by design or for the exploitation of coherence sweet-spots) and having the simplicity of microwave-only operation.

Quantum non‐demolition measurement of a superconducting qubit

We present experiments that address the issue of measurement of superconducting qubits. A quantum non‐demolition (QND) type of readout is used to implement a projective measurement, which is an important component of many protocols in quantum information. The state of a persistent current qubit is measured using a driven non‐linear resonator, based on DC‐SQUID whose Josephson inductance is qubit‐state dependent. When properly optimized, the readout is efficient and projective. We discuss the relation between the concept of QND detection and the observed projective character of the measurement.