Two-qubit System Research Articles

Correcting on-chip distortion of control pulses with silicon spin qubits

Abstract In semiconductor quantum dot systems, pulse distortion is a significant source of coherent errors, which impedes qubit characterization and control. Here, we demonstrate two calibration methods using a two-qubit system as a detector to correct distortion and calibrate the transfer function of the control line. Both methods are straightforward to implement, robust against noise, and applicable to a wide range of qubit types. The two methods differ in correction accuracy and complexity. The first, the Coarse Predistortion (CPD) method, partially mitigates distortion. The second, the All Predistortion (APD) method, measures the transfer function and significantly enhances exchange oscillation uniformity. Both methods use exchange oscillation homogeneity as the metric and are suitable for any qubit driven by a diabatic pulse. We believe these methods will enhance qubit characterization accuracy and operation quality in future applications.

Infidelity Analysis of Digital Counter-Diabatic Driving in Simple Two-Qubit System.

Digitized counter-diabatic (CD) optimization algorithms have been proposed and extensively studied to enhance performance in quantum computing by accelerating adiabatic processes while minimizing energy transitions. While adding approximate counter-diabatic terms can initially introduce adiabatic errors that decrease over time, Trotter errors from decomposition approximation persist. On the other hand, increasing the high-order nested commutators for CD terms may improve adiabatic errors but could also introduce additional Trotter errors. In this article, we examine the two-qubit model to explore the interplay between approximate CD, adiabatic errors, Trotter errors, coefficients, and commutators. Through these analyses, we aim to gain insights into optimizing these factors for better fidelity, a shallower circuit depth, and a reduced gate number in near-term gate-based quantum computing.

Non-Markovian dynamics control of an open quantum system in a Schwarzschild space–time

By considering two qubits respectively coupled with two independent reservoirs and ignoring the interaction between them, two different cases are studied in two models: only one qubit accelerates and hovers near the event horizon or both two qubits accelerate and hover near the event horizon. The first model is given by referring to the damping Jaynes–Cummings model with a reservoir described by Lorentzian spectral density. And the second model is a pure dephasing model with a reservoir described by Ohmic spectral density. We investigate the impact of acceleration and Hawking temperature on the non-Markovianity and the quantum speed limit time of a two-qubit open quantum system. Through the numerical calculation, it is found that for these two models, by reducing the acceleration of qubits and the Hawking temperature outside the event horizon, the non-Markovianity of the dynamic process of the quantum system in the Schwarzschild space–time can be enhanced until it approaches the non-Markovianity when both qubits are in the inertial frame. However, we find that in the first model, the evolution speed of quantum state can be accelerated with decreasing acceleration and Hawking temperature. While in the second model, the quantum state evolution speed can be accelerated with increasing acceleration and Hawking temperature. For both models, the evolution speed of the quantum state of the system in the Markovian dynamics can still be accelerated.

Quantum steering of a pulse-driven two-qubit system

Quantum steering of a pulse-driven two-qubit system

Non-Markovian noise mitigation in quantum teleportation: enhancing fidelity and entanglement

Maintaining quantum coherence and entanglement in the presence of environmental noise, particularly within non-Markovian contexts, represents a significant challenge for the progression of quantum information science and technology. This study offers a substantial advancement by investigating the dynamics of a two-qubit system subjected to diverse noise conditions, encompassing relaxation, dephasing, and their cumulative effects. By employing quantum-state-diffusion equations specifically crafted for non-Markovian environments, we introduce an innovative strategy to counteract the detrimental influences of environmental noise on quantum teleportation fidelity and entanglement concurrence. Our results underscore the potential for external interventions to markedly improve the resilience of quantum information processing tasks over prolonged durations, especially in settings where dephasing noise prevails. A key revelation is the intricate relationship between dephasing noise and the initial state of entanglement, which profoundly impacts the occurrence of entanglement sudden death. This research not only deepens our comprehension of quantum system dynamics under noisy circumstances but also furnishes practical directives for engineering robust quantum systems, a necessity for the development of scalable quantum technologies.

Entanglement signature in quantum work statistics in the slow-driving regime

In slowly driven classical systems, work is a stochastic quantity and its probability distribution is known to satisfy the work fluctuation-dissipation relation, which states that the mean and variance of the dissipated work are linearly related. Recently, it was shown that generation of quantum coherence in the instantaneous energy eigenbasis leads to a correction to this linear relation in the slow-driving regime. Here, we go even further by investigating nonclassical features of work fluctuations in setups with more than one system. To do this, we first generalize slow control protocols to encompass multipartite systems, allowing for the generation of quantum correlations during the driving process. Then, focusing on two-qubit systems, we show that entanglement generation leads to a positive contribution to the dissipated work, which is distinct from the quantum correction due to local coherence generation known from previous work. Our results show that entanglement generated during slow control protocols, e.g., as an unavoidable consequence of qubit crosstalk, comes at the cost of increased dissipation. Published by the American Physical Society 2024

Entanglement generation from athermality

We investigate the thermodynamic constraints on the pivotal task of entanglement generation using out-of-equilibrium states through a model-independent framework with minimal assumptions. We establish a necessary and sufficient condition for a thermal process to generate bipartite qubit entanglement, starting from an initially separable state. Consequently, we identify the set of system states that cannot be entangled, when no external work is invested. In the regime of infinite temperature, we analytically construct this set; while for finite temperature, we provide a simple criterion to verify whether any given initial state is or is not entangleable. Furthermore, we provide an explicit construction of the future thermal cone of entanglement—the set of entangled states that a given separable state can thermodynamically evolve to. We offer a detailed discussion on the properties of this cone, focusing on the interplay between entanglement and its volumetric properties. We conclude with several key remarks on the generation of entanglement beyond two-qubit systems, and discuss its dynamics in the presence of dissipation. Published by the American Physical Society 2024

Dynamics analysis of non-inertial observers under Ohmic-induced decoherence

We investigate the dynamics of quantum features in a two-qubit system subjected to acceleration in one or both subsystems while interacting with Ohmic or super-Ohmic noisy reservoirs. Metrics such as quantum discord, negativity, and entropic uncertainty are deployed to analyze the dynamical map of quantum states under various conditions. Our findings suggest that increasing the number of accelerated qubits negatively impacts quantum correlations. Furthermore, assigning non-uniform values of acceleration magnitude to the two qubits also leads to higher decay and uncertainty generation. Additionally, an increase in the bosonic reservoir frequency and ohmicity parameter exhibits opposite effects to those prevailed by the purity of states by promoting decay. Notably, discord proves to be sensitive to acceleration and non-uniformity, while negativity is strongly influenced by low purity values. The role of Ohmic noisy reservoirs is emphasized, as they display less decay compared to super-Ohmic reservoirs. Overall, the super-Ohmic noisy reservoir induced higher decoherence and uncertainty, causing larger quantum correlation decay compared to the Ohmic noise.

Distributed Partial Quantum Consensus of Qubit Networks With Connected Topologies.

In this article, we consider the partial quantum consensus problem of a qubit network in a distributed view. The local quantum operation is designed based on the Hamiltonian by using the local information of each quantum system in a network of qubits. We construct the unitary transformation for each quantum system to achieve the partial quantum consensus, that is, the directions of the quantum states in the Bloch ball will reach an agreement. A simple case of two-qubit quantum systems is considered first, and a minimum completing time of reaching partial consensus is obtained based on the geometric configuration of each qubit. Furthermore, we extend the approaches to deal with the more general N -qubit networks. Two partial quantum consensus protocols, based on the Lyapunov method for chain graphs and the geometry method for connected graphs, are proposed. The geometry method can be utilized to deal with more general connected graphs, while for the Lyapunov method, the global consensus can be obtained. The numerical simulation over a qubit network is demonstrated to verify the validity and the effectiveness of the theoretical results.

Dynamical theory of single-photon transport through a qubit chain coupled to a one-dimensional nanophotonic waveguide

We study the dynamics of a single-photon pulse traveling through a linear qubit chain coupled to continuum modes in a one-dimensional (1D) photonic waveguide. We derive a time-dependent dynamical theory for qubits’ amplitudes and for transmitted and reflected spectra. We show that the requirement for the photon-qubit coupling to exist only for positive frequencies can significantly change the dynamics of the system. First, it leads to the additional photon-mediated dipole-dipole interaction between qubits which results in the violation of the phase coherence between them. Second, the spectral lines of transmitted and reflected spectra crucially depend on the shape of the incident pulse and on the initial distance between the pulse center and the first qubit in the chain. We apply our theory to one-qubit and two-qubit systems. For these cases we obtain the explicit expressions for the qubits’ amplitudes and for the photon radiation spectra as time tends to infinity. Specific calculations are performed for superconducting qubits operating in GHz frequency range. For the incident Gaussian wave packet we calculate the line shapes of transmitted and reflected photons.

Certification of two-qubit quantum systems with temporal inequality

Certification of two-qubit quantum systems with temporal inequality

Note on quantum discord

Quantum discord goes beyond entanglement and exists in a wide range of quantum states that may be separable, playing a crucial role in quantum information tasks. In this paper, we firstly proposed a zero-discord criterion for two-qubit system based on the partial transposition of density matrix, and then extended it to the qubit–qudit system. By detailed examples we demonstrate the effectiveness of these criteria in detecting discord. Moreover, we provide an analytical lower bound of geometric quantum discord(GQD) using eigenvalue vectors of density matrix. Finally, we presented a one-way work deficit lower bound based on our lower bound of GQD.

Entanglement detection with classical deep neural networks

In this study, we introduce an autonomous method for addressing the detection and classification of quantum entanglement, a core element of quantum mechanics that has yet to be fully understood. We employ a multi-layer perceptron to effectively identify entanglement in both two- and three-qubit systems. Our technique yields impressive detection results, achieving nearly perfect accuracy for two-qubit systems and over 90%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$90\\%$$\\end{document} accuracy for three-qubit systems. Additionally, our approach successfully categorizes three-qubit entangled states into distinct groups with a success rate of up to 77%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$77\\%$$\\end{document}. These findings indicate the potential for our method to be applied to larger systems, paving the way for advancements in quantum information processing applications.

Dynamics of a two-qubit Tavis-Cummings model in the presence of an Ising-type interaction between qubits

In this paper, we investigated the dynamics of entanglement of two qubits interacting non-resonantly with the thermal field of a one-mode lossless resonator, taking into account the Ising-type direct interaction between qubits. Based on the exact solution of the quantum Liouville equation, we found the density matrix of the system under consideration. With its help, the reduced qubit-qubit density matrix was calculated and the entanglement criteriоn of the two-qubit system, Pres-Horodeсki parameter, was found. It was shown that for the resonance model and separable initial states of qubits, the direct interaction of qubits leads to a significant increase in the maximum degree of their entanglement. It was also found that for the nonresonant interaction between qubits and field, the increase of the maximum degree of entanglement of qubits is much greater than that due to direct interaction. For the original entangled Bell-type state of the qubits, the direct interaction was found to lead to the vanishing of the effect of the sudden death of entanglement in the case of a resonant qubit-field interaction and, conversely, to an increase in this effect for a nonresonant interaction.

Trade-off between bagging and boosting for quantum separability-entanglement classification

Certifying whether an arbitrary quantum system is entangled or not, is, in general, an NP-hard problem. Though various necessary and sufficient conditions have already been explored in this regard for lower-dimensional systems, it is hard to extend them to higher dimensions. Recently, an ensemble bagging and convex hull approximation (CHA) approach (together, BCHA) was proposed and it strongly suggests employing a machine learning technique for the separability-entanglement classification problem. However, BCHA does only incorporate the balanced dataset for classification tasks which results in lower average accuracy. In order to solve the data imbalance problem in the present literature, an exploration of the boosting technique has been carried out, and a trade-off between the boosting and bagging-based ensemble classifier is explored for quantum separability problems. For the two-qubit and two-qutrit quantum systems, the pros and cons of the proposed random under-sampling boost CHA (RUSBCHA) for the quantum separability problem are compared with the state-of-the-art CHA and BCHA approaches. As the data are highly unbalanced, performance measures such as overall accuracy, average accuracy, F-measure, and G-mean are evaluated for a fair comparison. The outcomes suggest that RUSBCHA is an alternative to the BCHA approach. Also, for several cases, performance improvements are observed for RUSBCHA since the data are imbalanced.

Sensitivity versus selectivity in entanglement detection via collective witnesses

In this paper, we introduce a supervised learning technique that harnesses artificial neural networks, along with the outcomes of collective entanglement measurements, to estimate the negativity of quantum states in two-qubit and qubit-qutrit systems. The resulting deep-learned collective entanglement witnesses offer the unique capability of continuous sensitivity and selectivity tuning. This instrument enables us to explore the tradeoff between sensitivity and selectivity in entanglement detection, a dimension not accessible to previously employed analytical witnesses. In particular, we demonstrate that there are experimentally cost-effective methods (in terms of the number of measurements) where sensitivity can be significantly improved at a slight expense of the selectivity of entanglement detection. This chosen approach is also favored due to its high generality and potential for superior performance compared to other types of entanglement witnesses. Our findings may pave the way for the development of more efficient and accurate entanglement detection methods in complex quantum systems, especially when considering realistic experimental imperfections. Published by the American Physical Society 2024

Entanglement and Bell inequalities with boosted tt¯

The Large Hadron Collider provides a unique opportunity to study quantum entanglement and violation of Bell inequalities at the highest energy available today. In this paper, we will investigate these quantum correlations with top quark pair production, which represents a system of two-qubits. The semileptonic top pair channel has a factor of 6 increase in statistics and easier reconstruction with respect to the dileptonic channel. Although measuring the spin polarization of the hadronic top quark is known to be challenging, our study indicates that it is feasible to reconstruct the spin density matrix of the two-qubit system using an optimal hadronic polarimeter. This is achieved with the aid of jet substructure techniques and NN-inspired reconstruction methods, which improve the mapping between subjets and quarks. We find that entanglement can already be observed at more than the 5σ level with existing data, and violation of Bell inequalities may be probed above the 4σ level at the HL-LHC with 3 ab−1 of data. Published by the American Physical Society 2024

Real-time parameter estimation for two-qubit systems based on hybrid control

Real-time parameter estimation for two-qubit systems based on hybrid control

Dynamics of quantum coherence and non-classical correlations between non-interacting two 2-level atoms in thermal baths

This paper delves into the exploration of quantum resources within a two-qubit system composed of two 2-level atoms connected to distinct thermal baths. Various quantifiers are employed to evaluate different aspects of the system’s quantum characteristics. Specifically, the [Formula: see text]-norm and relative entropy of coherence ([Formula: see text] and [Formula: see text]) are utilized to gauge quantum coherence, while local quantum Fisher information (LQFI) is used to quantify non-classical correlations within the system. The findings suggest that the amount of quantum correlations and coherence decline as the spontaneous emission rate [Formula: see text] and the mean thermal photon number n increase. However, it is observed that manipulating parameters defining the initial state of the two-level atoms system can enhance non-classical correlations and quantum coherence between the two atoms. Additionally, it is noted that these three key metrics entirely vanish in the asymptotic limit of time. Our research underscores the importance of precisely adjusting the parameters of the initial system state, which is prepared in an extended Werner-like state (EWL), to protect quantum resources shared between the two atoms from environmental influences.

Thermal entanglement versus quantum-memory-assisted entropic uncertainty relation in a two-qubit Heisenberg system with Herring–Flicker coupling under Dzyaloshinsky–Moriya interaction

Thermal entanglement versus quantum-memory-assisted entropic uncertainty relation in a two-qubit Heisenberg system with Herring–Flicker coupling under Dzyaloshinsky–Moriya interaction