arXiv subjects

Simon E. Nigg

Publications and source records attributed to Simon E. Nigg.

At least 19 recordsLinked to original sources

arXiv2019

Towards a heralded eigenstate preserving measurement of multi-qubit parity in circuit QED

Eigenstate-preserving multi-qubit parity measurements lie at the heart of stabilizer quantum error correction, which is a promising approach to mitigate the problem of decoherence in quantum computers. In this work we explore a high-fidelity, eigenstate-preserving parity readout for superconducting qubits dispersively coupled to a microwave resonator, where the parity bit is encoded in the amplitude of a coherent state of the resonator. Detecting photons emitted by the resonator via a current biased Josephson junction yields information about the parity bit. We analyse theoretically the measurement back-action in the limit of a strongly coupled fast detector and show that in general such a parity measurement, while approximately Quantum Non-Demolition (QND) is not eigenstate-preserving. To remediate this shortcoming we propose a simple dynamical decoupling technique during photon detection, which greatly reduces decoherence within a given parity subspace. Furthermore, by applying a sequence of fast displacement operations interleaved with the dynamical decoupling pulses, the natural bias of this binary detector can be efficiently suppressed. Finally, we introduce the concept of a heralded parity measurement, where a detector click guarantees successful multi-qubit parity detection even for finite detection efficiency.

quant-ph↗

arXiv2017

Quantum Synchronization Blockade: Energy Quantization hinders Synchronization of Identical Oscillators

Classically, the tendency towards spontaneous synchronization is strongest if the natural frequencies of the self-oscillators are as close as possible. We show that this wisdom fails in the deep quantum regime, where the uncertainty of amplitude narrows down to the level of single quanta. Under these circumstances identical self-oscillators cannot synchronize and detuning their frequencies can actually help synchronization. The effect can be understood in a simple picture: Interaction requires an exchange of energy. In the quantum regime, the possible quanta of energy are discrete. If the extractable energy of one oscillator does not exactly match the amount the second oscillator may absorb, interaction, and thereby synchronization is blocked. We demon- strate this effect, which we coin quantum synchronization blockade, in the minimal example of two Kerr-type self-oscillators and predict consequences for small oscillator networks, where synchronization between blocked oscillators can be mediated via a detuned oscillator. We also propose concrete implementations with super- conducting circuits and trapped ions. This paves the way for investigations of new quantum synchronization phenomena in oscillator networks both theoretically and experimentally.

quant-ph↗

arXiv2017

Observing quantum synchronization blockade in circuit quantum electrodynamics

High quality factors, strong nonlinearities, and extensive design flexibility make superconducting circuits an ideal platform to investigate synchronization phenomena deep in the quantum regime. Recently~\cite{Loerch-2017}, it was predicted that energy quantization and conservation can block the synchronization of two identical, weakly coupled nonlinear self-oscillators. Here we propose a Josephson junction circuit realization of such a system along with a simple homodyne measurement scheme to observe this effect. We also show that at finite detuning, where phase synchronization takes place, the two oscillators are entangled in the steady state as witnessed by the positivity of the logarithmic negativity.

quant-ph↗

arXiv2016

Superconducting grid-bus surface code architecture for hole-spin qubits

We present a scalable hybrid architecture for the 2D surface code combining superconducting resonators and hole-spin qubits in nanowires with tunable direct Rashba spin-orbit coupling. The back-bone of this architecture is a square lattice of capacitively coupled coplanar waveguide resonators each of which hosts a nanowire hole-spin qubit. Both the frequency of the qubits and their coupling to the microwave field are tunable by a static electric field applied via the resonator center pin. In the dispersive regime, an entangling two-qubit gate can be realized via a third order process, whereby a virtual photon in one resonator is created by a first qubit, coherently transferred to a neighboring resonator, and absorbed by a second qubit in that resonator. Numerical simulations with state-of-the-art coherence times yield gate fidelities approaching the $99\%$ fault tolerance threshold.

quant-ph↗

arXiv2016

Robust quantum optimizer with full connectivity

Quantum phenomena have the potential to speed up the solution of hard optimization problems. For example quantum annealing, based on the quantum tunneling effect, has recently been shown to scale exponentially better with system size as compared with classical simulated annealing. However, current realizations of quantum annealers with superconducting qubits face two major challenges. First, the connectivity between the qubits is limited, excluding many optimization problems from a direct implementation. Second, decoherence degrades the success probability of the optimization. We address both of these shortcomings and propose an architecture in which the qubits are robustly encoded in continuous variable degrees of freedom. Remarkably, by leveraging the phenomenon of flux quantization, all-to-all connectivity is obtained without overhead. Furthermore, we demonstrate the robustness of this architecture by simulating the optimal solution of a small instance of the NP-hard and fully connected number partitioning problem in the presence of dissipation.

quant-ph↗

arXiv2016

Decoherence of high-energy electrons in weakly disordered quantum Hall edge states

We investigate theoretically the phase coherence of electron transport in edge states of the integer quantum Hall effect at filling factor $ν=2$, in the presence of disorder and inter-edge state Coulomb interaction. Within a Fokker-Planck approach, we calculate analytically the visibility of the Aharonov-Bohm oscillations of the current through an electronic Mach-Zehnder interferometer. In agreement with recent experiments, we find that the visibility is independent of the energy of the current-carrying electrons injected high above the Fermi sea. Instead, it is the amount of disorder at the edge that sets the phase space available for inter-edge state energy exchange and thereby controls the visibility suppression.

cond-mat.mes-hall↗

arXiv2016

Non local quantum state engineering with the Cooper pair splitter beyond the Coulomb blockade regime

A Cooper pair splitter consists of two quantum dots side-coupled to a conventional superconductor. Usually, the quantum dots are assumed to have a large charging energy compared to the superconducting gap, in order to suppress processes other than the coherent splitting of Cooper pairs. In this work, in contrast, we investigate the limit in which the charging energy is smaller than the superconducting gap. This allows us, in particular, to study the effect of a Zeeman field comparable to the charging energy. We find analytically that in this parameter regime the superconductor mediates an inter-dot tunneling term with a spin symmetry determined by the Zeeman field. Together with electrostatically tunable quantum dots, we show that this makes it possible to engineer a spin triplet state shared between the quantum dots. Compared to previous works, we thus extend the capabilities of the Cooper pair splitter to create entangled non local electron pairs.

cond-mat.mes-hall↗

arXiv2016

Statistical theory of relaxation of high energy electrons in quantum Hall edge states

We investigate theoretically the energy exchange between electrons of two co-propagating, out-of-equilibrium edge states with opposite spin polarization in the integer quantum Hall regime. A quantum dot tunnel-coupled to one of the edge states locally injects electrons at high energy. Thereby a narrow peak in the energy distribution is created at high energy above the Fermi level. A second downstream quantum dot performs an energy resolved measurement of the electronic distribution function. By varying the distance between the two dots, we are able to follow every step of the energy exchange and relaxation between the edge states - even analytically under certain conditions. In the absence of translational invariance along the edge, e.g. due to the presence of disorder, energy can be exchanged by non-momentum conserving two-particle collisions. For weakly broken translational invariance, we show that the relaxation is described by coupled Fokker-Planck equations. From these we find that relaxation of the injected electrons can be understood statistically as a generalized drift-diffusion process in energy space for which we determine the drift-velocity and the dynamical diffusion parameter. Finally, we provide a physically appealing picture in terms of individual edge state heating as a result of the relaxation of the injected electrons.

cond-mat.mes-hall↗

arXiv2015

Detecting nonlocal Cooper pair entanglement by optical Bell inequality violation

Based on the Bardeen Cooper Schrieffer (BCS) theory of superconductivity, the coherent splitting of Cooper pairs from a superconductor to two spatially separated quantum dots has been predicted to generate nonlocal pairs of entangled electrons. In order to test this hypothesis, we propose a scheme to transfer the spin state of a split Cooper pair onto the polarization state of a pair of optical photons. We show that the produced photon pairs can be used to violate a Bell inequality, unambiguously demonstrating the entanglement of the split Cooper pairs.

cond-mat.mes-hall↗

arXiv2014

Deterministic Hadamard gate for microwave "cat-state" qubits in cQED

We propose the implementation of a deterministic Hadamard gate for logical photonic qubits encoded in superpositions of coherent states of a harmonic oscillator. The proposed scheme builds on a recently introduced set of conditional operations in the strong dispersive regime of circuit QED [Z. Leghtas et al. Phys. Rev. A. {\bf 87} (2013)]. We further propose an architecture for coupling two such logical qubits and provide a universal set of deterministic quantum gates. Based on parameter values taken from the current state of the art, we give estimates for the achievable gate fidelities accounting for fundamental gate imperfections and finite coherence time due to photon loss.

quant-ph↗

arXiv2013

Stabilizer quantum error correction toolbox for superconducting qubits

We present a general protocol for stabilizer measurements and pumping in a system of N superconducting qubits. We assume always-on, equal dispersive couplings to a single mode of a high-Q microwave resonator in the ultra-strong dispersive limit where the dispersive shifts largely exceed the spectral linewidth. In this limit, we show how to map the two eigenvalues of an arbitrary weight M < N Pauli operator, onto two quasi-orthogonal coherent states of the cavity. Together with a fast cavity readout, this enables the efficient measurement of stabilizer operators.

quant-ph↗

arXiv2012

Observation of quantum state collapse and revival due to the single-photon Kerr effect

Photons are ideal carriers for quantum information as they can have a long coherence time and can be transmitted over long distances. These properties are a consequence of their weak interactions within a nearly linear medium. To create and manipulate nonclassical states of light, however, one requires a strong, nonlinear interaction at the single photon level. One approach to generate suitable interactions is to couple photons to atoms, as in the strong coupling regime of cavity QED systems. In these systems, however, one only indirectly controls the quantum state of the light by manipulating the atoms. A direct photon-photon interaction occurs in so-called Kerr media, which typically induce only weak nonlinearity at the cost of significant loss. So far, it has not been possible to reach the single-photon Kerr regime, where the interaction strength between individual photons exceeds the loss rate. Here, using a 3D circuit QED architecture, we engineer an artificial Kerr medium which enters this regime and allows the observation of new quantum effects. We realize a Gedankenexperiment proposed by Yurke and Stoler, in which the collapse and revival of a coherent state can be observed. This time evolution is a consequence of the quantization of the light field in the cavity and the nonlinear interaction between individual photons. During this evolution non-classical superpositions of coherent states, i.e. multi-component Schroedinger cat states, are formed. We visualize this evolution by measuring the Husimi Q-function and confirm the non-classical properties of these transient states by Wigner tomography. The single-photon Kerr effect could be employed in QND measurement of photons, single photon generation, autonomous quantum feedback schemes and quantum logic operations.

quant-ph↗

arXiv2012

Decoherence of superconducting qubits caused by quasiparticle tunneling

In superconducting qubits, the interaction of the qubit degree of freedom with quasiparticles defines a fundamental limitation for the qubit coherence. We develop a theory of the pure dephasing rate Γ_ϕ caused by quasiparticles tunneling through a Josephson junction and of the inhomogeneous broadening due to changes in the occupations of Andreev states in the junction. To estimate Γ_ϕ, we derive a master equation for the qubit dynamics. The tunneling rate of free quasiparticles is enhanced by their large density of states at energies close to the superconducting gap. Nevertheless, we find that Γ_ϕ is small compared to the rates determined by extrinsic factors in most of the current qubit designs (phase and flux qubits, transmon, fluxonium). The split transmon, in which a single junction is replaced by a SQUID loop, represents an exception that could make possible the measurement of Γ_ϕ. Fluctuations of the qubit frequency leading to inhomogeneous broadening may be caused by the fluctuations in the occupation numbers of the Andreev states associated with a phase-biased Josephson junction. This mechanism may be revealed in qubits with small-area junctions, since the smallest relative change in frequency it causes is of the order of the inverse number of transmission channels in the junction.

cond-mat.mes-hall↗

arXiv2012

Black-box superconducting circuit quantization

We present a semi-classical method for determining the effective low-energy quantum Hamiltonian of weakly anharmonic superconducting circuits containing mesoscopic Josephson junctions coupled to electromagnetic environments made of an arbitrary combination of distributed and lumped elements. A convenient basis, capturing the multi-mode physics, is given by the quantized eigenmodes of the linearized circuit and is fully determined by a classical linear response function. The method is used to calculate numerically the low-energy spectrum of a 3D-transmon system, and quantitative agreement with measurements is found.

cond-mat.mes-hall↗

arXiv2009

Interaction induced edge channel equilibration

The electronic distribution functions of two Coulomb coupled chiral edge states forming a quasi-1D system with broken translation invariance are found using the equation of motion approach. We find that relaxation and thereby energy exchange between the two edge states is determined by the shot noise of the edge states generated at a quantum point contact (QPC). In close vicinity to the QPC, we derive analytic expressions for the distribution functions. We further give an iterative procedure with which we can compute numerically the distribution functions arbitrarily far away from the QPC. Our results are compared with recent experiments of Le Sueur et al..

cond-mat.mes-hall↗

arXiv2009

Universal detector efficiency of a mesoscopic capacitor

We investigate theoretically a novel type of high frequency quantum detector based on the mesoscopic capacitor recently realized by Gabelli et al., [Science {\bf 313}, 499 (2006)], which consists of a quantum dot connected via a single channel quantum point contact to a single lead. We show that the state of a double quantum dot charge qubit capacitively coupled to this detector can be read out in the GHz frequency regime with near quantum limited efficiency. To leading order, the quantum efficiency is found to be universal owing to the universality of the charge relaxation resistance of the mesoscopic capacitor.

cond-mat.mes-hall↗

arXiv2008

Role of coherence in resistance quantization

The quantization of resistances in the quantum Hall effect and ballistic transport through quantum point contacts is compared with the quantization of the charge relaxation resistance of a coherent mesoscopic capacitor. While the former two require the existence of a perfectly transmitting channel, the charge relaxation resistance remains quantized for arbitrary backscattering. The quantum Hall effect and the quantum point contact require only local phase coherence. In contrast quantization of the charge relaxation resistance requires global phase coherence.

cond-mat.mes-hall↗

arXiv2007

Quantum to Classical Transition of the Charge Relaxation Resistance of a Mesoscopic Capacitor

We present an analysis of the effect of dephasing on the single channel charge relaxation resistance of a mesoscopic capacitor in the linear low frequency regime. The capacitor consists of a cavity which is via a quantum point contact connected to an electron reservoir and Coulomb coupled to a gate. The capacitor is in a perpendicular high magnetic field such that only one (spin polarized) edge state is (partially) transmitted through the contact. In the coherent limit the charge relaxation resistance for a single channel contact is independent of the transmission probability of the contact and given by half a resistance quantum. The loss of coherence in the conductor is modeled by attaching to it a fictitious probe, which draws no net current. In the incoherent limit one could expect a charge relaxation resistance that is inversely proportional to the transmission probability of the quantum point contact. However, such a two terminal result requires that scattering is between two electron reservoirs which provide full inelastic relaxation. We find that dephasing of a single edge state in the cavity is not sufficient to generate an interface resistance. As a consequence the charge relaxation resistance is given by the sum of one constant interface resistance and the (original) Landauer resistance. The same result is obtained in the high temperature regime due to energy averaging over many occupied states in the cavity. Only for a large number of open dephasing channels, describing spatially homogenous dephasing in the cavity, do we recover the two terminal resistance, which is inversely proportional to the transmission probability of the QPC. We compare different dephasing models and discuss the relation of our results to a recent experiment.

cond-mat.mes-hall↗