Quantum Systems Research Articles

Nonadiabatic Field with Triangle Window Functions on Quantum Phase Space.

Recent progress on the constraint coordinate-momentum phase space (CPS) formulation of finite-state quantum systems has revealed that the triangle window function approach is an isomorphic representation of the exact population-population correlation function of the two-state system. We use the triangle window (TW) function and the CPS mapping kernel element to formulate a novel useful representation of discrete electronic degrees of freedom (DOFs). When it is employed with nonadiabatic field (NaF) dynamics, a new variant of the NaF approach (i.e., NaF-TW) is proposed. The NaF-TW expression of the population of any adiabatic state is always positive semidefinite. Extensive benchmark tests of model systems in both the condensed phase and gas phase demonstrate that the NaF-TW approach is able to faithfully capture the dynamical interplay between electronic and nuclear DOFs in a broad region, including where the states remain coupled all the time, as well as where the bifurcation characteristic of nuclear motion is important.

Notes on time entanglement and pseudo-entropy

Following arXiv:2210.12963 [hep-th], we investigate aspects of the time evolution operator regarded as a density operator and associated entanglement-like structures in various quantum systems. These involve timelike separations and generically lead to complex-valued entropy, although there are interesting real subfamilies. There are many parallels and close relations with reduced transition matrices and pseudo-entropy, which we discuss and clarify. For instance, a related quantity involves the time evolution operator along with a projection onto some initial state, which amounts to analysing pseudo-entropy for the initial state and its time-evolved final state.

Coherence-mixedness trade-offs

Abstract Quantum coherence constitutes a foundational characteristic of quantum mechanics and is integral to emerging quantum resource theories. However, quantum coherence is severely restricted by environmental noise in general quantum processing, indicated by the loss of information of a quantum system. Such processing can be described by the trade-offs between the coherence and the mixedness. Based on the l2 norm coherence, conditional von Neumann entropy and Wigner-Yanase skew information, we derive basis-independent constraints on the attainable quantum coherence imposed by the mixedness of a quantum state, which generalize the prior basis-dependent relations, provide fundamental insights into the latent coherence resources present within arbitrary quantum systems that undergo decoherence and quantify the inherent limits on extractable coherence imposed by environmental noise.

Understanding dynamical phase transitions in a spinor Bose-Einstein condensate via quantum and semiclassical analyses

Abstract Phase transitions in nonequilibrium dynamics of many body quantum systems, 
known as dynamical phase transitions (DPTs), play an important role for understanding
various dynamical phenomena observed in different branches of physics.
In general, there are two types of DPTs, the first one is characterized by 
distinct evolutionary behaviors of a physical observable, while the second one is marked by 
the vanishing overlap between the time-evolved and initial states. 
Here, we focus on exploring such DPTs from both quantum and semiclassical perspectives 
in a spinor Bose-Einstein condensate (BEC), an ideal platform for
investigating nonequilibrium dynamics.
Utilizing the sudden quench process, we demonstrate that the system exhibits 
both types of DPTs as the control parameter is quenched through
the critical value, referring to as the critical quenching. 
We show analytically how to determine the critical quenching via
the semiclassical approach and carry out a detailed examination of both semiclassical 
and quantum signatures of DPTs. 
In particular, we reveal that the occurrence of DPTs is triggered by
the separatrix in the underlying semiclassical system.
Our findings offer deeper insights into the properties of DPTs and verify the usefulness 
of semiclassical analysis for studying DPTs in quantum systems 
with well-defined semiclassical limit. 

Quantum state engineering by steering in the presence of errors

Quantum state engineering plays a vital role in various applications in the field of quantum information. Different strategies, including drive-and-dissipation, adiabatic cooling, and measurement-based steering, have been proposed for state generation and manipulation, each with its upsides and downsides. Here, we address a class of measurement-based state engineering protocols where a sequence of generalized measurements is employed to steer a quantum system toward a desired (pure or mixed) target state. Previously studied measurement-based protocols relied on idealized procedures and avoided exploration of the effects of various errors stemming from imperfections of experimental realizations and external noise. We employ the quantum trajectory formalism to provide a detailed analysis of the robustness of these steering protocols against multiple classes of errors. We study a set of realistic errors that can be classified as dynamic or static, depending on whether they remain unchanged while running the protocol. More specifically, we investigate the impact of the erroneous choice of detector-system coupling, erroneous re-initialization of the detector state following a measurement step, fluctuating steering directions, and environmentally induced errors in the detector-system interaction. We show that the protocol remains fully robust against the erroneous choice of detector-system coupling parameters and presents reasonable robustness against other types of errors. Our analysis employs various quantifiers such as fidelity, trace distance, and linear entropy to characterize the protocol's robustness and provide analytical results for these quantifiers against various errors. We introduce averaging hierarchies of stochastic equations describing individual quantum trajectories associated with detector readouts. Subsequently, we demonstrate the commutation between the classical expectation value and the time-ordering operator of the exponential of a Hamiltonian with multiplicative white noise, as well as the commutation of the expectation value and the partial trace with respect to detector outcomes. Our ideas are implemented and demonstrated for a specific class of steering platforms, addressing a single qubit. Published by the American Physical Society 2024

Wideband and low-spurious optical waveform generator for optically addressable quantum systems manipulation and control

Wideband and low-spurious optical waveform generator for optically addressable quantum systems manipulation and control

Entanglement Assisted Probe of the Non-Markovian to Markovian Transition in Open Quantum System Dynamics

Entanglement Assisted Probe of the Non-Markovian to Markovian Transition in Open Quantum System Dynamics

Unveiling the interplay of Mollow physics and perturbed free induction decay by nonlinear optical signals of a dynamically driven two-level system

Nonlinear optical signals in optically driven quantum systems can reveal coherences and thereby open up the possibility for manipulation of quantum states. While the limiting cases of ultrafast and continuous-wave excitation have been extensively studied, the time dynamics of finite pulses bear interesting phenomena. In this paper, we explore the nonlinear optical probe signals of a two-level system excited with a laser pulse of finite duration. In addition to the prominent Mollow peaks, the probe spectra feature several smaller peaks for certain time delays. Similar features have been recently observed for resonance fluorescence signals [K. Boos , ]. We discuss that the emergent phenomena can be explained by a combination of Mollow triplet physics and perturbed free induction decay effects, providing an insightful understanding of the underlying physics. Published by the American Physical Society 2024

Coherent optical coupling to surface acoustic wave devices

Surface acoustic waves (SAW) and associated devices are ideal for sensing, metrology, and hybrid quantum devices. While the advances demonstrated to date are largely based on electromechanical coupling, a robust and customizable coherent optical coupling would unlock mature and powerful cavity optomechanical control techniques and an efficient optical pathway for long-distance quantum links. Here we demonstrate direct and robust coherent optical coupling to Gaussian surface acoustic wave cavities with small mode volumes and high quality factors (>105 measured here) through a Brillouin-like optomechanical interaction. High-frequency SAW cavities designed with curved metallic acoustic reflectors deposited on crystalline substrates are efficiently optically accessed along piezo-active directions, as well as non-piezo-active (electromechanically inaccessible) directions. The precise optical technique uniquely enables controlled analysis of dissipation mechanisms as well as detailed transverse spatial mode spectroscopy. These advantages combined with simple fabrication, large power handling, and strong coupling to quantum systems make SAW optomechanical platforms particularly attractive for sensing, material science, and hybrid quantum systems.

Control of Qubit Dynamics Using Reinforcement Learning

The progress in machine learning during the last decade has had a considerable impact on many areas of science and technology, including quantum technology. This work explores the application of reinforcement learning (RL) methods to the quantum control problem of state transfer in a single qubit. The goal is to create an RL agent that learns an optimal policy and thus discovers optimal pulses to control the qubit. The most crucial step is to mathematically formulate the problem of interest as a Markov decision process (MDP). This enables the use of RL algorithms to solve the quantum control problem. Deep learning and the use of deep neural networks provide the freedom to employ continuous action and state spaces, offering the expressivity and generalization of the process. This flexibility helps to formulate the quantum state transfer problem as an MDP in several different ways. All the developed methodologies are applied to the fundamental problem of population inversion in a qubit. In most cases, the derived optimal pulses achieve fidelity equal to or higher than 0.9999, as required by quantum computing applications. The present methods can be easily extended to quantum systems with more energy levels and may be used for the efficient control of collections of qubits and to counteract the effect of noise, which are important topics for quantum sensing applications.

Fidelity susceptibility probes of dynamical quantum criticality

Fidelity susceptibility is a quantum information-based approach that has been an effective tool for detecting and characterizing quantum phase transitions in an equilibrium setting. Motivated by the usefulness of the static counterpart, we propose that it can serve as a versatile tool to identify dynamical quantum phase transitions. Further, we develop linear-scale simulation methods for dynamical fidelity susceptibility calculations, which are based on the Chebyshev polynomial-expansion approach. We study the Aubry–André model as a benchmark for the validation of the computational technique. Numerical simulations show nonanalytic behaviors of the fidelity susceptibility in the time domain, signaling the existence of dynamical quantum phase transitions triggered by the incommensurate potential modulation of quantum quench systems. In addition, we find an excellent scaling collapse of the data onto a single curve in the limiting quench processes, which leads to a single-parameter scaling in the fidelity susceptibility. The feasibility of experimental measurement of the fidelity susceptibility opens up a new avenue toward an understanding of the nonequilibrium transport of quantum systems.

Analog quantum simulation of partial differential equations

Abstract Quantum simulators were originally proposed for simulating one partial differential equation in particular -- Schrodinger's equation. Can quantum simulators also efficiently simulate other partial differential equations? While most computational methods for partial differential equations -- both classical and quantum -- are digital (they must be discretised first), partial differential equations have continuous degrees of freedom. This suggests that an analog representation can be more natural. While digital quantum degrees of freedom are usually described by qubits, the analog or continuous quantum degrees of freedom can be captured by qumodes. Based on a method called Schrodingerisation, we show how to directly map D-dimensional linear partial differential equations onto a (D+1)-qumode quantum system where analog or continuous-variable Hamiltonian simulation on D+1 qumodes can be used. This very simple methodology does not require one to discretise partial differential equations first, and it is not only applicable to linear partial differential equations but also to some nonlinear partial differential equations and systems of nonlinear ordinary differential equations. We show some examples using this method, including the Liouville equation, heat equation, Fokker-Planck equation, Black-Scholes equations, wave equation and Maxwell's equations. We also devise new protocols for linear partial differential equations with random coefficients, important in uncertainty quantification, where it is clear how the analog or continuous-variable framework is most natural. This also raises the possibility that some partial differential equations may be simulated directly on analog quantum systems by using Hamiltonians natural for those quantum systems.

Relating interfacial Rossby wave interaction in shear flows with Feynman's two-state coupled quantum system model for the Josephson junction

Relating interfacial Rossby wave interaction in shear flows with Feynman's two-state coupled quantum system model for the Josephson junction

Quantum sensing with tunable superconducting qubits: optimization and speed-up

Abstract Sensing and metrology are crucial in both fundamental science and practical applications. They meet the constant demand for precise data, enabling more dependable assessments of theoretical models’ validity. Sensors, now a common feature in many fields, play a vital role in applications like gravity imaging, geology, navigation, security, timekeeping, spectroscopy, chemistry, magnetometry, healthcare, and medicine. The advancements in quantum technologies have sparked interest in employing quantum systems as sensors, offering enhanced capabilities and new possibilities. This article describes the optimization of the quantum-enhanced sensing
of magnetic fluxes with a Kitaev phase estimation algorithm based on frequency tunable transmon qubits. It provides the optimal flux biasing point for sensors with different qubit transition frequencies and gives an estimation of decoherence rates and achievable sensitivity. The use of 2- and 3-qubit entangled states are compared in simulation with the single-qubit case. The flux sensing accuracy reaches 10-8·Φ0 and scales inversely with time, which proves the speed-up of sensing with high ultimate accuracy.

Beyond Dynamics: Learning to Discover Conservation Principles

Abstract The discovery of conservation principles is crucial for understanding the fundamental behavior of both classical and quantum physical systems across numerous domains. This paper introduces an innovative method that merges representation learning and topological analysis to explore the topology of conservation law spaces. Notably, the robustness of our approach to noise makes it suitable for complex experimental setups and its aptitude extends to the analysis of quantum systems, as successfully demonstrated in our paper. We exemplify our method’s potential to unearth previously unknown conservation principles and endorse interdisciplinary research through a variety of physical simulations. In conclusion, this work emphasizes the significance of data-driven techniques in deepening our comprehension of the principles governing classical and quantum physical systems.

Two-dimensional symmetry-protected topological phases and transitions in open quantum systems

Two-dimensional symmetry-protected topological phases and transitions in open quantum systems

Enhancement of vibrationally assisted energy transfer by proximity to exceptional points, probed by fluorescence-detected vibrational spectroscopy

Emulation of energy transfer processes in natural systems on quantum platforms can further our understanding of complex dynamics in nature. One notable example is the demonstration of vibrationally assisted energy transfer (VAET) on a trapped-ion quantum emulator, which offers insights for the energetics of light harvesting. In this work, we expand the study of VAET simulation with trapped ions to a non-Hermitian quantum system comprising a PT-symmetric chromophore dimer weakly coupled to a vibrational mode. We first characterize exceptional points (EPs) and non-Hermitian features of the excitation energy transfer processes in the absence of the vibration, finding a degenerate pair of second-order EPs. Exploring the non-Hermitian dynamics of the whole system including vibrations, we find that energy transfer accompanied by absorption of phonons from a vibrational mode can be significantly enhanced near such a degenerate EP. Our calculations reveal a unique spectral feature accompanying the coalescing of eigenstates and eigenenergies that provides a unique approach to probe the degenerate EP by fluorescence-detected vibrational spectroscopy. Enhancement of the VAET process near the EP is found to be due to maximal favorability of phonon absorption at the degenerate EP, enabling multiple simultaneous excitations. Our work on improving VAET processes in non-Hermitian quantum systems paves the way for leveraging non-Hermiticity in quantum dynamics related to excitation energy transfer. Published by the American Physical Society 2024

Physics-informed neural networks for an optimal counterdiabatic quantum computation

A novel methodology that leverages physics-informed neural networks to optimize quantum circuits in systems with NQ qubits by addressing the counterdiabatic (CD) protocol is introduced. The primary purpose is to employ physics-inspired deep learning techniques for accurately modeling the time evolution of various physical observables within quantum systems. To achieve this, we integrate essential physical information into an underlying neural network to effectively tackle the problem. Specifically, the imposition of the solution to meet the principle of least action, along with the hermiticity condition on all physical observables, among others, ensuring the acquisition of appropriate CD terms based on underlying physics. This approach provides a reliable alternative to previous methodologies relying on classical numerical approximations, eliminating their inherent constraints. The proposed method offers a versatile framework for optimizing physical observables relevant to the problem, such as the scheduling function, gauge potential, temporal evolution of energy levels, among others. This methodology has been successfully applied to 2-qubit representing H2 molecule using the STO-3G basis, demonstrating the derivation of a desirable decomposition for non-adiabatic terms through a linear combination of Pauli operators. This attribute confers significant advantages for practical implementation within quantum computing algorithms.

Sketching phase diagrams using low-depth variational quantum algorithms

Abstract Mapping out phase diagrams of quantum systems using classical simulations can be challenging or intractable due to the computational resources required to simulate even small quantum systems far away from the thermodynamic limit. We investigate using quantum computers and the Variational Quantum Eigensolver (VQE) for this task. In contrast to the task of preparing the exact ground state using VQE, sketching phase diagrams might require less quantum resources and accuracy, because low fidelity approximations to the ground state may be enough to correctly identify different phases. We used classical numerical simulations of low-depth VQE circuits to compute order parameters for four well-studied spin and fermion models which represent a mix of 1D and 2D, and exactly-solvable and classically hard systems. We find that it is possible to predict the location of phase transitions up to reasonable accuracy using states produced by VQE even when their overlap with the true ground state is small. Further, we introduce a model-agnostic predictor of phase transitions based on the speed with which the VQE energy improves with respect to the circuit depth, and find that in some cases this is also able to predict phase transitions.

Non-Hermitian Quantum Rényi Entropy Dynamics in Anyonic-PT Symmetric Systems

We reveal the continuous change of information dynamics patterns in anyonic-PT symmetric systems that originates from the continuity of anyonic-PT symmetry. We find there are three information dynamics patterns for anyonic-PT symmetric systems: damped oscillations with an overall decrease (increase) and asymptotically stable damped oscillations, which are three-fold degenerate and are distorted using the Hermitian quantum Rényi entropy or distinguishability. It is the normalization of the non-unitary evolved density matrix that causes the degeneracy and distortion. We give a justification for non-Hermitian quantum Rényi entropy being negative. By exploring the mathematics and physical meaning of the negative entropy in open quantum systems, we connect negative non-Hermitian quantum Rényi entropy and negative quantum conditional entropy, paving the way to rigorously investigate negative entropy in open quantum systems.