arXiv subjects

Sabre Kais

Publications and source records attributed to Sabre Kais.

At least 55 records · Page 3Linked to original sources

arXiv2024

Time resolved quantum tomography in molecular spectroscopy by the Maximal Entropy Approach

Attosecond science offers unprecedented precision in probing the initial moments of chemical reactions, revealing the dynamics of molecular electrons that shape reaction pathways. A fundamental question emerges: what role, if any, do quantum coherences between molecular electron states play in photochemical reactions? Answering this question necessitates quantum tomography: the determination of the electronic density matrix from experimental data, where the off-diagonal elements represent these coherences. The Maximal Entropy (MaxEnt) based Quantum State Tomography (QST) approach offers unique advantages in studying molecular dynamics, particularly with partial tomographic data. Here, we explore the application of MaxEnt-based QST on photoexcited ammonia, necessitating the operator form of observables specific to the performed measurements. We present two methodologies for constructing these operators: one leveraging Molecular Angular Distribution Moments (MADMs) which accurately capture the orientation-dependent vibronic dynamics of molecules; and another utilizing Angular Momentum Coherence Operators to construct measurement operators for the full rovibronic density matrix in the symmetric top basis. A key revelation of our study is the direct link between Lagrange multipliers in the MaxEnt formalism and the unique set of MADMs. Furthermore, we achieve a groundbreaking milestone by constructing, for the first time, the entanglement entropy of the electronic subsystem: a metric that was previously inaccessible. The entropy vividly reveals and quantifies the effects of coupling between the excited electron and nuclear degrees of freedom. Consequently, our findings open new avenues for research in ultrafast molecular spectroscopy within the broader domain of quantum information science.

physics.chem-ph↗

arXiv2024

Non-native Quantum Generative Optimization with Adversarial Autoencoders

Large-scale optimization problems are prevalent in several fields, including engineering, finance, and logistics. However, most optimization problems cannot be efficiently encoded onto a physical system because the existing quantum samplers have too few qubits. Another typical limiting factor is that the optimization constraints are not compatible with the native cost Hamiltonian. This work presents a new approach to address these challenges. We introduce the adversarial quantum autoencoder model (AQAM) that can be used to map large-scale optimization problems onto existing quantum samplers while simultaneously optimizing the problem through latent quantum-enhanced Boltzmann sampling. We demonstrate the AQAM on a neutral atom sampler, and showcase the model by optimizing 64px by 64px unit cells that represent a broad-angle filter metasurface applicable to improving the coherence of neutral atom devices. Using 12-atom simulations, we demonstrate that the AQAM achieves a lower Renyi divergence and a larger spectral gap when compared to classical Markov Chain Monte Carlo samplers. Our work paves the way to more efficient mapping of conventional optimization problems into existing quantum samplers.

quant-ph↗

arXiv2024

Simulating Chemistry on Bosonic Quantum Devices

Bosonic quantum devices offer a novel approach to realize quantum computations, where the quantum two-level system (qubit) is replaced with the quantum (an)harmonic oscillator (qumode) as the fundamental building block of the quantum simulator. The simulation of chemical structure and dynamics can then be achieved by representing or mapping the system Hamiltonians in terms of bosonic operators. In this perspective, we review recent progress and future potential of using bosonic quantum devices for addressing a wide range of challenging chemical problems, including the calculation of molecular vibronic spectra, the simulation of gas-phase and solution-phase adiabatic and nonadiabatic chemical dynamics, the efficient solution of molecular graph theory problems, and the calculations of electronic structure.

quant-ph↗

arXiv2024

Experimental test of generalized multipartite entropic uncertainty relations

Entropic uncertainty relation (EUR) formulates the restriction of the inherent uncertainty of quantum mechanics from the information-theoretic perspective. A tighter lower bound for uncertainty relations can provide information-theoretic security to quantum communication protocols. Recently, a generalized EUR (GEUR) for the measurement of multiple observables in arbitrary many-body systems has been formulated. Here, we experimentally test this GEUR using a four-photon entangled state with a controllable decoherence channel and show that for the tripartite scenario, the GEUR improves the entropic bound from Renes--Boileau's famous results. As an application, we further demonstrate an improvement of the secure key rate in quantum key distribution from the GEUR. Our results extend the test of EURs into multipartite regimes and may find applications in practical quantum cryptography tasks.

quant-ph↗

arXiv2024

Quantum Algorithms and Applications for Open Quantum Systems

Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction of static and dynamic molecular properties. In recent years, quantum algorithms have been leveraged for the computation of open quantum systems as the predicted quantum advantage of quantum devices over classical ones may allow previously inaccessible applications. Accomplishing this goal will require input and expertise from different research perspectives, as well as the training of a diverse quantum workforce, making a compilation of current quantum methods for treating open quantum systems both useful and timely. In this Review, we first provide a succinct summary of the fundamental theory of open quantum systems and then delve into a discussion on recent quantum algorithms. We conclude with a discussion of pertinent applications, demonstrating the applicability of this field to realistic chemical, biological, and material systems.

quant-ph↗

arXiv2024

Simulation of Chemical Reactions on a Quantum Computer

Studying chemical reactions, particularly in the gas phase, relies heavily on computing scattering matrix elements. These elements are essential for characterizing molecular reactions and accurately determining reaction probabilities. However, the intricate nature of quantum interactions poses challenges, necessitating the use of advanced mathematical models and computational approaches to tackle the inherent complexities. In this study, we develop and apply a quantum algorithm for the calculation of scattering matrix elements. In our approach, we employ the time-dependent method based on the Möller operator formulation where the S-matrix element between the respective reactant and product channels is determined through the time correlation function of the reactant and product Möller wavepackets. We successfully apply our quantum algorithm to calculate scattering matrix elements for 1D semi-infinite square well potential and on the co-linear hydrogen exchange reaction. As we navigate the complexities of quantum interactions, this quantum algorithm is general and emerges as a promising avenue, shedding light on new possibilities for simulating chemical reactions on quantum computers.

quant-ph↗

arXiv2024

Entropy corrected geometric Brownian motion

The geometric Brownian motion (GBM) is widely employed for modeling stochastic processes, yet its solutions are characterized by the log-normal distribution. This comprises predictive capabilities of GBM mainly in terms of forecasting applications. Here, entropy corrections to GBM are proposed to go beyond log-normality restrictions and better account for intricacies of real systems. It is shown that GBM solutions can be effectively refined by arguing that entropy is reduced when deterministic content of considered data increases. Notable improvements over conventional GBM are observed for several cases of non-log-normal distributions, ranging from a dice roll experiment to real world data.

physics.data-an↗

arXiv2024

Designing variational ansatz for quantum-enabled simulation of non-unitary dynamical evolution -- an excursion into Dicke supperradiance

Adaptive Variational Quantum Dynamics (AVQD) algorithms offer a promising approach to providing quantum-enabled solutions for systems treated within the purview of open quantum dynamical evolution. In this study, we employ the unrestricted vectorization variant of AVQD to simulate and benchmark various non-unitarily evolving systems. We exemplify how construction of an expressible ansatz unitary and the associated operator pool can be implemented to analyze examples such as the Fenna Matthews Olson complex (FMO) and even the permutational invariant Dicke model of quantum optics. We furthermore show an efficient decomposition scheme for the ansatz used, which can extend its applications to a wide range of other open quantum system scenarios in near future. In all cases the results obtained are in excellent agreement with exact numerical computations which bolsters the effectiveness of this technique. Our successful demonstrations pave the way for utilizing this adaptive variational technique to study complex systems in chemistry and physics, like light harvesting devices, thermal, and opto mechanical switches, to name a few.

quant-ph↗

arXiv2024

The qubit information logic theory for understanding multi-qubit entanglement and designing exotic entangled states

We develop a "qubit information logic" (QIL) theory that uses the "qubit information equation" (QIE) and logic to describe the correlation behaviors of multi-qubit entanglement. Introducing the "global information status" and "local information availability", the QIL gives an alternative and natural interpretation of the "spooky action" and the quantum no-communication theorem. Compared to the conventional entropy-based entanglement theories, the QIL directly describes the correlation of each possible pair of qubits and how the correlation changes when other qubits are measured. This makes the QIL more advantageous in describing the correlation properties of multi-qubit entanglement, which is illustrated by studying the dormant entanglement phenomenon. The QIL theory's usefulness is further demonstrated by designing an exotic quantum state where two qubits can be entangled but not correlated in any arbitrary basis. Overall the QIL provides an alternative and intuitive understanding of multi-qubit entanglement that is, compared to the conventional theories, directly focused on the correlation behaviors between qubits and thus more suitable for designing exotic quantum states that may be used in quantum algorithms.

quant-ph↗

arXiv2024

Defect-induced localization of information in 1D Kitaev model

We discuss one-dimensional(1D) spin compass model or 1D Kitaev model in the presence of local bond defects. Three types of local disorders concerning both bond-nature and bond-strength that occur on kitaev materials have been investigated. Using exact diagonalization, two-point spin-spin structural correlations and four-point Out-of-Time-Order Correlators(OTOC) have been computed for the defective spin chains. The proposed quantities give signatures of these defects in terms of their responses to location and strength of defects. A key observation is that the information in the OTOC space gets trapped at the defect site giving rise to the phenomena of localization of information thus making these correlators a suitable diagnostic tool to detect and characterize these defects.

cond-mat.str-el↗

arXiv2024

Random Projection using Random Quantum Circuits

The random sampling task performed by Google's Sycamore processor gave us a glimpse of the "Quantum Supremacy era". This has definitely shed some spotlight on the power of random quantum circuits in this abstract task of sampling outputs from the (pseudo-) random circuits. In this manuscript, we explore a practical near-term use of local random quantum circuits in dimensional reduction of large low-rank data sets. We make use of the well-studied dimensionality reduction technique called the random projection method. This method has been extensively used in various applications such as image processing, logistic regression, entropy computation of low-rank matrices, etc. We prove that the matrix representations of local random quantum circuits with sufficiently shorter depths ($\sim O(n)$) serve as good candidates for random projection. We demonstrate numerically that their projection abilities are not far off from the computationally expensive classical principal components analysis on MNIST and CIFAR-100 image data sets. We also benchmark the performance of quantum random projection against the commonly used classical random projection in the tasks of dimensionality reduction of image datasets and computing Von Neumann entropies of large low-rank density matrices. And finally using variational quantum singular value decomposition, we demonstrate a near-term implementation of extracting the singular vectors with dominant singular values after quantum random projecting a large low-rank matrix to lower dimensions. All such numerical experiments unequivocally demonstrate the ability of local random circuits to randomize a large Hilbert space at sufficiently shorter depths with robust retention of properties of large datasets in reduced dimensions.

quant-ph↗

arXiv2023

Physics inspired quantum simulation of resonating valence bond states -- a prototypical template for a spin-liquid ground state

Spin-liquids -- an emergent, exotic collective phase of matter -- have garnered enormous attention in recent years. While experimentally, many prospective candidates have been proposed and realized, theoretically modeling real materials that display such behavior may pose serious challenges due to the inherently high correlation content of emergent phases. Over the last few decades, the second-quantum revolution has been the harbinger of a novel computational paradigm capable of initiating a foundational evolution in computational physics. In this report, we strive to use the power of the latter to study a prototypical model -- a spin-$\frac{1}{2}$-unit cell of a Kagome anti-ferromagnet. Extended lattices of such unit cells are known to possess a magnetically disordered spin-liquid ground state. We employ robust classical numerical techniques like Density-Matrix Renormalization Group (DMRG) to identify the nature of the ground state through a matrix-product state (MPS) formulation. We subsequently use the gained insight to construct an auxillary hamiltonian with reduced measurables and also design an ansatz that is modular and gate efficient. With robust error-mitigation strategies, we are able to demonstrate that the said ansatz is capable of accurately representing the target ground state even on a real IBMQ backend within $1\%$ accuracy in energy. Since the protocol is linearly scaling $O(n)$ in the number of unit cells, gate requirements, and the number of measurements, it is straightforwardly extendable to larger Kagome lattices which can pave the way for efficient construction of spin-liquid ground states on a quantum device.

cond-mat.str-el↗

arXiv2023

Simulating Open Quantum System Dynamics on NISQ Computers with Generalized Quantum Master Equations

We present a quantum algorithm based on the Generalized Quantum Master Equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the Lindblad equation, which assumes weak system-bath coupling and Markovity, by providing a rigorous derivation of the equations of motion for any subset of elements of the reduced density matrix. The memory kernel resulting from the effect of the remaining degrees of freedom is used as input to calculate the corresponding non-unitary propagator. We demonstrate how the Sz.-Nagy dilation theorem can be employed to transform the non-unitary propagator into a unitary one in a higher-dimensional Hilbert space, which can then be implemented on quantum circuits of NISQ computers. We validate our quantum algorithm as applied to the spin-boson benchmark model by analyzing the impact of the quantum circuit depth on the accuracy of the results when the subset is limited to the diagonal elements of the reduced density matrix. Our findings demonstrate that our approach yields reliable results on NISQ IBM computers.

quant-ph↗

arXiv2023

Møller-Plesset Perturbation Theory Calculations on Quantum Devices

Accurate electronic structure calculations might be one of the most anticipated applications of quantum computing.The recent landscape of quantum simulations within the Hartree-Fock approximation raises the prospect of substantial theory and hardware developments in this context.Here we propose a general quantum circuit for Møller-Plesset perturbation theory (MPPT) calculations, which is a popular and powerful post-Hartree-Fock method widly harnessed in solving electronic structure problems. MPPT improves on the Hartree-Fock method by including electron correlation effects wherewith Rayleigh-Schrodinger perturbation theory. Given the Hartree-Fock results, the proposed circuit is designed to estimate the second order energy corrections with MPPT methods. In addition to demonstration of the theoretical scheme, the proposed circuit is further employed to calculate the second order energy correction for the ground state of Helium atom, and the total error rate is around 2.3%. Experiments on IBM 27-qubit quantum computers express the feasibility on near term quantum devices, and the capability to estimate the second order energy correction accurately. In imitation of the classical MPPT, our approach is non-heuristic, guaranteeing that all parameters in the circuit are directly determined by the given Hartree-Fock results. Moreover, the proposed circuit shows a potential quantum speedup comparing to the traditional MPPT calculations. Our work paves the way forward the implementation of more intricate post-Hartree-Fock methods on quantum hardware, enriching the toolkit solving electronic structure problems on quantum computing platforms.

quant-ph↗

arXiv2023

Dormant entanglement that can be activated or destroyed by the basis choice of measurements on an external system

We propose a new form of entanglement called the dormant entanglement that can be activated or destroyed by the basis choice of measurements on an external system. The dormant entanglement without activation cannot be used as a quantum communication resource and has reduced correlation as compared to the Bell states. A particular form of the dormant entanglement is so weak that, without activation, no correlation in any basis can be observed between the entangled qubits. The dormant entanglement showcases a unique quantum behavior that the physical description of a local system remains incomplete until the information on all external systems entangled with the local system becomes available. For a potential application, we propose an n-party collective quantum communication channel that allows any 2 out of the n parties to activate an entanglement pair with the complete consensus of all other parties.

quant-ph↗

arXiv2023

Mapping Molecular Hamiltonians into Hamiltonians of Modular cQED Processors

We introduce a general method based on the operators of the Dyson-Masleev transformation to map the Hamiltonian of an arbitrary model system into the Hamiltonian of a circuit Quantum Electrodynamics (cQED) processor. Furthermore, we introduce a modular approach to program a cQED processor with components corresponding to the mapping Hamiltonian. The method is illustrated as applied to quantum dynamics simulations of the Fenna-Matthews-Olson (FMO) complex and the spin-boson model of charge transfer. Beyond applications to molecular Hamiltonians, the mapping provides a general approach to implement any unitary operator in terms of a sequence of unitary transformations corresponding to powers of creation and annihilation operators of a single bosonic mode in a cQED processor.

quant-ph↗

arXiv2023

Cutoff phenomenon and entropic uncertainty for random quantum circuits

How fast a state of a system converges to a stationary state is one of the fundamental questions in science. Some Markov chains and random walks on finite groups are known to exhibit the non-asymptotic convergence to a stationary distribution, called the cutoff phenomenon. Here, we examine how quickly a random quantum circuit could transform a quantum state to a Haar-measure random quantum state. We find that random quantum states, as stationary states of random walks on a unitary group, are invariant under the quantum Fourier transform. Thus the entropic uncertainty of random quantum states has balanced Shannon entropies for the computational bases and the quantum Fourier transform bases. By calculating the Shannon entropy for random quantum states and the Wasserstein distances for the eigenvalues of random quantum circuits, we show that the cutoff phenomenon occurs for the random quantum circuit. It is also demonstrated that the Dyson-Brownian motion for the eigenvalues of a random unitary matrix as a continuous random walk exhibits the cutoff phenomenon. The results here imply that random quantum states could be generated with shallow random circuits.

quant-ph↗

arXiv2023

Towards Perturbation Theory Methods on a Quantum Computer

Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which evoked an explosion of applications with the blooming of atomic and subatomic physics. Even though PT is well-used today, techniques for PT are significantly lacking in quantum computing. Here we present a quantum circuit estimating both the energy and eigenstates corrections with PT methods, which we claim is far superior to the classical version when estimating the second order energy correction. Our approach is further demonstrated with an application on the extended Hubbard model, where numerical simulation based on qiskit is also presented. Unlike the popular quantum variational circuit, there is no training or optimizing process in our circuit, and all parameters are derived from the unperturbed Hamiltonian. Our work offers a new approach to studying complex systems with quantum devices, which might shed light on the quantum implementation of the more intricate methods based on PT.

quant-ph↗