In apparent contradiction to the laws of thermodynamics, Maxwell's demon is able to cyclically extract work from a system in contact with a thermal bath, exploiting the information about its microstate. The resolution of this paradox required the insight that an intimate relationship exists between information and thermodynamics. Here, we realize a Maxwell demon experiment that tracks the state of each constituent in both the classical and quantum regimes. The demon is a microwave cavity that encodes quantum information about a superconducting qubit and converts information into work by powering up a propagating microwave pulse by stimulated emission. Thanks to the high level of control of superconducting circuits, we directly measure the extracted work and quantify the entropy remaining in the demon's memory. This experiment provides an enlightening illustration of the interplay of thermodynamics with quantum information.quantum thermodynamics | superconducting circuits | quantum information I n 1867, pondering the newly developed thermodynamic laws, Maxwell came to the disturbing conclusion that a "demon" can extract work cyclically from a thermodynamic system beyond the limits set by the second law when acting upon the information it obtains about the system (1). This paradox was resolved a century later when Landauer realized that information processing has an entropic cost and Bennett argued that the demon's memory must take full part in the thermodynamic cycle (2). Recent experiments have realized classical versions of elementary Maxwell demons in various physical systems (3-8). Although quantum versions have long been investigated theoretically (9-13), experimental realizations are in their infancy (7,8), and a full characterization is still missing. Using superconducting circuits, we reveal the inner mechanics of a quantum Maxwell demon that is able to extract work from a quantum system. Importantly, we are able to directly probe the extracted work by measuring the output power emitted by the system through stimulated emission, without inferring it from system trajectories (3-6, 14). We are thus able to demonstrate how the information stored in the demon's memory affects the extracted work. To make the characterization complete, we also measure the entropy and energy of the system and the demon. Superconducting circuits thus reveal themselves as a suitable experimental testbed for the blooming field of quantum thermodynamics of information (15)(16)(17)(18)(19).In the experiment, the system S is a transmon superconducting qubit (20) with energy difference hfS = h × 7.09 GHz between its ground |g and excited |e states. It is embedded in a microwave cavity that resonates at fD = 7.91 GHz and plays the role of the demon's memory D. The dispersive Hamiltonian reads H = hfS |e e|S + hfD d † d − hχd † d |e e|S , where d is the annihilation operator of a photon in the cavity. The last term induces a frequency shift of the cavity by −χ = −33 MHz when the qubit is excited. Reciprocally, the qubit frequency is shif...
We present the first experimental realization of a widely frequency tunable, nondegenerate three-wave mixing device for quantum signals at gigahertz frequency. It is based on a new superconducting building block consisting of a ring of four Josephson junctions shunted by a cross of four linear inductances. The phase configuration of the ring remains unique over a wide range of magnetic fluxes threading the loop. It is thus possible to vary the inductance of the ring with flux while retaining a strong, dissipation-free, and noiseless nonlinearity. The device has been operated in amplifier mode, and its noise performance has been evaluated by using the noise spectrum emitted by a voltage-biased tunnel junction at finite frequency as a test signal. The unprecedented accuracy with which the crossover between zero-point fluctuations and shot noise has been measured provides an upper bound for the noise and dissipation intrinsic to the device.
Making a system state follow a prescribed trajectory despite fluctuations and errors commonly consists of monitoring an observable (temperature, blood-glucose level, etc.) and reacting on its controllers (heater power, insulin amount, etc.). In the quantum domain, there is a change of paradigm in feedback, since measurements modify the state of the system, most dramatically when the trajectory goes through superpositions of measurement eigenstates. Here, we demonstrate the stabilization of an arbitrary trajectory of a superconducting qubit by measurement-based feedback. The protocol benefits from the long coherence time (T 2 > 10 s) of the 3D transmon qubit, the high efficiency (82%) of the phasepreserving Josephson amplifier, and fast electronics that ensure less than 500 ns total delay. At discrete time intervals, the state of the qubit is measured and corrected in case an error is detected. For Rabi oscillations, where the discrete measurements occur when the qubit is supposed to be in the measurement pointer states, we demonstrate an average fidelity of 85% to the targeted trajectory. For Ramsey oscillations, which do not go through pointer states, the average fidelity reaches 76%. Incidentally, we demonstrate a fast reset protocol that allows us to cool a 3D transmon qubit down to 0:6% in the excited state.
The fluorescence of a resonantly driven superconducting qubit is measured in the time domain, providing a weak probe of the qubit dynamics. Prior preparation and final, single-shot measurement of the qubit allows to average fluorescence records conditionally on past and future knowledge. The resulting interferences reveal purely quantum features characteristic of weak values. We demonstrate conditional averages that go beyond classical boundaries and probe directly the jump operator associated with relaxation. The experimental results are remarkably captured by a recent theory, which generalizes quantum mechanics to open quantum systems whose past and future are known.In quantum physics, measurement results are random but their statistics can be predicted assuming some knowledge about the system in the past. Additional knowledge from a future measurement [1] deeply changes the statistics in the present and leads to purely quantum features [2,3]. In particular conditioned average outcomes of a weak measurement, revealing the so-called weak values, were shown to go beyond the classically allowed range and give a way to directly measure complex quantities [4]. Recently, these concepts have been considered in the general case of open quantum systems where decoherence occurs [5][6][7]. Then, what are the properties of weak values for the unavoidable measurement associated to decoherence, the one performed by the environment? Here, we answer this question in the simplest open quantum system: a quantum bit in presence of a relaxation channel. We continuously monitor the fluorescence emitted by a superconducting qubit driven at resonance. Conditioned on initial preparation and final single shot measurement outcome of the qubit state, we probe weak values displaying non-classical properties. The fluorescence signal exhibits interferences between oscillations associated to past and future quantum states [5][6][7]. The measured data are in complete agreement with theory.A two-level system irradiated at resonance undergoes Rabi oscillations between ground state |g and excited state |e . Conversely, these oscillations leave a footprint in the emitted fluorescence field. In the spectral domain, two side peaks appear around resonance frequency, constituting the Mollow triplet [8]. They were first observed in quantum optics and more recently in the microwave range [9]. If the detection setup allows monitoring fluorescence in the time domain, one gets a weak probe of the qubit. To access weak values of the associated qubit operator, one additionally needs to post-select the experiments depending on qubit state, which therefore needs to * These two authors contributed equally to this work be measured in a single-shot manner. Superconducting qubits in cavity are fit for this task [10][11][12][13]. The principle of our experiment is described in Fig. 1. A transmon qubit with frequency ν q = 5.19 GHz is enclosed in a nonresonant superconducting 3D cavity [14], connected to two transmission lines. Line a is coupled as weakly as the i...
In quantum error correction, information is encoded in a high-dimensional system to protect it from the environment. A crucial step is to use natural, low-weight operations with an ancilla to extract information about errors without causing backaction on the encoded system. Essentially, ancilla errors must not propagate to the encoded system and induce errors beyond those which can be corrected. The current schemes for achieving this fault-tolerance to ancilla errors come at the cost of increased overhead requirements. An efficient way to extract error syndromes in a fault-tolerant manner is by using a single ancilla with strongly biased noise channel. Typically, however, required elementary operations can become challenging when the noise is extremely biased. We propose to overcome this shortcoming by using a bosonic-cat ancilla in a parametrically driven nonlinear cavity. Such a cat-qubit experiences only bit-flip noise and is stabilized against phase-flips. To highlight the flexibility of this approach, we illustrate the syndrome extraction process in a variety of codes such as qubit-based toric codes, bosonic cat-and Gottesman-Kitaev-Preskill (GKP) codes. Our results open a path for realizing hardware-efficient, fault-tolerant error syndrome extraction.
A qubit can relax by fluorescence, which prompts the release of a photon into its electromagnetic environment. By counting the emitted photons, discrete quantum jumps of the qubit state can be observed. The succession of states occupied by the qubit in a single experiment, its quantum trajectory, depends in fact on the kind of detector. How are the quantum trajectories modified if one measures continuously the amplitude of the fluorescence field instead? Using a superconducting parametric amplifier, we perform heterodyne detection of the fluorescence of a superconducting qubit. For each realization of the measurement record, we can reconstruct a different quantum trajectory for the qubit. The observed evolution obeys quantum state diffusion, which is characteristic of quantum measurements subject to zeropoint fluctuations. Independent projective measurements of the qubit at various times provide a quantitative verification of the reconstructed trajectories. By exploring the statistics of quantum trajectories, we demonstrate that the qubit states span a deterministic surface in the Bloch sphere at each time in the evolution. Additionally, we show that when monitoring fluorescence field quadratures, coherent superpositions are generated during the decay from excited to ground state. Counterintuitively, measuring light emitted during relaxation can give rise to trajectories with increased excitation probability.
We report electron spin resonance spectroscopy measurements performed at millikelvin temperatures in a custom-built spectrometer comprising a superconducting micro-resonator at 7 GHz and a Josephson parametric amplifier. Owing to the small ∼10 −12 λ 3 magnetic resonator mode volume and to the low noise of the parametric amplifier, the spectrometer sensitivity reaches 260 ± 40 spins/echo and 65 ± 10 spins/ √ Hz, respectively.PACS numbers: 07.57. Pt, Electron spin resonance (ESR) is a well-established spectroscopic method to analyze paramagnetic species, utilized in materials science, chemistry and molecular biology to characterize reaction products and complex molecules 1 . In a conventional ESR spectrometer based on the so-called inductive detection method, the paramagnetic spins precess in an external magnetic field B 0 and radiate weak microwave signals into a resonant cavity, whose emissions are amplified and measured.Despite its widespread use, ESR has limited sensitivity, and large amounts of spins are necessary to accumulate sufficient signal. Most conventional ESR spectrometers operate at room temperature and employ three-dimensional cavities. At X-band 2 , they require on the order of ∼10 13 spins to obtain sufficient signal in a single echo 1 . Enhancing this sensitivity to smaller spin ensembles and eventually the singlespin limit is highly desirable and is a major research subject. This has been achieved by employing alternative detection schemes including optically detected magnetic resonance (ODMR) 3,4 , scanning probe based techniques 5-9 , SQUIDs 10 and electrically detected magnetic resonance 11,12 . For instance, ODMR achieves single spin sensitivity through optical readout of the spin state. However, this requires the presence of suitable opa) sebastian.probst@cea.fr tical transitions in the energy spectrum of the system of interest, which makes it less versatile.In recent years, there has been a parallel effort to enhance the sensitivity of inductive ESR detection [13][14][15][16][17][18][19][20] . This development has been triggered by the progress made in the field of circuit quantum electrodynamics (cQED) 21 , where high fidelity detection of weak microwave signals is essential for the measurement and manipulation of superconducting quantum circuits. In particular, it has been theoretically predicted 22 that single-spin sensitivity should be reachable by combining high quality factor superconducting micro-resonators and Josephson Parametric Amplifiers (JPAs) 23 , which are sensitive microwave amplifiers adding as little noise as allowed by quantum mechanics to the incoming spin signal.Based on this principle, ESR spectroscopy measurements 18 demonstrated a sensitivity of 1700 spins/ √ Hz. In this work, we build on these efforts and show that, by optimizing the superconducting resonator design, the sensitivity can be enhanced to the level of 65 spins/ √ Hz. Figure 1(a) shows a schematic design of the spectrometer consisting of a superconducting LC resonant circuit capacitively coupled to the...
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