Dual Exponential Coupled Cluster Theory: Unitary Adaptation, Implementation in the Variational Quantum Eigensolver Framework and Pilot Applications

• URL: http://arxiv.org/abs/2207.05318v1
• Date: Tue, 12 Jul 2022 05:10:58 GMT
• Title: Dual Exponential Coupled Cluster Theory: Unitary Adaptation, Implementation in the Variational Quantum Eigensolver Framework and Pilot Applications
• Authors: Dipanjali Halder, V. S. Prasannaa, Rahul Maitra
• Abstract summary: We have developed a unitary variant of a double exponential coupled cluster theory. The method relies upon the nontrivial action of a unitary, containing a set of rank-two scattering operators. We have shown that all our schemes can perform uniformly well throughout the molecular potential energy surface.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we have developed a unitary variant of a double exponential coupled cluster theory, which is capable of mimicking the effects of connected excitations of arbitrarily high rank, using only rank-one and rank-two parametrization of the wavefunction ansatz. While its implementation in a classical computer necessitates the construction of an effective Hamiltonian which involves infinite number of terms with arbitrarily high many-body rank, the same can easily be implemented in the hybrid quantum-classical variational quantum eigensolver framework with a reasonably shallow quantum circuit. The method relies upon the nontrivial action of a unitary, containing a set of rank-two scattering operators, on entangled states generated via cluster operators. We have further introduced a number of variants of the ansatz with different degrees of expressibility by judiciously approximating the scattering operators. With a number of applications on strongly correlated molecules, we have shown that all our schemes can perform uniformly well throughout the molecular potential energy surface without significant additional implementation cost and quantum complexity over the unitary coupled cluster approach with single and double excitations.

Related papers

• Constructing Arbitrary Coherent Rearrangements in Optical Lattices [36.94429692322632]
  Coherent control of motional degrees of freedom of ultracold atoms in optical lattices offers a promising route towards programmable quantum dynamics with massive particles.<n>We propose and analyze a scheme for implementing coherent rearrangement of ultracold atoms, corresponding to arbitrary unitary transformations on single-particle motional states.
  arXiv  Detail & Related papers  (2026-03-04T15:57:12Z)
• Digitized Counterdiabatic Quantum Feature Extraction [35.670314643295036]
  We introduce a Hamiltonian-based quantum feature extraction method that generates complex features via the dynamics of $k$-local many-body spins Hamiltonians.<n>We assess the approach on high-dimensional, real-world datasets, including molecular toxicity classification and image recognition.<n>The results suggest that combining quantum and classical feature extraction can provide consistent improvements across diverse machine learning tasks.
  arXiv  Detail & Related papers  (2025-10-15T17:59:35Z)
• Path integral approach to quantum thermalization [39.25860941747971]
  We introduce a quasiclassical Green function approach describing the unitary yet irreversible dynamics of quantum systems.<n>We show that it is capable of describing a wide range of system classes and disorder models.<n>We present our formalism in a self-contained and pedagogical manner, aiming to provide a transferable toolbox for the first-principles description of many-body chaotic quantum systems.
  arXiv  Detail & Related papers  (2025-09-07T12:10:48Z)
• Speeding up quantum Markov processes through lifting [15.031583573428481]
  We generalize the concept of non-reversible lifts for diffusion reversible processes initiated by Eberle and Lorler (2024) to quantum Markov dynamics.<n>We prove that the $L2$ convergence rate of the lifted process is bounded above by the square root of the spectral gap of its overdamped dynamics.
  arXiv  Detail & Related papers  (2025-05-18T01:19:08Z)
• Realization of universal nonadiabatic holonomic quantum gates in trapped ion system [5.92470368943469]
  We set out from the simplest and most fundamental Jaynes-Cummings model of ion trap system to implement single-qubit logical operations.<n>We take advantage of the interaction of two ions with a pair of laser pulses to implement two-qubit logical operations.
  arXiv  Detail & Related papers  (2025-05-04T14:57:30Z)
• QAMA: Scalable Quantum Annealing Multi-Head Attention Operator for Deep Learning [48.12231190677108]
  Quantum Annealing Multi-Head Attention (QAMA) is proposed, a novel drop-in operator that reformulates attention as an energy-based Hamiltonian optimization problem.<n>In this framework, token interactions are encoded into binary quadratic terms, and quantum annealing is employed to search for low-energy configurations.<n> Empirically, evaluation on both natural language and vision benchmarks shows that, across tasks, accuracy deviates by at most 2.7 points from standard multi-head attention.
  arXiv  Detail & Related papers  (2025-04-15T11:29:09Z)
• Projective Quantum Eigensolver with Generalized Operators [0.0]
  We develop a methodology for determining the generalized operators in terms of a closed form residual equations in the PQE framework. With the application on several molecular systems, we have demonstrated our ansatz achieves similar accuracy to the (disentangled) UCC with singles, doubles and triples.
  arXiv  Detail & Related papers  (2024-10-21T15:40:22Z)
• Simulating continuous-space systems with quantum-classical wave functions [0.0]
  Non-relativistic interacting quantum many-body systems are naturally described in terms of continuous-space Hamiltonians. Current algorithms require discretization, which usually amounts to choosing a finite basis set, inevitably introducing errors. We propose an alternative, discretization-free approach that combines classical and quantum resources in a global variational ansatz.
  arXiv  Detail & Related papers  (2024-09-10T10:54:59Z)
• Entanglement of photonic modes from a continuously driven two-level system [34.50067763557076]
  We experimentally generate entangled photonic modes by continuously exciting a quantum emitter, a superconducting qubit, with a coherent drive. We show that entanglement is generated between modes extracted from the two sidebands of the resonance fluorescence spectrum. Our approach can be utilized to distribute entanglement at a high rate in various physical platforms.
  arXiv  Detail & Related papers  (2024-07-10T18:48:41Z)
• Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement [39.58317527488534]
  Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application. We analyse the generation of random states in PQCs under restrictions on the qubits connectivities. We place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement.
  arXiv  Detail & Related papers  (2024-05-03T17:32:55Z)
• Unitary Basis Transformations in Mixed Quantum-Classical Dynamics [0.0]
  A common approach to minimizing the cost of quantum computations is by transforming a quantum system into a basis that can be optimally truncated. Here, we derive classical equations of motion subjected to similar unitary transformations, and propose their integration into mixed quantum-classical dynamics. We demonstrate the potential of the resulting approach by means of surface hopping calculations of an electronic carrier scattering onto a single impurity in the presence of phonons.
  arXiv  Detail & Related papers  (2024-04-24T03:08:05Z)
• Towards Efficient Quantum Hybrid Diffusion Models [68.43405413443175]
  We propose a new methodology to design quantum hybrid diffusion models. We propose two possible hybridization schemes combining quantum computing's superior generalization with classical networks' modularity.
  arXiv  Detail & Related papers  (2024-02-25T16:57:51Z)
• Supersymmetric Quantum Mechanics of Hypergeometric-like Differential Operators [0.0]
  Systematic iterative algorithms of supersymmetric quantum mechanics (SUSYQM) type for solving the eigenequation of principal hypergeometric-like differential operator (HLDO) These algorithms provide a simple SUSYQM answer to the question regarding why there exist simultaneously a series of principal as well as associated eigenfunctions for the same HLDO. Due to their relatively high efficiency, algebraic elementariness and logical independence, the iterative SUSYQM algorithms developed in this paper could become the hopefuls for supplanting some traditional methods for solving the eigenvalue problems of principal HLDOs and their associated cousins.
  arXiv  Detail & Related papers  (2023-07-29T09:59:54Z)
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive [52.77024349608834]
  We present a self consistent field approach (SCF) within the Adaptive Derivative-Assembled Problem-Assembled Ansatz Variational Eigensolver (ADAPTVQE) This framework is used for efficient quantum simulations of chemical systems on nearterm quantum computers.
  arXiv  Detail & Related papers  (2022-12-21T23:15:17Z)
• Interaction of quantum systems with single pulses of quantized radiation [68.8204255655161]
  We describe the interaction of a propagating pulse of quantum radiation with a localized quantum system. By transformation to an appropriate picture, we identify the usual Jaynes-Cummings Hamiltonian between the scatterer and a superposition of the initial and final mode. The transformed master equation offers important insights into the system dynamics and it permits numerically efficient solutions.
  arXiv  Detail & Related papers  (2022-03-14T20:23:23Z)
• Entanglement catalysis for quantum states and noisy channels [41.94295877935867]
  We investigate properties of entanglement and its role for quantum communication. For transformations between bipartite pure states, we prove the existence of a universal catalyst. We further develop methods to estimate the number of singlets which can be established via a noisy quantum channel.
  arXiv  Detail & Related papers  (2022-02-10T18:36:25Z)
• Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation [0.7734726150561086]
  We propose a quantum-classical hybrid scheme for implementing the nonunitary Gutzwiller factor. The proposed scheme is demonstrated with numerical simulations for the half-filled Fermi-Hubbard model.
  arXiv  Detail & Related papers  (2022-01-27T08:57:04Z)
• Training Hybrid Classical-Quantum Classifiers via Stochastic Variational Optimization [32.562122826341266]
  Quantum machine learning has emerged as a potential practical application of near-term quantum devices. In this work, we study a two-layer hybrid classical-quantum classifier in which a first layer of quantum neurons implementing generalized linear models (QGLMs) is followed by a second classical combining layer. Experiments show the advantages of the approach for a variety of activation functions implemented by QGLM neurons.
  arXiv  Detail & Related papers  (2022-01-21T10:30:24Z)
• Experimental Realization of Nonadiabatic Holonomic Single-Qubit Quantum Gates with Two Dark Paths in a Trapped Ion [41.36300605844117]
  We show nonadiabatic holonomic single-qubit quantum gates on two dark paths in a trapped $171mathrmYb+$ ion based on four-level systems with resonant drives. We find that nontrivial holonomic two-qubit quantum gates can also be realized within current experimental technologies.
  arXiv  Detail & Related papers  (2021-01-19T06:57:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.