arXiv subjects

Jonathan L. DuBois

Publications and source records attributed to Jonathan L. DuBois.

12 recordsLinked to original sources

arXiv2024

Stochastic modeling of superconducting qudits in the dispersive regime

The field of superconducting quantum computing, based on Josephson junctions, has recently seen remarkable strides in scaling the number of logical qubits. In particular, the fidelities of one- and two-qubit gates have reached the breakeven point with the novel error mitigation and correction methods. Parallel to these advances is the effort to expand the Hilbert space within a single junction or device by employing high-dimensional qubits, otherwise known as qudits. Research has demonstrated the possibility of driving higher-order transitions in a transmon or designing innovative multimode superconducting circuits, termed multimons. These advances can significantly expand the computational basis while simplifying the interconnects in a large-scale quantum processor. In this work we extend the measurement theory of a conventional superconducting qubit to that of a qudit, focusing on modeling the dispersive quadrature measurement in an open quantum system. Under the Markov assumption, the qudit Lindblad and stochastic master equations are formulated and analyzed; in addition, both the ensemble-averaged and the quantum-jump approach of decoherence analysis are detailed with analytical and numerical comparisons. We verify our stochastic model with a series of experimental results on a transmon-type qutrit, verifying the validity of our high-dimensional formalism.

quant-ph↗

arXiv2023

Enhancing Qubit Readout with Autoencoders

In addition to the need for stable and precisely controllable qubits, quantum computers take advantage of good readout schemes. Superconducting qubit states can be inferred from the readout signal transmitted through a dispersively coupled resonator. This work proposes a novel readout classification method for superconducting qubits based on a neural network pre-trained with an autoencoder approach. A neural network is pre-trained with qubit readout signals as autoencoders in order to extract relevant features from the data set. Afterwards, the pre-trained network inner layer values are used to perform a classification of the inputs in a supervised manner. We demonstrate that this method can enhance classification performance, particularly for short and long time measurements where more traditional methods present lower performance.

quant-ph↗

arXiv2022

Phase-Slip Lines and Anomalous Josephson Effects in a Tungsten Clusters-Topological Insulator Microbridge

Superconducting topological systems formed by a strong 3D topological insulator (TI) in proximity to a conventional $s$-wave superconductor (SC) have been intensely studied as they may host Majorana zero modes. However, there are limited experimental realizations of TI-SC systems in which robust superconducting pairing is induced on the surface states of the TI and a topological superconducting state is established. Here, we fabricate a novel TI-SC system by depositing, via focused ion beam, tungsten (W) nanoscale clusters on the surface of TI Bi$_{0.91}$Sb$_{0.09}$. We find that the resulting heterostructure supports phase-slip lines that act as effective Josephson junctions. We probe the response of the system to microwave radiation. We find that for some ac frequencies, and powers, the resulting Shapiro steps' structure of the voltage-current characteristic exhibits a missing first step and an unexpectedly wide second Shapiro step. The theoretical analysis of the measurements shows that the unusual Shapiro response arises from the interplay between a static Josephson junction and a dynamic one, and allows us to identify the conditions under which the missing first step can be attributed to the topological nature of the Josephson junctions formed by the phase-slip lines. Our results suggest a new approach to induce superconductivity in a TI, a novel route to realizing highly-transparent topological Josephson junctions, and show how the response of superconducting systems to microwave radiation can be used to infer the dynamics of phase-slip lines.

cond-mat.supr-con↗

arXiv2022

Model predictive control for robust quantum state preparation

A critical engineering challenge in quantum technology is the accurate control of quantum dynamics. Model-based methods for optimal control have been shown to be highly effective when theory and experiment closely match. Consequently, realizing high-fidelity quantum processes with model-based control requires careful device characterization. In quantum processors based on cold atoms, the Hamiltonian can be well-characterized. For superconducting qubits operating at milli-Kelvin temperatures, the Hamiltonian is not as well-characterized. Unaccounted for physics (i.e., mode discrepancy), coherent disturbances, and increased noise compromise traditional model-based control. This work introduces model predictive control (MPC) for quantum control applications. MPC is a closed-loop optimization framework that (i) inherits a natural degree of disturbance rejection by incorporating measurement feedback, (ii) utilizes finite-horizon model-based optimizations to control complex multi-input, multi-output dynamical systems under state and input constraints, and (iii) is flexible enough to develop synergistically alongside other modern control strategies. We show how MPC can be used to generate practical optimized control sequences in representative examples of quantum state preparation. Specifically, we demonstrate for a qubit, a weakly-anharmonic qubit, and a system undergoing crosstalk, that MPC can realize successful model-based control even when the model is inadequate. These examples showcase why MPC is an important addition to the quantum engineering control suite.

quant-ph↗

arXiv2021

Quantum Optimal Control for Pure-State Preparation Using One Initial State

This paper presents a framework for solving the pure-state preparation problem using numerical optimal control. As an example, we consider the case where a number of qubits are dispersively coupled to a readout cavity. We model open system quantum dynamics using the Markovian Lindblad master equation, driven by external control pulses. The main result of this paper develops a basis of density matrices (a parameterization) where each basis element is a density matrix itself. Utilizing a specific objective function, we show how an ensemble of the basis elements can be used as a single initial state throughout the optimization process - independent of the system dimension. We apply the general framework to the specific application of ground-state reset of one and two qubits coupled to a readout cavity.

quant-ph↗

arXiv2020

Discrete Adjoints for Accurate Numerical Optimization with Application to Quantum Control

This paper considers the optimal control problem for realizing logical gates in a closed quantum system. The quantum state is governed by Schrodinger's equation, which we formulate as a time-dependent Hamiltonian system in terms of the real and imaginary parts of the state vector. The system is discretized with the Stormer-Verlet scheme, which is a symplectic partitioned Runge-Kutta method. Our main theoretical contribution is the derivation of a compatible time-discretization of the adjoint state equation, such that the gradient of the discrete objective function can be calculated exactly, at a computational cost of solving two Schrödinger systems, independently of the number of parameters in the control functions. A parameterization of the control functions based on B-splines with built-in carrier waves is also introduced. The carrier waves are used to specify the frequency spectra of the control functions, while the B-spline functions specify their envelope and phase. This approach allows the number of control parameters to be independent of, and significantly smaller than, the number of time steps for integrating Schrodinger's equation. We consider Hamiltonians that model the dynamics of a superconducting multi-level qudit and present numerical examples of how the proposed technique can be combined with the interior point L-BFGS algorithm from the IPOPT package for realizing quantum gates. In a set of test cases, the proposed algorithm is shown to compare favorably with QuTiP/pulse_optim and Grape-Tensorflow.

quant-ph↗

arXiv2020

Improving Qubit Readout with Hidden Markov Models

We demonstrate the application of pattern recognition algorithms via hidden Markov models (HMM) for qubit readout. This scheme provides a state-path trajectory approach capable of detecting qubit state transitions and makes for a robust classification scheme with higher starting state assignment fidelity than when compared to a multivariate Gaussian (MVG) or a support vector machine (SVM) scheme. Therefore, the method also eliminates the qubit-dependent readout time optimization requirement in current schemes. Using a HMM state discriminator we estimate fidelities reaching the ideal limit. Unsupervised learning gives access to transition matrix, priors, and IQ distributions, providing a toolbox for studying qubit state dynamics during strong projective readout.

quant-ph↗

arXiv2017

Number squeezed and fragmented states of strongly interacting bosons in a double well

We present a systematic study of the phenomena of number squeezing and fragmentation for a repulsive Bose-Einstein condensate (BEC) in a three dimensional double well potential over a range of interaction strengths and barrier heights, including geometries that exhibit appreciable overlap in the one-body wavefunctions localized in the left and right wells. We compute the properties of the condensate with numerically exact, full dimensional path integral ground state (PIGS) Quantum Monte Carlo simulations and compare with results obtained from using two- and eight-mode truncated basis models. The truncated basis models are found to agree with the numerically exact PIGS simulations for weak interactions, but fail to correctly predict the amount of number squeezing and fragmentation exhibited by the PIGS simulations for strong interactions. We find that both number squeezing and fragmentation of the BEC show non-monotonic behavior at large values of interaction strength a. The number squeezing shows a universal scaling with the product of number of particles and interaction strength (Na) but no such universal behavior is found for fragmentation. Detailed analysis shows that the introduction of repulsive interactions not only suppresses number fluctuations to enhance number squeezing, but can also enhance delocalization across wells and tunneling between wells, each of which may suppress number squeezing. This results in a dynamical competition whose resolution shows a complex dependence on all three physical parameters defining the system: interaction strength, number of particles, and barrier height.

cond-mat.quant-gas↗

arXiv2014

Magnetic fluctuation from oxygen deficiency centers on the SiO$_2$ surface

The magnetic stability of oxygen deficiency centers on the surface of α-quartz is investigated with first- principles calculations to understand their role in contributing to magnetic flux noise in superconducting qubits (SQs) and superconducting quantum interference devices (SQUIDs) fabricated on amorphous silica substrates. Magnetic defects on the substrate are likely responsible for some of the 1/f noise that plagues these systems. Dangling-bonds associated with three-coordinated Si atoms allow electron density transfer between spin up and down channels, resulting in low energy magnetic states. Such under-coordinated Si defects are common in both stoichiometric and oxygen deficient silica and quartz and are a probable source of magnetic flux fluctuations in SQs and SQUIDs.

cond-mat.mtrl-sci↗

arXiv2013

Exchange-correlation energy for the 3D homogeneous electron gas at arbitrary temperature

We fit finite-temperature path integral Monte Carlo calculations of the exchange-correlation energy of the 3D finite-temperature homogeneous electron gas in the warm-dense regime (r_{s} = (3/4πn)^{1/3} a_{B}^{-1} < 40 and Θ= T/T_{F} > 0.0625). In doing so, we construct a Padé approximant which collapses to Debye-Hückel theory in the high-temperature, low-density limit. Likewise, the zero-temperature limit matches the numerical results of ground-state quantum Monte Carlo, as well as analytical results in the high-density limit.

cond-mat.str-el↗

arXiv2012

Path Integral Monte Carlo Simulation of the Warm-Dense Homogeneous Electron Gas

We perform calculations of the {3D} finite-temperature homogeneous electron gas (HEG) in the warm-dense regime ({r_{s} \equiv (3/4πn)^{1/3}a_{B}^{- 1} = 1.0- 40.0} and {Θ\equiv T/T_{F} = 0.0625- 8.0}) using restricted path integral Monte Carlo (RPIMC). Precise energies, pair correlation functions, and structure factors are obtained. For all densities, we find a significant discrepancy between the ground state parameterized local density approximation (LDA) and our results around {T_{F}} . These results can be used as a benchmark for improved functionals, as well as input for orbital-free DFT formulations.

cond-mat.str-el↗

arXiv2003

Natural Orbitals and BEC in traps, a diffusion Monte Carlo analysis

We investigate the properties of hard core Bosons in harmonic traps over a wide range of densities. Bose-Einstein condensation is formulated using the one-body Density Matrix (OBDM) which is equally valid at low and high densities. The OBDM is calculated using diffusion Monte Carlo methods and it is diagonalized to obtain the "natural" single particle orbitals and their occupation, including the condensate fraction. At low Boson density, $na^3 < 10^{-5}$, where $n = N/V$ and $a$ is the hard core diameter, the condensate is localized at the center of the trap. As $na^3$ increases, the condensate moves to the edges of the trap. At high density it is localized at the edges of the trap. At $na^3 \leq 10^{-4}$ the Gross-Pitaevskii theory of the condensate describes the whole system within 1%. At $na^3 \approx 10^{-3}$ corrections are 3% to the GP energy but 30% to the Bogoliubov prediction of the condensate depletion. At $na^3 \gtrsim 10^{-2}$, mean field theory fails. At $na^3 \gtrsim 0.1$, the Bosons behave more like a liquid $^4$He droplet than a trapped Boson gas.

cond-mat.soft↗