Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “unitary coupled cluster”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Quantum Computing for Energy-Related Applications

Growing interest in quantum computing and simulations have created opportunities for its deployment to improve processes pertaining to energy production, distribution, and consumption. While quantum computing is considered as a paradigm shift in our basic understanding of physical computation, effective implementation of quantum computing in energy applications also depends on progress and development in the dimensions of both quantum computing hardware and quantum computing algorithms. To fully address the status and future challenges of quantum information science (QIS) applied within the energy sector, in this presentation, we firstly summarize recent advancements on the applications of quantum computing to energy infrastructure and materials, complex energy system processes, advanced manufacturing, and energy system security. Then, we will demonstrate the results of quantum computing both on a simulator and a quantum device accessing from OLCF. Our first example is to use the variational quantum eigensolver (VQE) with a unitary coupled cluster with singles and doubles (UCCSD) ansatz to simulate a series of LixHyq molecules (q=-1, 0, +1). The obtained results showed that the quantum computing VQE-UCCSD is comparable to classical CCSD for small systems like LiH with respect to full configuration interaction (FCI). Targeting on CO2 capture application, our second example is to use VQE to quantify molecular vibrational energies and reaction pathways between CO2 and a simplified amine-based solvent model—NH3 to form H2NCOOH. This research showcases quantum computing applications in the study of CO2 capture reactions.

Duan, Yuhua↗
NASA NTRSDate not supplied

Quantum Hardware-Enabled Molecular Dynamics via Transfer Learning

The ability to perform ab initio molecular dynamics simulations using potential energy surfaces provided by quantum computers would open the door to virtually exact dynamics for a variety of chemical and biochemical systems, with impacts on catalysis and biophysics. Nonetheless, performing molecular dynamics on surfaces produced by quantum hardware has been hampered by the noisy energies typically produced by quantum computers and challenges associated with computing gradients and scaling to large systems interest. A recent set of advances in machine learning, known as transfer learning, provides a new path forward for molecular dynamics simulations on quantum hardware. Transfer learning offers a workaround, where one first trains models on larger, less accurate classical datasets and then refines them on smaller, more accurate quantum datasets. We explore this approach by training machine learning models to predict a molecule's potential energy based on its geometric structure using Behler-Parrinello neural networks. When successfully trained, the model enables energy gradient predictions necessary for dynamic simulations. To reduce the quantum resources needed, the model is initially trained with data derived from classical density functional theory and subsequently refined with a smaller dataset obtained from a variational quantum eigensolver optimization of the unitary coupled cluster ansatz. We show that this approach significantly reduces the size of the needed quantum training dataset while capturing the high accuracies needed within quantum chemistry simulations. The success of this two-step training method opens more opportunities to apply machine learning models on quantum data, a significant stride towards efficient quantum-classical hybrid computational models.

quantum computing↗
DOE OSTI2023

State Preparation of Antisymmetrized Geminal Power on a Quantum Computer without Number Projection

The antisymmetrized geminal power (AGP) is equivalent to the number projected Bardeen–Cooper–Schrieffer (PBCS) wave function. It is also an elementary symmetric polynomial (ESP) state. We generalize previous research on deterministically implementing the Dicke state to a state preparation algorithm for an ESP state, or equivalently AGP, on a quantum computer. Our method is deterministic and has polynomial cost, and it does not rely on number symmetry breaking and restoration. We also show that our circuit is equivalent to a disentangled unitary paired coupled cluster operator and a layer of unitary Jastrow operator acting on a single Slater determinant. Here, the method presented herein highlights the ability of disentangled unitary coupled cluster to capture nontrivial entanglement properties that are hardly accessible with traditional Hartree–Fock based electronic structure methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Excited-state downfolding using ground-state formalisms

Downfolding coupled cluster (CC) techniques are powerful tools for reducing the dimensionality of many-body quantum problems. This work investigates how ground-state downfolding formalisms can target excited states using non-Aufbau reference determinants, paving the way for applications of quantum computing in excited-state chemistry. This study focuses on doubly excited states for which canonical equation-of-motion CC approaches struggle to describe unless one includes higher-than-double excitations. The downfolding technique results in state-specific effective Hamiltonians that, when diagonalized in their respective active spaces, provide ground- and excited-state total energies (and therefore excitation energies) comparable to high-level CC methods. The performance of this procedure is examined with doubly excited states of H 2 , Methylene, Formaldehyde, and Nitroxyl.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Quantum Simulations of Fermionic Hamiltonians with Efficient Encoding and Ansatz Schemes

Here, we propose a computational protocol for quantum simulations of fermionic Hamiltonians on a quantum computer, enabling calculations on spin defect systems which were previously not feasible using conventional encodings and a unitary coupled-cluster ansatz of variational quantum eigensolvers. We combine a qubit-efficient encoding scheme mapping Slater determinants onto qubits with a modified qubitcoupled cluster ansatz and noise-mitigation techniques. Our strategy leads to a substantial improvement in the scaling of circuit gate counts and in the number of required qubits, and to a decrease in the number of required variational parameters, thus increasing the resilience to noise. We present results for spin defects of interest for quantum technologies, going beyond minimum models for the negatively charged nitrogen vacancy center in diamonds and the double vacancy in 4H silicon carbide (4H-SiC) and tackling a defect as complex as negatively charged silicon vacancy in 4H-SiC for the first time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Classical Preoptimization Approach for ADAPT-VQE: Maximizing the Potential of High-Performance Computing Resources to Improve Quantum Simulation of Chemical Applications

The ADAPT-VQE algorithm is a promising method for generating a compact ansatz based on derivatives of the underlying cost function, and it yields accurate predictions of electronic energies for molecules. In this work, we report the implementation and performance of ADAPT-VQE with our recently developed sparse wave function circuit solver (SWCS) in terms of accuracy and efficiency for molecular systems with up to 52 spin orbitals. The SWCS can be tuned to balance computational cost and accuracy, which extends the application of ADAPT-VQE for molecular electronic structure calculations to larger basis sets and a larger number of qubits. Using this tunable feature of the SWCS, we propose an alternative optimization procedure for ADAPT-VQE to reduce the computational cost of the optimization. Furthermore, by preoptimizing a quantum simulation with a parametrized ansatz generated with ADAPT-VQE/SWCS, we aim to utilize the power of classical high-performance computing in order to minimize the work required on noisy intermediate-scale quantum hardware, which offers a promising path toward demonstrating quantum advantage for chemical applications.

ADAPT-VQE↗
DOE OSTI2025

A quantum eigenvalue solver based on tensor networks

Electronic ground states are of central importance in chemical simulations, but have remained beyond the reach of efficient classical algorithms except in cases of weak electron correlation or one-dimensional spatial geometry. We introduce a hybrid quantum-classical eigenvalue solver that constructs a wavefunction ansatz from a linear combination of matrix product states in rotated orbital bases, enabling the characterization of strongly correlated ground states with arbitrary spatial geometry. The energy is converged via a gradient-free generalized sweep algorithm based on quantum subspace diagonalization, with a potentially exponential speedup in the off-diagonal matrix element contractions upon translation into compact quantum circuits of linear depth in the number of qubits. Chemical accuracy is attained in numerical experiments for both a stretched water molecule and an octahedral arrangement of hydrogen atoms, achieving substantially better correlation energies compared to a unitary coupled-cluster benchmark, with orders of magnitude reductions in quantum resource estimates and a surprisingly high tolerance to shot noise. This proof-of-concept study suggests a promising new avenue for scaling up simulations of strongly correlated chemical systems on near-term quantum hardware.

chemistry↗
DOE OSTI2025

Closed-form expressions for unitaries of spin-adapted fermionic operators

One of the open challenges in quantum computing simulations of problems of chemical interest is the proper enforcement of spin symmetry. Efficient quantum circuits implementing unitaries generated by spin-adapted operators remain elusive, while naïve Trotterization schemes break spin symmetry. Here, in this work, we analyze the mathematical structure of spin-adapted operators and derive closed-form expressions for unitaries generated by singlet spin-adapted generalised single and double excitations. These results represent significant progress toward the economical enforcement of spin symmetry in quantum simulations.

fermionic algebra↗
DOE OSTI2023

Description of reaction and vibrational energetics of CO 2 –NH 3 interaction using quantum computing algorithms

CO 2 capture is critical to solving global warming. Amine-based solvents are extensively used to chemically absorb CO 2 . Thus, it is crucial to study the chemical absorption of CO 2 by amine-based solvents to better understand and optimize CO 2 capture processes. Here, we use quantum computing algorithms to quantify molecular vibrational energies and reaction pathways between CO 2 and a simplified amine-based solvent model—NH 3 . Molecular vibrational properties are important to understanding kinetics of reactions. However, the molecule size correlates with the strength of anharmonicity effect on vibrational properties, which can be challenging to address using classical computing. Quantum computing can help enhance molecular vibrational calculations by including anharmonicity. We implement a variational quantum eigensolver (VQE) algorithm in a quantum simulator to calculate ground state vibrational energies of reactants and products of the CO 2 and NH 3 reaction. The VQE calculations yield ground vibrational energies of CO 2 and NH 3 with similar accuracy to classical computing. In the presence of hardware noise, Compact Heuristic for Chemistry (CHC) ansatz with shallower circuit depth performs better than Unitary Vibrational Coupled Cluster. The “Zero Noise Extrapolation” error-mitigation approach in combination with CHC ansatz improves the vibrational calculation accuracy. Excited vibrational states are accessed with quantum equation of motion method for CO 2 and NH 3 . Using quantum Hartree–Fock (HF) embedding algorithm to calculate electronic energies, the corresponding reaction profile compares favorably with Coupled Cluster Singles and Doubles while being more accurate than HF. Our research showcases quantum computing applications in the study of CO 2 capture reactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRSDate not supplied

Incorporating ADAPT-VQE with a Sparse Wavefunction Circuit Simulator to Find Compact Quantum Circuits for Chemical Applications

We implemented the ADAPT-VQE algorithm into our recent classical sparse wavefunction circuit simulator to demonstrate that classical resources can (1) efficiently find a physically motivated compact wavefunction ansatz for further refinement on near-term quantum hardware and (2) benchmark expected results of VQE-based algorithms once the quantum hardware is available to study large-scale applications. In particular, we study the role of the ADAPT-VQE operator pool, molecular basis set selection, and variations such as TETRIS-ADAPT-VQE on the performance of our classical circuit simulator. This work demonstrates the promise of using classical resources to generate highly accurate wavefunctions that can be prepared on quantum hardware to initiate other quantum algorithms such as phase estimation. Our approach harnesses the power of high-performance computing resources with the more limited available quantum computers to map a path toward quantum advantage for electronic structure calculations in chemistry and materials science.

Quantum Computing↗
DOE OSTI2026

Benchmarking quantum trial wavefunctions for phaseless auxiliary-field quantum Monte Carlo

The phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) method is a stochastic imaginary-time projection technique for computing ground-state properties of strongly correlated quantum systems, with accuracy that depends critically on the choice of trial wavefunction. Here, we investigate ph-AFQMC with trial states prepared using parameterized quantum circuits. In this work, we present a comprehensive benchmarking study of quantum trial wavefunctions spanning unitary coupled-cluster, Hamiltonian-informed, Jastrow-inspired, and adaptively constructed ansatze. The benchmarking evaluates accuracy, expressibility, and scalability of these ansatze within the QC-AFQMC framework. We test these ansatze on linear hydrogen chains under bond stretching and find that several ansatz families produce chemically accurate ph-AFQMC energies across the dissociation curve. We have performed simulations using the CUDA-Q quantum development platform on the GPU partition of the Perlmutter supercomputer. When comparing ansatze at similar numbers of variational parameters, we find that different ansatz families yield comparable ph-AFQMC results despite exhibiting substantially different variational energies, optimization costs, and circuit depths. Our results indicate that the variational energy of an ansatz is not always a reliable indicator of its quality for ph-AFQMC and reveal instances of over-parameterization. In the strongly correlated regime, trial wavefunctions obtained from adaptive ansatze, exemplified here by ADAPT-VQE with the UCCSD operator pool, can outperform their fixed-ansatz counterparts (UCCSD) in terms of projected energies while using substantially more compact circuits, providing a flexible route to optimize quantum resources within the ph-AFQMC framework.

Rofougaran, Rod [LBNL, Berkeley; Columbia U.; PNL,↗
DOE OSTI2022

Hybrid quantum-classical approach for coupled-cluster Green's function theory

The three key elements of a quantum simulation are state preparation, time evolution, and measurement. While the complexity scaling of time evolution and measurements are well known, many state preparation methods are strongly system-dependent and require prior knowledge of the system's eigenvalue spectrum. Here, we report on a quantum-classical implementation of the coupled-cluster Green's function (CCGF) method, which replaces explicit ground state preparation with the task of applying unitary operators to a simple product state. While our approach is broadly applicable to many models, we demonstrate it here for the Anderson impurity model (AIM). The method requires a number of T gates that grows as O ( N 5 ) per time step to calculate the impurity Green's function in the time domain, where N is the total number of energy levels in the AIM. Since the number of T gates is analogous to the computational time complexity of a classical simulation, we achieve an order of magnitude improvement over a classical CCGF calculation of the same order, which requires O ( N 6 ) computational resources per time step.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Exact relationships between the GW approximation and equation-of-motion coupled-cluster theories through the quasi-boson formalism

We describe the relationship between the GW approximation and various equation-of-motion (EOM) coupled-cluster (CC) theories. We demonstrate the exact equivalence of the G0W0 approximation and the propagator theory for an electron–boson problem in a particular excitation basis. From there, we establish equivalence within the quasi-boson picture to the IP+EA-EOM unitary CC propagator. We analyze the incomplete description of screening provided by the standard similarity-transformed IP+EA-EOM-CC and the recently introduced G0W0 Tamm–Dancoff approximation. We further consider the approximate decoupling of IP and EA sectors in EOM-CC treatments and devise the analogous particle–hole decoupling approach for the G0W0 approximation. Finally, we numerically demonstrate the exact relationships and magnitude of the approximations in the calculations of a set of molecular ionization potentials and electron affinities.

Chemistry↗
DOE OSTI2025

Toward a Balanced Description of Ground and Excited States with Transcorrelated F12 Methods

By correlating only the 1-particle states occupied in the reference determinant, the conventional design for the single-reference R12/F12 explicitly correlated methods biases them toward the ground-state description, thereby making the treatment of response properties of the ground state, and energies and other properties of excited states less robust. While the use of multireference methods and/or extensions of the standard SP-projected geminals can achieve a more balanced description of ground and excited states, here we show that the same goals can be achieved by extending the action of F12 correlators to the occupied and valence unoccupied 1-particle states only. This design choice reflects the strong dependence of the optimal correlation length scale of the F12 ansatz on the orbital energies/structure, and helps to avoid the unphysical raising of the ground-state energy if the F12 geminals are used to correlate pairs of all 1-particle states. The improved F12 geminal design is incorporated into the unitary transcorrelation framework to produce a unitary 2-body Hamiltonian that incorporates the short-range dynamical correlation physics for ground and low-energy excited states in a balanced manner. This explicitly correlated effective Hamiltonian reduces the basis set requirement on the correlation-consistent basis cardinal number by 1 or more over the uncorrelated counterpart for the description of ground-state coupled-cluster singles and doubles (CCSD) energies, vertical excitation energies, and harmonic vibrational frequencies of equation-of-motion CCSD low-energy excited states.

Hamiltonians↗
DOE OSTI2025

Exact closed-form unitary transformations of fermionic operators

Unitary transformations play a fundamental role in many-body physics, and except for special cases, they are not expressible in closed form. We present closed-form expressions for unitary transformations generated by a single fermionic operator for Hermitian and anti-Hermitian generators. We demonstrate the usefulness of these expressions in formal analyses of unitary transformations and numerical applications to Hamiltonian downfolding in quantum computing and Heisenberg dynamics. Furthermore, this work paves the way for new analytical treatments of unitary transformations and numerical many-body methods for fermions.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Dimensionality reduction of the many-body problem using coupled-cluster subsystem flow equations: classical and quantum computing perspective

We discuss reduced-scaling strategies employing recently introduced sub-system embedding sub-algebras coupled-cluster formalism (SES-CC) to describe many-body systems. These strategies utilize properties of the SES-CC formulations where the equations describing certain classes of sub- systems can be integrated into a computational flows composed coupled eigenvalue problems of reduced dimensionality. Additionally, these flows can be defined at the level of the CC Ansatz defined by selected classes of cluster amplitudes, which define the wave function ”memory” of possible partitionings of the many-body system into constituent sub-systems. One of the possible ways of solving these coupled problems is through implementing procedures, where the information is passed between the sub-systems in a self-consistent manner. As a special case, we consider local flow formulations where the so-called local character of correlation effects can be closely related to properties of sub-system embedding sub-algebras employing localized molecular basis. We also generalize flow equations to the time domain and to downfolding methods utilizing double exponential unitary CC Ansatz (DUCC), where reduced dimensionality of constituent sub-problems offer a possibility of efficient utilization of limited quantum resources in modeling realistic systems.

Electron correlation, quantum chemistry, quantum c↗
DOE OSTI2022

Coupled Cluster Downfolding Methods: the effect of double commutator terms on the accuracy of ground-state energies

Downfolding coupled cluster (CC) techniques have recently been introduced into quantum chemistry as a tool for the dimensionality reduction of the many-body quantum problem. As opposed to earlier formulations in physics and chemistry based on the concept of effective Hamiltonians, the appearance of the downfolded Hamiltonians is a natural consequence of the single-reference exponential parametrization of the wave function. In this paper, we discuss the impact of higher-order terms originating in double commutators. In analogy to previous studies, we consider the case when only one- and two-body interactions are included in the downfolded Hamiltonians. We demonstrate the efficiency of the many-body expansions involving single and double commutators for the unitary extension of the downfolded Hamiltonians on the example of the beryllium atom, and bond-breaking processes in the Li2 and H2O molecules. For the H2O system, we also analyze energies obtained with downfolding procedures as functions of the active space size.

quantum computing, quantum algorithms, electronic ↗