arXiv subjects

Nikolay V. Tkachenko

Publications and source records attributed to Nikolay V. Tkachenko.

7 recordsLinked to original sources

arXiv2025

Beyond real: Alternative unitary cluster Jastrow models for molecular electronic structure calculations on near-term quantum computers

Near-term quantum devices require wavefunction ansätze that are expressive while also of shallow circuit depth in order to both accurately and efficiently simulate molecular electronic structure. While unitary coupled cluster (e.g., UCCSD) has become a standard, the high gate count associated with the implementation of this limits its feasibility on noisy intermediate-scale quantum (NISQ) hardware. K-fold unitary cluster Jastrow (uCJ) ansätze mitigate this challenge by providing $O(kN^2)$ circuit scaling and favorable linear depth circuit implementation. Previous work has focused on the real orbital-rotation (Re-uCJ) variant of uCJ, which allows an exact (Trotter-free) implementation. Here we extend and generalize the $k$-fold uCJ framework by introducing two new variants, Im-uCJ and g-uCJ, which incorporate imaginary and fully complex orbital rotation operators, respectively. Similar to Re-uCJ, both of the new variants achieve quadratic gate-count scaling. Our results focus on the simplest $k=1$ model, and show that the uCJ models frequently maintain energy errors within chemical accuracy. Both g-uCJ and Im-uCJ are more expressive in terms of capturing electron correlation and are also more accurate than the earlier Re-uCJ ansatz. We further show that Im-uCJ and g-uCJ circuits can also be implemented exactly, without any Trotter decomposition. Numerical tests using $k=1$ on $H_2$, $H_3^+$, $Be_2$, $C_2H_4$, $C_2H_6$ and $C_6H_6$ in various basis sets confirm the practical feasibility of these shallow Jastrow-based ansätze for applications on near-term quantum hardware.

quant-ph↗

arXiv2025

An Error Mitigated Non-Orthogonal Quantum Eigensolver via Shadow Tomography

We present a shadow-tomography-enhanced Non-Orthogonal Quantum Eigensolver (NOQE) for more efficient and accurate electronic structure calculations on near-term quantum devices. By integrating shadow tomography into the NOQE, the measurement cost scales linearly rather than quadratically with the number of reference states, while also reducing the required qubits and circuit depth by half. This approach enables extraction of all matrix elements via randomized measurements and classical postprocessing. We analyze its sample complexity and show that, for small systems, it remains constant in the high-precision regime, while for larger systems, it scales linearly with the system size. We further apply shadow-based error mitigation to suppress noise-induced bias without increasing quantum resources. Demonstrations on the hydrogen molecule in the strongly correlated regime achieve chemical accuracy under realistic noise, showing that our method is both resource-efficient and noise-resilient for practical quantum chemistry simulations in the near term.

quant-ph↗

arXiv2023

Quantum Davidson Algorithm for Excited States

Excited state properties play a pivotal role in various chemical and physical phenomena, such as charge separation and light emission. However, the primary focus of most existing quantum algorithms has been the ground state, as seen in quantum phase estimation and the variational quantum eigensolver (VQE). Although VQE-type methods have been extended to explore excited states, these methods grapple with optimization challenges. In contrast, the quantum Krylov subspace (QKS) method has been introduced to address both ground and excited states, positioning itself as a cost-effective alternative to quantum phase estimation. Our research presents an economic QKS algorithm, which we term the quantum Davidson (QDavidson) algorithm. This innovation hinges on the iterative expansion of the Krylov subspace and the incorporation of a pre-conditioner within the Davidson framework. By using the residues of eigenstates to expand the Krylov subspace, we manage to formulate a compact subspace that aligns closely with the exact solutions. This iterative subspace expansion paves the way for a more rapid convergence in comparison to other QKS techniques, such as the quantum Lanczos. Using quantum simulators, we employ the novel QDavidson algorithm to delve into the excited state properties of various systems, spanning from the Heisenberg spin model to real molecules. Compared to the existing QKS methods, the QDavidson algorithm not only converges swiftly but also demands a significantly shallower circuit. This efficiency establishes the QDavidson method as a pragmatic tool for elucidating both ground and excited state properties on quantum computing platforms.

quant-ph↗

arXiv2023

Two-dimensional bimetal-embedded expanded phthalocyanine monolayers: a class of multifunctional materials with fascinating properties

The expanded phthalocyanine (EPc) single-layer sheets with double transition metals (labeled as TM2EPc, TM = Sc-Zn) are predicted to be a new class of two-dimensional (2D) metal-organic materials with a series of favorable functional properties by means of systematic first-principle calculations and molecular dynamics simulations. The strong coordination between metal and EPc substrate accounts for the excellent structural stability. Chemical bonding analysis has demonstrated the absence of TM-TM bonding. Each metal center is isolated, but connected to the organic framework by four 2c-2e TM-N σ-bonds to form an extended 2D network. Unexpectedly, it is found that the V2EPc is an antiferromagnetic metal with Dirac cone, while Cr2EPc exhibits ferromagnetic Dirac half-metallicity, which is not common in 2D materials. Excitingly, the ferromagnetic Cr2EPc and antiferromagnetic Mn2- and Fe2-EPc have high magnetic transition temperatures of 223, 217, and 325 K, respectively, which are crucial for the practical applications of spintronics. Cr2EPc can maintain the Dirac half-metallicity under -6 % ~ 2 % biaxial strains, and Fe2EPc can transform from semiconductor to half-metal by applying -6 % ~ -10 % compressive strains. Additionally, the TM2EPc monolayers exhibit a full response to visible light and some materials have strong absorption in the ultraviolet and infrared regions in addition to visible light, showing extraordinary solar light-harvesting ability. Notably, the designed type-II heterojunctions Fe2EPc/SnC, Co2EPc/GeS, and Ni2EPc/2H-WSe2 have high power conversion efficiency (PCE > 15%), especially the PCE of Ni2EPc/2H-WSe2 reaches 25.19%, which has great potential in solar cell applications. All these desired properties render 2D TM2EPc monolayers promising candidates for future applications in nanoelectronics, spintronics,optoelectronics, and photovoltaic devices.

cond-mat.mtrl-sci↗

arXiv2021

Performance Analysis of CP2K Code for Ab Initio Molecular Dynamics

Using a realistic molecular catalyst system, we conduct scaling studies of ab initio molecular dynamics simulations using the CP2K code on both Intel Xeon CPU and NVIDIA V100 GPU architectures. We explore using process placement and affinity to gain additional performance improvements. We also use statistical methods to understand performance changes in spite of the variability in runtime for each molecular dynamics timestep. We found ideal conditions for CPU runs included at least four MPI ranks per node, bound evenly across each socket, and fully utilizing processing cores with one OpenMP thread per core, no benefit was shown from reserving cores for the system. The CPU-only simulations scaled at 70% or more of the ideal scaling up to 10 compute nodes, after which the returns began to diminish more quickly. Simulations on a single 40-core node with two NVIDIA V100 GPUs for acceleration achieved over 3.7x speedup compared to the fastest single 36-core node CPU-only version, and showed 13% speedup over the fastest time we achieved across five CPU-only nodes.

cs.PF↗

arXiv2020

Novel Strongly Correlated Europium Superhydrides

We conducted a joint experimental-theoretical investigation of the high-pressure chemistry of europium polyhydrides at pressures of 86-130 GPa. We discovered several novel magnetic Eu superhydrides stabilized by anharmonic effects: cubic $EuH_{9}$, hexagonal $EuH_{9}$, and an unexpected cubic (Pm-3n) clathrate phase, $Eu_{8}H_{46}$. Monte Carlo simulations indicate that cubic $EuH_{9}$ has antiferromagnetic ordering with T(Neel) up to 24 K, whereas hexagonal $EuH_{9}$ and Pm-3n-$Eu_{8}H_{46}$ possess ferromagnetic ordering with T(Curie) = 137 and 336 K, respectively. The electron-phonon interaction is weak in all studied europium hydrides, and their magnetic ordering excludes s-wave superconductivity, except, perhaps, for distorted pseudohexagonal $EuH_{9}$. The equations of state predicted within the DFT+U approach (the Hubbard corrections were found within linear response theory) are in close agreement with the experimental data. This work shows the great influence of the atomic radius on symmetry-breaking distortions of the crystal structures of superhydrides and on their thermodynamic stability.

cond-mat.str-el↗

arXiv2020

Correlation-Informed Permutation of Qubits for Reducing Ansatz Depth in VQE

The Variational Quantum Eigensolver (VQE) is a method of choice to solve the electronic structure problem for molecules on near-term gate-based quantum computers. However, the circuit depth is expected to grow significantly with problem size. Increased depth can both degrade the accuracy of the results and reduce trainability. In this work, we propose a novel approach to reduce ansatz circuit depth. Our approach, called PermVQE, adds an additional optimization loop to VQE that permutes qubits in order to solve for the qubit Hamiltonian that minimizes long-range correlations in the ground state. The choice of permutations is based on mutual information, which is a measure of interaction between electrons in spin-orbitals. Encoding strongly interacting spin-orbitals into proximal qubits on a quantum chip naturally reduces the circuit depth needed to prepare the ground state. For representative molecular systems, LiH, H$_2$, (H$_2$)$_2$, H$_4$, and H$_3^+$, we demonstrate for linear qubit connectivity that placing entangled qubits in close proximity leads to shallower depth circuits required to reach a given eigenvalue-eigenvector accuracy. This approach can be extended to any qubit connectivity and can significantly reduce the depth required to reach a desired accuracy in VQE. Moreover, our approach can be applied to other variational quantum algorithms beyond VQE.

quant-ph↗