arXiv subjects

Kiyoto Nakamura

Publications and source records attributed to Kiyoto Nakamura.

7 recordsLinked to original sources

arXiv2026

Entanglement dynamics and performance of two-qubit gates for superconducting qubits under non-Markovian effects

Within a numerically exact simulation technique, the dissipative dynamics of a two-qubit architecture is considered in which each qubit couples to its individual noise source (reservoir). The goal is to reveal the role of subtle qubit-reservoir correlations including non-Markovian processes as a prerequisite to guide further improvements of quantum computing devices. This paper addresses the following three topics. First, we examine the validity of the rotating wave approximation imposed previously on the qubit-reservoir coupling with respect to the disentanglement dynamics. Second, generation of the entanglement as well as destruction are analyzed by monitoring the reduced dynamics during and after application of a $\sqrt{\mbox{iSWAP}^\dagger}$ gate, also focusing on memory effects caused by reservoirs. Finally, the performance of a Hadamard + CNOT sequence is analyzed for different gate decomposition schemes. In all three cases, various types of noise sources and qubit parameters are considered.

quant-ph↗

arXiv2025

Impact of time-retarded noise on dynamical decoupling schemes for qubits

One of the simplest and least resource-intensive methods to suppress decoherence for qubit operations, namely, dynamical decoupling (DD), is investigated for a broad range of realistic noise sources with time-retarded feedback. By way of example, the Carr-Purcell-Meiboom-Gill (CPMG) sequence is analyzed in a numerically rigorous manner accounting also for correlations between qubits and environments. Since experimentally noise sources are characterized through spectral densities, we adopt the spin-boson model as a suitable framework to describe the qubit dynamics under DD for a given spectral density $J(ω) \propto ω^s$. Motivated by the situation for superconducting qubits, the spectral exponent $s$ is varied from $s=1$ (Ohmic bath) to a substantially small value $0 < s \ll 1$ (deep sub-Ohmic bath), in order to investigate the impact of time-nonlocal back action on DD performances for enhanced coherence times. As reference to the DD schemes, dynamics of a single qubit subject to Ramsey sequences without any pules and Hahn echo (HE) sequences are also investigated.

quant-ph↗

arXiv2024

Gate Operations for Superconducting Qubits and Non-Markovianity

While the accuracy of qubit operations has been greatly improved in the last decade, further development is demanded to achieve the ultimate goal: a fault-tolerant quantum computer that can solve real-world problems more efficiently than classical computers. With growing fidelities even subtle effects of environmental noise such as qubit-reservoir correlations and non-Markovian dynamics turn into the focus for both circuit design and control. To guide progress, we disclose, in a numerically rigorous manner, a comprehensive picture of the single-qubit dynamics in presence of a broad class of noise sources and for entire sequences of gate operations. Thermal reservoirs ranging from Ohmic to deep $1/f^{\varepsilon}$-like sub-Ohmic behavior are considered to imitate realistic scenarios for superconducting qubits. Apart from dynamical features, fidelities of the qubit performance over entire sequences are analyzed as a figure of merit. The relevance of retarded feedback and long-range qubit-reservoir correlations is demonstrated on a quantitative level, thus, providing a deeper understanding of the limitations of performances for current devices and guiding the design of future ones.

quant-ph↗

arXiv2024

Qubit Dynamics beyond Lindblad: Non-Markovianity versus Rotating Wave Approximation

With increasing performance of actual qubit devices, even subtle effects in the interaction between qubits and environmental degrees of freedom become progressively relevant and experimentally visible. This applies particularly to the timescale separations that are at the basis of the most commonly used numerical simulation platform for qubit operations, namely, the conventional Lindblad master equation (LE): the Markov approximation and the rotating wave approximation (RWA). In this contribution we shed light on the questions (i) to which extent it is possible to monitor violations of either of these timescale separations experimentally and (ii) which of them is the most severe to provide highly accurate predictions within (approximate) numerical schemes in relevant parameter ranges. For this purpose, we compare three simulation methods for the reduced density matrix with progressively growing accuracy. In particular, predictions for relaxation and decoherence of a qubit system in the presence of reservoirs with Ohmic and sub-Ohmic spectral densities are explored and, with the aid of proper protocols based on Ramsey experiments, the role of non-Markovianity and RWA are revealed. We discuss potential implications for future experiments and the design of approximate yet accurate numerical approaches.

quant-ph↗

arXiv2021

Open quantum dynamics theory for a complex subenvironment system with a quantum thermostat: Application to a spin heat bath

Complex environments, such as molecular matrices and biological material, play a fundamental role in many important dynamic processes in condensed phases. Because it is extremely difficult to conduct full quantum dynamics simulations on such environments due to their many degrees of freedom, here we treat in detail the environment only around the main system of interest (the subenvironment), while the other degrees of freedom needed to maintain the equilibrium temperature are described by a simple harmonic bath, which we call a quantum thermostat. The noise generated by the subenvironment is spatially non-local and non-Gaussian and cannot be characterized by the fluctuation-dissipation theorem. We describe this model by simulating the dynamics of a two-level system (TLS) that interacts with a subenvironment consisting of a one-dimensional $XXZ$ spin chain. The hierarchical Schrödinger equations of motion are employed to describe the quantum thermostat, allowing time-irreversible simulations of the dynamics at arbitrary temperature. To see the effects of a quantum phase transition of the subenvironment, we investigate the decoherence and relaxation processes of the TLS at zero and finite temperatures for various values of the spin anisotropy. We observed the decoherence of the TLS at finite temperature, even when the anisotropy of the $XXZ$ model is enormous. We also found that the population relaxation dynamics of the TLS changed in a complex manner with the change of the anisotropy and the ferromagnetic or antiferromagnetic orders of the spins.

quant-ph↗

arXiv2021

Optical response of laser-driven charge-transfer complex described by Holstein-Hubbard model coupled to heat baths: Hierarchical equations of motion approach

We investigate the optical response of a charge-transfer complex in a condensed phase driven by an external laser field. Our model includes an instantaneous short-range Coulomb interaction and a local optical vibrational mode described by the Holstein-Hubbard (HH) model. Although characterization of the HH model for a bulk system has typically been conducted using a complex phase diagram, this approach is not sufficient for investigations of dynamical behavior at finite temperature, in particular for studies of nonlinear optical properties, where the time irreversibility of the dynamics that arises from the environment becomes significant. We therefore include heat baths with infinite heat capacity in the model to introduce thermal effects characterized by fluctuation and dissipation to the system dynamics. By reducing the number of degrees of freedom of the heat baths, we derive numerically "exact" hierarchical equations of motion (HEOM) for the reduced density matrix of the HH system. As demonstrations, we calculate the optical response of the system in two- and four-site cases under external electric fields. The results indicate that the effective strength of the system-bath coupling becomes large as the number of sites increases. Excitation of electrons promotes the conductivity when the Coulomb repulsion is equivalent to or dominates the electron-phonon coupling, whereas excitation of optical vibrations always suppresses the conductivity.

cond-mat.str-el↗

arXiv2018

Hierarchical Schrödinger Equations of Motion for Open Quantum Dynamics

We rigorously investigate the quantum non-Markovian dissipative dynamics of a system coupled to a harmonic oscillator bath by deriving hierarchical Schrodinger equations of motion (HSEOM) and studying their dynamics. The HSEOM are the equations for wave functions derived on the basis of the Feynman-Vernon influence functional formalism for the density operator, $\langle q|ρ(t)|q' \rangle$, where $\langle q|$ and $|q' \rangle$ are the left- and right-hand elements. The time evolution of $\langle q|$ is computed from time $0$ to $t$, and subsequently, the time evolution of $|q' \rangle$ is computed from time $t$ to $0$ along a contour in the complex time plane. By appropriately choosing functions for the bath correlation function and the spectral density, we can take advantage of an HSEOM method to carry out simulations without the need for a great amount of computational memory. As a demonstration, quantum annealing simulation for a ferromagnetic $p$-spin model is studied.

quant-ph↗