arXiv subjects

Sahel Ashhab

Publications and source records attributed to Sahel Ashhab.

At least 37 records · Page 2Linked to original sources

arXiv2024

Superconducting flux qubit with ferromagnetic Josephson $π$-junction operating at zero magnetic field

Conventional superconducting flux qubits require the application of a precisely tuned magnetic field to set the operation point at half a flux quantum through the qubit loop, which complicates the on-chip integration of this type of device. It has been proposed that by inducing a $π$-phase shift in the superconducting order parameter using a precisely controlled nanoscale-thickness superconductor/ferromagnet/superconductor Josephson junction, commonly referred to as $π$-junction, it is possible to realize a flux qubit operating at zero magnetic flux. Here, we report the realization of a zero-flux-biased flux qubit based on three NbN/AlN/NbN Josephson junctions and a NbN/PdNi/NbN ferromagnetic $π$-junction. The qubit lifetime is in the microsecond range, which we argue is limited by quasiparticle excitations in the metallic ferromagnet layer. Our results pave the way for developing quantum coherent devices, including qubits and sensors, that utilize the interplay between ferromagnetism and superconductivity.

cond-mat.supr-con↗

arXiv2024

Using machine learning to find exact analytic solutions to analytically posed physics problems

We investigate the use of machine learning for solving analytic problems in theoretical physics. In particular, symbolic regression (SR) is making rapid progress in recent years as a tool to fit data using functions whose overall form is not known in advance. Assuming that we have a mathematical problem that is posed analytically, e.g.~through equations, but allows easy numerical evaluation of the solution for any given set of input variable values, one can generate data numerically and then use SR to identify the closed-form function that describes the data, assuming that such a function exists. In addition to providing a concise way to represent the solution of the problem, such an obtained function can play a key role in providing insight and allow us to find an intuitive explanation for the studied phenomenon. We use a state-of-the-art SR package to demonstrate how an exact solution can be found and make an attempt at solving an unsolved physics problem. We use the Landau-Zener problem and a few of its generalizations as examples to motivate our approach and illustrate how the calculations become increasingly complicated with increasing problem difficulty. Our results highlight the capabilities and limitations of the presently available SR packages, and they point to possible modifications of these packages to make them better suited for the purpose of finding exact solutions as opposed to good approximations. Our results also demonstrate the potential for machine learning to tackle analytically posed problems in theoretical physics.

physics.comp-ph↗

arXiv2024

High-frequency suppression of inductive coupling between flux qubit and transmission line resonator

We perform theoretical calculations to investigate the naturally occurring high-frequency cutoff in a circuit comprising a flux qubit coupled inductively to a transmission line resonator (TLR). Specifically, a decoupling occurs between the qubit and the high-frequency modes. The coupling strength between the qubit and resonator modes increases with mode frequency $ω$ as $\sqrtω$ at low frequencies and decreases as $1/\sqrtω$ at high frequencies. This result is similar to those of past studies that considered somewhat similar circuit designs. By avoiding the approximation of ignoring the qubit-TLR coupling in certain steps in the analysis, we obtain effects not captured in previous studies. In particular, we obtain a resonance effect that shifts the TLR mode frequencies close to qubit oscillation frequencies. We derive expressions for the TLR mode frequencies, qubit-TLR coupling strengths and qubit Lamb shift. We identify features in the spectrum of the system that can be used in future experiments to test and validate the theoretical model.

quant-ph↗

arXiv2023

Controlling qubit-oscillator systems using linear parameter sweeps

We investigate the dynamics of a qubit-oscillator system under the influence of a linear sweep of system parameters. We consider two main cases. In the first case, we consider sweeping the parameters between the regime of a weakly correlated ground state and the regime of a strongly correlated ground state, a situation that can be viewed as a finite-duration quench between two phases of matter: the normal phase and the superradiant phase. Excitations are created as a result of this quench. We investigate the dependence of the excitation probabilities on the various parameters. We find a qualitative asymmetry in the dynamics between the cases of a normal-to-superradiant and superradiant-to-normal quench. The second case of parameter sweeps that we investigate is the problem of a Landau-Zener sweep in the qubit bias term for a qubit coupled to a harmonic oscillator. We analyze a theoretical formula based on the assumption that the dynamics can be decomposed into a sequence of independent Landau-Zener transitions. In addition to establishing the conditions of validity for the theoretical formula, we find that under suitable conditions, deterministic and robust multi-photon state preparation is possible in this system.

quant-ph↗

arXiv2023

Extremely large Lamb shift in a deep-strongly coupled circuit QED system with a multimode resonator

We report experimental and theoretical results on the extremely large Lamb shift in a multimode circuit quantum electrodynamics (QED) system in the deep-strong coupling (DSC) regime, where the qubit-resonator coupling strength is comparable to or larger than the qubit and resonator frequencies. The system comprises a superconducting flux qubit (FQ) and a quarter-wavelength coplanar waveguide resonator ($λ/4$ CPWR) that are coupled inductively through a shared edge that contains a Josephson junction to achieve the DSC regime. Spectroscopy is performed around the frequency of the fundamental mode of the CPWR, and the spectrum is fitted by the single-mode quantum Rabi Hamiltonian to obtain the system parameters. Since the qubit is also coupled to a large number of higher modes in the resonator, the single-mode fitting does not provide the bare qubit energy but a value that incorporates the renormalization from all the other modes. We derive theoretical formulas for the Lamb shift in the multimode resonator system. As shown in previous studies, there is a cut-off frequency $ω_{\rm{cutoff}}$ for the coupling between the FQ and the modes in the CPWR, where the coupling grows as $\sqrt{ω_n}$ for $ω_n/ω_{\rm{cutoff}}\ll 1$ and decreases as $1/\sqrt{ω_n}$ for $ω_n/ω_{\rm{cutoff}}\gg 1$. Here $ω_n$ is the frequency of the $n$th mode. The cut-off effect occurs because the qubit acts as an obstacle for the current in the resonator, which suppresses the current of the modes above $ω_{\rm{cutoff}}$ at the location of the qubit and results in a reduced coupling strength. Using our observed spectrum and theoretical formulas, we estimate that the Lamb shift from the fundamental mode is 82.3\% and the total Lamb shift from all the modes is 96.5\%.

quant-ph↗

arXiv2022

Nonlinear Landau-Zener-Stückelberg-Majorana problem

In the standard Landau-Zener-Stückelberg-Majorana (LZSM) problem, the bias sweep rate and gap are both time independent and fully characterize the LZSM problem. We consider the nonlinear LZSM problem, in which at least one of the two characteristic parameters varies as the system traverses the avoided crossing region. This situation results in what could be thought of as a more accurate description of any realistic situation as compared to the idealized linear LZSM problem. We consider both the case of perturbative nonlinearities, where the nonlinearity adds small corrections to the linear problem, and the case of essential nonlinearities, where the sweep and/or minimum-gap functions are qualitatively different from those of the linear LZSM problem. In the case of perturbative nonlinearities, we derive analytic expressions for the LZSM transition probability based on the Dykhne-Davis-Pechukas (DDP) formula, taking into account the leading corrections to the standard LZSM formula. We compare the derived approximate expressions with numerical simulation results and comment on the validity of the approximations. In particular, if the nonlinear term is small in comparison to the linear term throughout the finite duration of the avoided crossing traversal, the perturbative approximation is valid. Our results also provide information about the validity of the DDP formula. In addition to reviewing cases of essential nonlinearity treated previously in the literature, we analyze the case of an essentially nonlinear sweep function that describes an almost square pulse.

quant-ph↗

arXiv2022

Numerical analysis of quantum circuits for state preparation and unitary operator synthesis

We perform optimal-control-theory calculations to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate configurations, we determine the maximum achievable fidelity as a function of quantum circuit size. This information allows us to identify the minimum circuit size needed for a specific target operation and enumerate the different gate configurations that allow a perfect implementation of the operation. We find that there are a large number of configurations that all produce the desired result, even at the minimum number of gates. We also show that the number of entangling gates can be reduced if we use multi-qubit entangling gates instead of two-qubit CNOT gates, as one might expect based on parameter counting calculations. In addition to treating the general case of arbitrary target states or unitary operators, we apply the numerical approach to the special case of synthesizing the multi-qubit Toffoli gate. This approach can be used to investigate any other specific few-qubit task and provides insight into the tightness of different bounds in the literature.

quant-ph↗

arXiv2022

Hamiltonian of a flux qubit-LC oscillator circuit in the deep-strong-coupling regime

We derive the Hamiltonian of a superconducting circuit that comprises a single-Josephson-junction flux qubit inductively coupled to an LC oscillator, and we compare the derived circuit Hamiltonian with the quantum Rabi Hamiltonian, which describes a two-level system coupled to a harmonic oscillator. We show that there is a simple, intuitive correspondence between the circuit Hamiltonian and the quantum Rabi Hamiltonian. While there is an overall shift of the entire spectrum, the energy level structure of the circuit Hamiltonian up to the seventh excited states can still be fitted well by the quantum Rabi Hamiltonian even in the case where the coupling strength is larger than the frequencies of the qubit and the oscillator, i.e., when the qubit-oscillator circuit is in the deep-strong-coupling regime. We also show that although the circuit Hamiltonian can be transformed via a unitary transformation to a Hamiltonian containing a capacitive coupling term, the resulting circuit Hamiltonian cannot be approximated by the variant of the quantum Rabi Hamiltonian that is obtained using an analogous procedure for mapping the circuit variables onto Pauli and harmonic oscillator operators, even for relatively weak coupling. This difference between the flux and charge gauges follows from the properties of the qubit Hamiltonian eigenstates.

quant-ph↗

arXiv2022

Speed limits for two-qubit gates with weakly anharmonic qubits

We consider the implementation of two-qubit gates when the physical systems used to realize the qubits possess additional quantum states in the accessible energy range. We use optimal control theory to determine the maximum achievable gate speed for two-qubit gates in the qubit subspace of the many-level Hilbert space, and we analyze the effect of the additional quantum states on the gate speed. We identify two competing mechanisms. On one hand, higher energy levels are generally more strongly coupled to each other. Under suitable conditions, this stronger coupling can be utilized to make two-qubit gates significantly faster than the reference value based on simple qubits. On the other hand, a weak anharmonicity constrains the speed at which the system can be adequately controlled: according to the intuitive picture, faster operations require stronger control fields, which are more likely to excite higher levels in a weakly anharmonic system, which in turn leads to faster decoherence and uncontrolled leakage outside the qubit space. In order to account for this constraint, we modify the pulse optimization algorithm to avoid pulses that lead to appreciable population of the higher levels. In this case we find that the presence of the higher levels can lead to a significant reduction in the maximum achievable gate speed. We also compare the optimal-control gate speeds with those obtained using the cross-resonance/selective-darkening gate protocol. We find that the latter, with some parameter optimization, can be used to achieve a relatively fast implementation of the CNOT gate. These results can help the search for optimized gate implementations in realistic quantum computing architectures, such as those based on superconducting circuits. They also provide guidelines for desirable conditions on anharmonicity that allow optimal utilization of the higher levels to achieve fast quantum gates.

quant-ph↗

arXiv2022

Quantum state preparation protocol for encoding classical data into the amplitudes of a quantum information processing register's wave function

We present a protocol for encoding $N$ real numbers stored in $N$ memory registers into the amplitudes of the quantum superposition that describes the state of $\log_2N$ qubits. This task is one of the main steps in quantum machine learning algorithms applied to classical data. The protocol combines partial CNOT gate rotations with probabilistic projection onto the desired state. The number of additional ancilla qubits used during the implementation of the protocol, as well as the number of quantum gates, scale linearly with the number of qubits in the processing register and hence logarithmically with $N$. The average time needed to successfully perform the encoding scales logarithmically with the number of qubits, in addition to being inversely proportional to the acceptable error in the encoded amplitudes. It also depends on the structure of the data set in such a way that the protocol is most efficient for non-sparse data.

quant-ph↗

arXiv2021

Enhanced coherence of all-nitride superconducting qubits epitaxially grown on silicon substrate

Improving the coherence of superconducting qubits is a fundamental step towards the realization of fault-tolerant quantum computation. However, coherence times of quantum circuits made from conventional aluminium-based Josephson junctions are limited by the presence of microscopic two-level systems in the amorphous aluminum oxide tunnel barriers. Here, we have developed superconducting qubits based on NbN/AlN/NbN epitaxial Josephson junctions on silicon substrates which promise to overcome the drawbacks of qubits based on Al/AlO$_{x}$/Al junctions. The all-nitride qubits have great advantages such as chemical stability against oxidation, resulting in fewer two-level fluctuators, feasibility for epitaxial tunnel barriers that reduce energy relaxation and dephasing, and a larger superconducting gap of $\sim$5.2 meV for NbN, compared to $\sim$0.3 meV for aluminium, which suppresses the excitation of quasiparticles. By replacing conventional MgO by a silicon substrate with a TiN buffer layer for epitaxial growth of nitride junctions, we demonstrate a qubit energy relaxation time $T$$_{1}$=16.3 $μ$s and a spin-echo dephasing time $T$$_{2}$=21.5 $μ$s. These significant improvements in quantum coherence are explained by the reduced dielectric loss compared to previously reported NbN-based qubits with MgO substrates ($T$$_{1}$$\approx$$T$$_{2}$$\approx$0.5 $μ$s). These results are an important step towards constructing a new platform for superconducting quantum hardware.

quant-ph↗

arXiv2021

Nonclassicality of open circuit QED systems in the deep-strong coupling regime

We investigate theoretically how the ground state of a qubit-resonator system in the deep-strong coupling (DSC) regime is affected by the coupling to an environment. We employ as a variational ansatz for the ground state of the qubit-resonator-environment system a superposition of coherent states displaced in qubit-state-dependent directions. We show that the reduced density matrix of the qubit-resonator system strongly depends on how the system is coupled to the environment, i.e., capacitive or inductive, because of the broken rotational symmetry of the eigenstates of the DSC system in the resonator phase space. When the resonator couples to the qubit and the environment in different ways (for instance, one is inductive and the other is capacitive), the system is almost unaffected by the resonator-waveguide coupling. In contrast, when the two couplings are of the same type (for instance, both are inductive), by increasing the resonator-waveguide coupling strength, the average number of virtual photons increases and the quantum superposition realized in the qubit-resonator entangled ground state is partially degraded. Since the superposition becomes more fragile with increasing the qubit-resonator coupling, there exists an optimal coupling strength to maximize the nonclassicality of the qubit-resonator system.

quant-ph↗

arXiv2019

Quantum Simulation of Resonant Transitions for Solving the Eigen-problem of an Effective Water Hamiltonian

It is difficult to calculate the energy levels and eigenstates of a large physical system on a classical computer because of the exponentially growing size of the Hilbert space. In this work, we experimentally demonstrate a quantum algorithm which could solve this problem via simulated resonant transitions. Using a four-qubit quantum simulator in which two qubits are used as ancillas for control and measurement, we obtain the energy spectrum of a 2-qubit low-energy effective Hamiltonian of the water molecule. The simulated transitions allow the state of the quantum simulator to transform and access large regions of the Hilbert space, including states that have no overlap with the initial state. Furthermore, we make use of this algorithm to efficiently prepare specific eigenstates on the simulator according to the measured eigenenergies.

quant-ph↗

arXiv2018

Inversion of Qubit Energy Levels in Qubit-Oscillator Circuits in the Deep-Strong-Coupling Regime

We report on experimentally measured light shifts of superconducting flux qubits deep-strongly coupled to LC oscillators, where the coupling constants are comparable to the qubit and oscillator resonance frequencies. By using two-tone spectroscopy, the energies of the six lowest levels of each circuit are determined. We find huge Lamb shifts that exceed 90% of the bare qubit frequencies and inversions of the qubits' ground and excited states when there are a finite number of photons in the oscillator. Our experimental results agree with theoretical predictions based on the quantum Rabi model.

quant-ph↗

arXiv2017

Characteristic spectra of circuit quantum electrodynamics systems from the ultrastrong- to the deep-strong-coupling regime

We report on spectra of circuit-quantum-electrodynamics (QED) systems in an intermediate regime that lies between the ultrastrong and deep-strong-coupling regimes, which have been reported previously in the literature. Our experimental results, along with numerical simulations, demonstrate that as the coupling strength increases, the spectrum of a circuit-QED system undergoes multiple qualitative transformations, such that several coupling regimes are identified, each with its own unique spectral features. The different spectral transformations can be related to crossings between energy level differences and to changes in the symmetries of the energy eigenstates. These results allow us to use qualitative spectral features to infer certain properties and parameters of the system.

quant-ph↗

arXiv2017

Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime

The interaction between an atom and the electromagnetic field inside a cavity has played a crucial role in the historical development of our understanding of light-matter interaction and is a central part of various quantum technologies, such as lasers and many quantum computing architectures. The emergence of superconducting qubits has allowed the realization of strong and ultrastrong coupling between artificial atoms and cavities. If the coupling strength $g$ becomes as large as the atomic and cavity frequencies ($Δ$ and $ω_{\rm o}$ respectively), the energy eigenstates including the ground state are predicted to be highly entangled. This qualitatively new regime can be called the deep strong-coupling regime, and there has been an ongoing debate over whether it is fundamentally possible to realize this regime in realistic physical systems. By inductively coupling a flux qubit and an LC oscillator via Josephson junctions, we have realized circuits with $g/ω_{\rm o}$ ranging from 0.72 to 1.34 and $g/Δ\gg 1$. Using spectroscopy measurements, we have observed unconventional transition spectra, with patterns resembling masquerade masks, that are characteristic of this new regime. Our results provide a basis for ground-state-based entangled-pair generation and open a new direction of research on strongly correlated light-matter states in circuit-quantum electrodynamics.

quant-ph↗

arXiv2016

Dynamics of a two-level system under strong driving: quantum gate optimization based on floquet theory

We consider the dynamics of a two-level system (qubit) driven by strong and short resonant pulses in the framework of Floquet theory. First we derive analytical expressions for the quasienergies and Floquet states of the driven system. If the pulse amplitude varies very slowly, the system adiabatically follows the instantaneous Floquet states, which acquire dynamical phases that depend on the evolution of the quasienergies over time. The difference between the phases acquired by the two Floquet states corresponds to a qubit state rotation, generalizing the notion of Rabi oscillations to the case of large driving amplitudes. If the pulse amplitude changes very fast, the evolution is non-adiabatic, with transitions taking place between the Floquet states. We quantify and analyze the nonadiabatic transitions during the pulse by employing adiabatic perturbation theory and exact numerical simulations. We find that, for certain combinations of pulse rise and fall times and maximum driving amplitude, a destructive interference effect leads to a remarkably strong suppression of transitions between the Floquet states. This effect provides the basis of a quantum control protocol, which we name Floquet Interference Efficient Suppression of Transitions in the Adiabatic basis (FIESTA), that can be used to design ultra-fast high-fidelity single-qubit quantum gates.

quant-ph↗

arXiv2016

Fast Quantum Communication in Linear Networks

Here we consider the speed at which quantum information can be transferred between the nodes of a linear network. Because such nodes are linear oscillators, this speed is also important in the cooling and state preparation of mechanical oscillators, as well as frequency conversion. We show that if there is no restriction on the size of the linear coupling between two oscillators, then there exist control protocols that will swap their respective states with high fidelity within a time much less than a single oscillation period. Standard gradient search methods fail to find these fast protocols. We were able to do so by augmenting standard search methods with a path-tracing technique, demonstrating that this technique has remarkable power to solve time-optimal control problems, as well as confirming the highly challenging nature of these problems. As a further demonstration of the power of path-tracing, first introduced by Moore-Tibbets et al. [Phys. Rev. A 86, 062309 (2012)], we apply it to the generation of entanglement in a linear network.

quant-ph↗