Evolution Of Qubit Research Articles

Experimental investigation of geometric quantum speed limits in an open quantum system

The quantum speed limit (QSL) is a fundamental lower bound on the evolution time for quantum systems, and its tightness has been observed to be dependent on the properties of the physical process. However, experimental studies exploring the QSL in open quantum systems are still missing. Here, we studied geometric quantum speed limits of a qubit subject to decoherence in an ensemble of chloroform molecules in a Nuclear Magnetic Resonance experiment. We controlled the system-reservoir interaction and the spin relaxation rates by adding a paramagnetic salt, allowing the observation of both Markovian and non-Markovian open system dynamics for the qubit. We used two distinguishability measures of quantum states to assess the speed of the qubit evolution: the quantum Fisher information (QFI) and Wigner-Yanase skew information (WY). For non-Markovianity and low salt concentrations, we found crossovers between QSLs related to those metrics. The WY metric sets the tighter QSL for high concentrations and Markovian dynamics. We also show that QSLs are sensitive even to small fluctuations in spin magnetization.

Enhancing quantum coherence in multiqubit-interacting system

Abstract We propose a quantum coherence protection scheme for a two-qubit system by considering the exact evolution of multi-interacting qubits in a common reservoir. We find that the l 1 norm of coherence and the relative entropy of coherence can be noticeably enhanced by increasing the number of qubits in the weak/strong system-environment coupling regime, which contrasts sharply with the impact of coupling between qubits. Moreover, in the infinite-time limit, all the coherence measures reach their steady values which are determined only by the number of qubits.

Entanglement between two charge qubits taking account the Kerr media

Background. The need to implement controlled coupling between qubits, which are the logical elements of quantum devices such as quantum computers and quantum networks, requires, along with the use of traditional methods, the development of new, more effective ways to organize the interaction of qubits with the microwave fields of resonators used to generate and control the entanglement of qubits. As one of these methods, a method based on the influence of frequency-regulated radio frequency signals on a superconducting Josephson qubit connected by a large Josephson junction to a free qubit has been proposed.
 Aim. The influence of the Kerr medium of the resonator, in which one of the two qubits is placed, on their entanglement induced by the coherent or thermal frequency-regulated radio frequency field of the resonator is considered.
 Methods. To analyze the dynamics of the system under consideration, the solution of the quantum Liouville equation for the full density matrix is studied. An exact solution o this equation is found in the case of initial separable and entangled states of qubits. The exact solution of the evolution equation is used to calculate the criterion of qubit-qubit entanglement – cconcurrence. Numerical modeling of the concurrence was carried out for various states of qubits, coherent and thermal fields of the resonator, as well as various values of the intensity of the resonator field and the Kerr nonlinearity parameter.
 Results. It is shown that for separable initial states of qubits, the inclusion of Kerr nonlinearity reduces the maximum degree of entanglement of qubits. For an entangled initial state of qubits, the possibility of creating long-lived entangled states in the presence of Kerr nonlinearity is shown.
 Conclusion. The type of initial states of qubits and the range of values of the intensities of the resonator fields and the Kerr nonlinearity parameters have been established, for which the most effective control and operation of the evolution of qubits, as well as the degree of their entanglement, in the physical system under consideration, is possible.

Dynamic phases induced by two-level system defects on driven qubits

Recent experimental evidences point to two-level defects, located in the oxides and on the interfaces of the Josephson junctions, as the major constituents of decoherence in superconducting qubits. How these defects affect the qubit evolution with the presence of external driving is less well understood since the semiclassical qubit-field coupling renders the Jaynes–Cummings model for qubit-defect coupling undiagonalizable. We analyze the decoherence dynamics in the continuous coherent state space induced by the driving and solve the master equation endowed with an extra decay-cladded driving term via a Fokker–Planck equation. The solutions for diffusion propagators as Gaussian distributions show four distinct dynamic phases: four types of convergence paths to limit cycles of varying radius by the distribution mean, which are determined by the competing external driving and the defect decays. The qubit trajectory resulted from these solutions is a super-Poissonian over displaced Fock states, which reduces to a Gibbs state of effective temperature decided by the defect at zero driving limit. Furthermore, the Poincare map shows the dependence of the rate of convergence on the initial state. In other words, the qubit evolution can serve as an indicator of the defect coupling strength through the variation of the driving strength as a parameter.

Characterization and correction of the pulse width effects on quantum sensing experiments using solid-state spin qubits

Pulse-level protocols are commonly used in quantum information and sensing experiments. However, finite pulse width, inevitable in many cases due to experimental conditions, can affect the overall performance of the quantum measurement. Here, we study the effect of finite pulse width on quantum sensing experiments based on the solid-state spin qubits: nitrogen-vacancy centers in diamond. We perform magnetic sensing experiments of DC and AC fields using canonical sensing protocols: Ramsey interferometry, Hahn echo, and XY8 dynamical decoupling. By varying the width of π/2 and π pulse used in the protocols, we estimate the amount of phase accumulation during the pulses and correct their effects by compensating the qubit evolution time for time offsets due to the phase accumulation. In this way, we are able to recover optimal conditions for maximum sensitivity.

A simulator of optical coherent-state evolution in quantum key distribution systems

Quantum key distribution (QKD) is believed to represent a viable solution to achieve theoretically unconditionally secure key generation. However, the available optical systems for experimental QKD, based on photon transmission, are flawed by non-idealities that ultimately limit the achievable performance. Classical simulation of the optical hardware employed in these systems may take on a determining role in engineering future QKD networks. In this article, attempts for developing a QKD simulator based on low-computational-cost models of the employed hardware are presented. In particular, the simulation infrastructure targets polarization-based QKD setups with faint laser sources, whose behaviour can be described by semiclassical coherent states and Mean Photon Number (MPN) per beam. The effects of passive optical components on the photonic qubit evolution are described by Jones matrices, whose coefficients, for some commercial devices, are stored in an ad-hoc library. Realistic eavesdropping attacks and non-idealities, such as optical losses, fibre attenuation, polarization misalignment and limited efficiency of single-photon detectors, are also taken into account. The infrastructure allows the user to describe the desired QKD configuration and it provides in output the MPN at the receiver and two fiducial performance parameters: Quantum Bit Error Rate (QBER) and secure key rate. The comparison of the simulation results with experimental data in the state-of-the-art literature highlights that this work is a step forward towards the definition of compact models for the hardware-dependent simulation of quantum-assisted communication networks.

Charge-noise spectroscopy of Si/SiGe quantum dots via dynamically-decoupled exchange oscillations

Electron spins in silicon quantum dots are promising qubits due to their long coherence times, scalable fabrication, and potential for all-electrical control. However, charge noise in the host semiconductor presents a major obstacle to achieving high-fidelity single- and two-qubit gates in these devices. In this work, we measure the charge-noise spectrum of a Si/SiGe singlet-triplet qubit over nearly 12 decades in frequency using a combination of methods, including dynamically-decoupled exchange oscillations with up to 512 π pulses during the qubit evolution. The charge noise is colored across the entire frequency range of our measurements, although the spectral exponent changes with frequency. Moreover, the charge-noise spectrum inferred from conductance measurements of a proximal sensor quantum dot agrees with that inferred from coherent oscillations of the singlet-triplet qubit, suggesting that simple transport measurements can accurately characterize the charge noise over a wide frequency range in Si/SiGe quantum dots.

Noise-resistant Landau-Zener sweeps from geometrical curves

Landau-Zener physics is often exploited to generate quantum logic gates and to perform state initialization and readout. The quality of these operations can be degraded by noise fluctuations in the energy gap at the avoided crossing. We leverage a recently discovered correspondence between qubit evolution and space curves in three dimensions to design noise-robust Landau-Zener sweeps through an avoided crossing. In the case where the avoided crossing is purely noise-induced, we prove that operations based on monotonic sweeps cannot be robust to noise. Hence, we design families of phase gates based on non-monotonic drives that are error-robust up to second order. In the general case where there is an avoided crossing even in the absence of noise, we present a general technique for designing robust driving protocols that takes advantage of a relationship between the Landau-Zener problem and space curves of constant torsion.

A silicon singlet–triplet qubit driven by spin-valley coupling

Spin–orbit effects, inherent to electrons confined in quantum dots at a silicon heterointerface, provide a means to control electron spin qubits without the added complexity of on-chip, nanofabricated micromagnets or nearby coplanar striplines. Here, we demonstrate a singlet–triplet qubit operating mode that can drive qubit evolution at frequencies in excess of 200 MHz. This approach offers a means to electrically turn on and off fast control, while providing high logic gate orthogonality and long qubit dephasing times. We utilize this operational mode for dynamical decoupling experiments to probe the charge noise power spectrum in a silicon metal-oxide-semiconductor double quantum dot. In addition, we assess qubit frequency drift over longer timescales to capture low-frequency noise. We present the charge noise power spectral density up to 3 MHz, which exhibits a 1/fα dependence consistent with α ~ 0.7, over 9 orders of magnitude in noise frequency.

Yu-Shiba-Rusinov Qubit

Magnetic impurities in $s$-wave superconductors lead to spin-polarized Yu-Shiba-Rusinov (YSR) in-gap states. Chains of magnetic impurities offer one of the most viable routes for the realization of Majorana bound states which hold a promise for topological quantum computing. However, this ambitious goal looks distant since no quantum coherent degrees of freedom have yet been identified in these systems. To fill this gap we propose an effective two-level system, a YSR qubit, stemming from two nearby impurities. Using a time-dependent wave-function approach, we derive an effective Hamiltonian describing the YSR qubit evolution as a function of distance between the impurity spins, their relative orientations, and their dynamics. We show that the YSR qubit can be controlled and read out using the state-of-the-art experimental techniques for manipulation of the spins. Finally, we address the effect of the spin noises on the coherence properties of the YSR qubit, and show a robust behaviour for a wide range of experimentally relevant parameters. Looking forward, the YSR qubit could facilitate the implementation of a universal set of quantum gates in hybrid systems where they are coupled to topological Majorana qubits.

Eternally non-Markovian dynamics of a qubit interacting with a single-photon wavepacket

An evolution of a two-level system (qubit) interacting with a single-photon wave packet is analyzed. It is shown that a hierarchy of master equations gives rise to phase covariant qubit evolution. The temporal correlations in the input field induce nontrivial memory effects for the evolution of a qubit. It is shown that in the resonant case whenever time-local generator is regular (does not display singularities) the qubit evolution never displays information backflow. However, in general the generator might be highly singular leading to intricate non-Markovian effects. A detailed analysis of the exponential profile is provided which allows to illustrate all characteristic feature of the qubit evolution.

Intrinsic and induced quantum quenches for enhancing qubit-based quantum noise spectroscopy

Quantum sensing protocols that exploit the dephasing of a probe qubit are powerful and ubiquitous methods for interrogating an unknown environment. They have a variety of applications, ranging from noise mitigation in quantum processors, to the study of correlated electron states. Here, we discuss a simple strategy for enhancing these methods, based on the fact that they often give rise to an inadvertent quench of the probed system: there is an effective sudden change in the environmental Hamiltonian at the start of the sensing protocol. These quenches are extremely sensitive to the initial environmental state, and lead to observable changes in the sensor qubit evolution. We show how these new features give access to environmental response properties. This enables methods for direct measurement of bath temperature, and for detecting non-thermal equilibrium states. We also discuss how to deliberately control and modulate this quench physics, which enables reconstruction of the bath spectral function. Extensions to non-Gaussian quantum baths are also discussed, as is the application of our ideas to a range of sensing platforms (e.g., nitrogen-vacancy (NV) centers in diamond, semiconductor quantum dots, and superconducting circuits).

Engineering Classical Capacity of Generalized Pauli Channels with Admissible Memory Kernels.

In this paper, we analyze the classical capacity of the generalized Pauli channels generated via memory kernel master equations. For suitable engineering of the kernel parameters, evolution with non-local noise effects can produce dynamical maps with a higher capacity than a purely Markovian evolution. We provide instructive examples for qubit and qutrit evolution. Interestingly, similar behavior is not observed when analyzing time-local master equations.

Thermodynamics and the quantum speed limit in the non-Markovian regime

Quantum speed limit (QSL) for open quantum systems in the non-Markovian regime is analyzed. We provide a the lower bound for the time required to transform an initial state to a final state in terms of thermodynamic quantities such as the energy fluctuation, entropy production rate and dynamical activity. Such bound was already analyzed for Markovian evolution satisfying detailed balance condition. Here we generalize this approach to deal with arbitrary evolution governed by time-local generator. Our analysis is illustrated by three paradigmatic examples of qubit evolution: amplitude damping, pure dephasing, and the eternally non-Markovian evolution.

Spontaneous decay of artificial atoms in a multi-qubit system

We consider a one-dimensional chain of N equidistantly spaced noninteracting qubits embedded in an open waveguide. In the frame of single-excitation subspace, we systematically study the evolution of qubits' amplitudes if the only qubit in the chain was initially excited. We show that the temporal dynamics of qubits' amplitudes crucially depend on the value of kd, where k is the wave vector, d is a distance between neighbor qubits. If kd is equal to an integer multiple of π, then the qubits are excited to a stationary level which scales as N−1. We show that in this case, it is the dark states which prevent qubits from decaying to zero even though they do not contribute to the output spectrum of photon emission. For other values of kd the excitations of qubits have the form of damping oscillations, which represent the vacuum Rabi oscillations in a multi-qubit system. In this case, the output spectrum of photon radiation is defined by a subradiant state with the smallest width.

Towards Compact Modeling of Noisy Quantum Computers: A Molecular-Spin-Qubit Case of Study

Classical simulation of Noisy Intermediate Scale Quantum computers is a crucial task for testing the expected performance of real hardware. The standard approach, based on solving Schrödinger and Lindblad equations, is demanding when scaling the number of qubits in terms of both execution time and memory. In this article, attempts in defining compact models for the simulation of quantum hardware are proposed, ensuring results close to those obtained with standard formalism. Molecular Nuclear Magnetic Resonance quantum hardware is the target technology, where three non-ideality phenomena—common to other quantum technologies—are taken into account: decoherence, off-resonance qubit evolution, and undesired qubit-qubit residual interaction. A model for each non-ideality phenomenon is embedded into a MATLAB simulation infrastructure of noisy quantum computers. The accuracy of the models is tested on a benchmark of quantum circuits, in the expected operating ranges of quantum hardware. The corresponding outcomes are compared with those obtained via numeric integration of the Schrödinger equation and the Qiskit’s QASMSimulator. The achieved results give evidence that this work is a step forward towards the definition of compact models able to provide fast results close to those obtained with the traditional physical simulation strategies, thus paving the way for their integration into a classical simulator of quantum computers.

Decoherence mitigation by real-time noise acquisition

We present a scheme to neutralize the dephasing effect induced by classical noise on a qubit. The scheme builds upon the key idea that this kind of noise can be recorded by a classical device during the qubit evolution, and that its effect can be undone by a suitable control sequence that is conditioned on the measurement result. We specifically demonstrate this scheme on a nitrogen-vacancy center that strongly couples to current noise in a nearby conductor. By conditioning the readout observable on a measurement of the current, we recover the full qubit coherence and the qubit's intrinsic coherence time T2. We demonstrate that this scheme provides a simple way to implement single-qubit gates with an infidelity of 10−2 even if they are driven by noisy sources, and we estimate that an infidelity of 10−5 could be reached with additional improvements. We anticipate this method to find widespread adoption in experiments using fast control pulses driven from strong currents, in particular, in nanoscale magnetic resonance imaging, where control of peak currents of 100 mA with a bandwidth of 100 MHz is required.

Nonlinear extension of the quantum dynamical semigroup

In this paper we consider deterministic nonlinear time evolutions satisfying so called convex quasi-linearity condition. Such evolutions preserve the equivalence of ensembles and therefore are free from problems with signaling. We show that if family of linear non-trace-preserving maps satisfies the semigroup property then the generated family of convex quasi-linear operations also possesses the semigroup property. Next we generalize the Gorini-Kossakowski-Sudarshan-Lindblad type equation for the considered evolution. As examples we discuss the general qubit evolution in our model as well as an extension of the Jaynes-Cummings model. We apply our formalism to spin density matrix of a charged particle moving in the electromagnetic field as well as to flavor evolution of solar neutrinos.

On the hybrid Davies like generator for quantum dissipation.

We provide a class of quantum evolution beyond Markovian semigroup. This class is governed by a hybrid Davies like generator such that dissipation is controlled by a suitable memory kernel and decoherence by standard Gorini-Kossakowski-Lindblad-Sudarshan generator. These two processes commute and both of them commute with the unitary evolution controlled by the systems Hamiltonian. The corresponding memory kernel gives rise to semi-Markov evolution of the diagonal elements of the density matrix. However, the corresponding evolution needs not be completely positive. The role of decoherence generator is to restore complete positivity. Hence, to pose the dynamical problem, one needs two processes generated by classical semi-Markov memory kernel and purely quantum decoherence generator. This scheme is illustrated for a qubit evolution.

Construction of propagators for divisible dynamical maps

Divisible dynamical maps play an important role in characterizing Markovianity on the level of quantum evolution. Divisible maps provide an important generalization of Markovian semigroups. Usually one analyzes either completely positive or just positive divisibility meaning that the corresponding propagators are defined in terms of completely positive or positive maps, respectively. For maps which are invertible at any moment of time the very existence of propagator is already guaranteed and hence the only issue is (complete) positivity and trace-preservation. However, for maps which are not invertible the problem is much more involved since even the existence of a propagator is not guaranteed. In this paper we propose a simple method to construct propagators of dynamical maps using the concept of generalized inverse. We analyze both time-continuous and time-discrete maps. Since the generalized inverse is not uniquely defined the same applies for the corresponding propagator. In simple examples of qubit evolution we analyze it turns out that the additional requirement of complete positivity possibly makes the propagator unique.