Energetics of a Single Qubit Gate.

Qubits are physical, a quantum gate thus not only acts on the information carried by the qubit but also on its energy. What is then the corresponding flow of energy between the qubit and the controller that implements the gate? Here we exploit a superconducting platform to answer this question in the case of a quantum gate realized by a resonant drive field. During the gate, the superconducting qubit becomes entangled with the microwave drive pulse so that there is a quantum superposition between energy flows. We measure the energy change in the drive field conditioned on the outcome of a projective qubit measurement. We demonstrate that the drive's energy change associated with the measurement backaction can exceed by far the energy that can be extracted by the qubit. This can be understood by considering the qubit as a weak measurement apparatus of the driving field.

Quantifying the quantum heat contribution from a driven superconducting circuit.

Heat flow management at the nanoscale is of great importance for emergent quantum technologies. For instance, a thermal sink that can be activated on-demand is a highly desirable tool that may accommodate the need to evacuate excess heat at chosen times, e.g., to maintain cryogenic temperatures or reset a quantum system to ground, and the possibility of controlled unitary evolution otherwise. Here we propose a design of such heat switch based on a single coherently driven qubit. We show that the heat flow provided by a hot source to the qubit can be switched on and off by varying external parameters, the frequency and the intensity of the driving. The complete suppression of the heat flow is a quantum effect occurring for specific driving parameters that we express and we analyze the role of the coherences in the free-qubit energy eigenbasis. We finally study the feasibility of this quantum heat switch in a circuit QED setup involving a charge qubit coupled to thermal resistances. We demonstrate robustness to experimental imperfections such as additional decoherence, paving the road towards experimental verification of this effect.

Experimental Realization of a Quantum Dot Energy Harvester.

We demonstrate experimentally an autonomous nanoscale energy harvester that utilizes the physics of resonant tunneling quantum dots. Gate-defined quantum dots on GaAs/AlGaAs high-electron-mobility transistors are placed on either side of a hot-electron reservoir. The discrete energy levels of the quantum dots are tuned to be aligned with low energy electrons on one side and high energy electrons on the other side of the hot reservoir. The quantum dots thus act as energy filters and allow for the conversion of heat from the cavity into electrical power. Our energy harvester, measured at an estimated base temperature of 75 mK in a He^{3}/He^{4} dilution refrigerator, can generate a thermal power of 0.13 fW for a temperature difference across each dot of about 67 mK.

Achieving Optimal Quantum Acceleration of Frequency Estimation Using Adaptive Coherent Control.

Precision measurements of frequency are critical to accurate time keeping and are fundamentally limited by quantum measurement uncertainties. While for time-independent quantum Hamiltonians the uncertainty of any parameter scales at best as 1/T, where T is the duration of the experiment, recent theoretical works have predicted that explicitly time-dependent Hamiltonians can yield a 1/T^{2} scaling of the uncertainty for an oscillation frequency. This quantum acceleration in precision requires coherent control, which is generally adaptive. We experimentally realize this quantum improvement in frequency sensitivity with superconducting circuits, using a single transmon qubit. With optimal control pulses, the theoretically ideal frequency precision scaling is reached for times shorter than the decoherence time. This result demonstrates a fundamental quantum advantage for frequency estimation.

Mapping the optimal route between two quantum states.

A central feature of quantum mechanics is that a measurement result is intrinsically probabilistic. Consequently, continuously monitoring a quantum system will randomly perturb its natural unitary evolution. The ability to control a quantum system in the presence of these fluctuations is of increasing importance in quantum information processing and finds application in fields ranging from nuclear magnetic resonance to chemical synthesis. A detailed understanding of this stochastic evolution is essential for the development of optimized control methods. Here we reconstruct the individual quantum trajectories of a superconducting circuit that evolves under the competing influences of continuous weak measurement and Rabi drive. By tracking individual trajectories that evolve between any chosen initial and final states, we can deduce the most probable path through quantum state space. These pre- and post-selected quantum trajectories also reveal the optimal detector signal in the form of a smooth, time-continuous function that connects the desired boundary conditions. Our investigation reveals the rich interplay between measurement dynamics, typically associated with wavefunction collapse, and unitary evolution of the quantum state as described by the Schrödinger equation. These results and the underlying theory, based on a principle of least action, reveal the optimal route from initial to final states, and may inform new quantum control methods for state steering and information processing.

Experimental violation of two-party Leggett-Garg inequalities with semiweak measurements.

We generalize the derivation of Leggett-Garg inequalities to systematically treat a larger class of experimental situations by allowing multiparticle correlations, invasive detection, and ambiguous detector results. Furthermore, we show how many such inequalities may be tested simultaneously with a single setup. As a proof of principle, we violate several such two-particle inequalities with data obtained from a polarization-entangled biphoton state and a semiweak polarization measurement based on Fresnel reflection. We also point out a nontrivial connection between specific two-party Leggett-Garg inequality violations and convex sums of strange weak values.

Contextual values of observables in quantum measurements.

We introduce contextual values as a generalization of the eigenvalues of an observable that takes into account both the system observable and a general measurement procedure. This technique leads to a natural definition of a general conditioned average that converges uniquely to the quantum weak value in the minimal disturbance limit. As such, we address the controversy in the literature regarding the theoretical consistency of the quantum weak value by providing a more general theoretical framework and giving several examples of how that framework relates to existing experimental and theoretical results.

Stochastic path integral formulation of full counting statistics.

We derive a stochastic path integral representation of counting statistics in semiclassical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to find the propagator for charge distributions with an arbitrary number of counting fields and generalized charges. The counting statistics is given by the saddle-point approximation to the path integral, and fluctuations around the saddle point are suppressed in the semiclassical approximation. We use this approach to derive the current cumulants of a chaotic cavity in the hot-electron regime.