Non-Iterative Disentangled Unitary Coupled-Cluster based on Lie-algebraic structure

• URL: http://arxiv.org/abs/2408.14289v2
• Date: Thu, 5 Sep 2024 15:18:32 GMT
• Title: Non-Iterative Disentangled Unitary Coupled-Cluster based on Lie-algebraic structure
• Authors: Mohammad Haidar, Olivier Adjoua, Siwar Baddredine, Alberto Peruzzo, Jean-Philip Piquemal,
• Abstract summary: Fixed Unitary Coupled-Cluster (UCC) ans"atze are attractive for performing quantum chemistry Variational Quantumsolver (VQE) computations. We introduce $k$-NI-DUCC, a fixed and Non-iterative Disentangled Unitary Coupled-Cluster compact ansatz.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Due to their non-iterative nature, fixed Unitary Coupled-Cluster (UCC) ans\"atze are attractive for performing quantum chemistry Variational Quantum Eigensolver (VQE) computations as they avoid pre-circuit measurements on a quantum computer. However, achieving chemical accuracy for strongly correlated systems with UCC requires further inclusion of higher-order fermionic excitations beyond triples increasing circuit depth. We introduce $k$-NI-DUCC, a fixed and Non-iterative Disentangled Unitary Coupled-Cluster compact ansatz, based on specific $"k"$ sets of "qubit" excitations, eliminating the needs for fermionic-type excitations. These elements scale linearly ($\mathcal{O}(n)$) by leveraging Lie algebraic structures, with $n$ being the number of qubits. The key excitations are screened through specific selection criteria, including the enforcement of all symmetries, to ensure the construction of a robust set of generators. NI-DUCC employs $"k"$ products of the exponential of $\mathcal{O}(n)$- anti-Hermitian Pauli operators, where each operator has a length $p$. This results in a fewer two-qubit CNOT gates circuit, $\mathcal{O}(knp)$, suitable for hardware implementations. Tested on LiH, H$_6$ and BeH$_2$, NI-DUCC-VQE achieves both chemical accuracy and rapid convergence even for molecules deviating significantly from equilibrium. It is hardware-efficient, reaching the exact Full Configuration Interaction energy solution at specific layers, while reducing significantly the VQE optimization steps. While NI-DUCC-VQE effectively addresses the gradient measurement bottleneck of ADAPT-VQE-like iterative algorithms, the classical computational cost of constructing the $\mathcal{O}(n)$ set of excitations increases exponentially with the number of qubits. We provide a first implementation for constructing the generators' set able to handle up to 20 qubits and discuss the efficiency perspectives.

Related papers

• Promise of Graph Sparsification and Decomposition for Noise Reduction in QAOA: Analysis for Trapped-Ion Compilations [5.451583832235867]
  We develop new approximate compilation schemes to solve the Max-Cut problem. Results are based on principles of graph sparsification and decomposition. We demonstrate significant reductions in noise are obtained in our new compilation approaches.
  arXiv  Detail & Related papers  (2024-06-20T14:00:09Z)
• Evaluating Ground State Energies of Chemical Systems with Low-Depth Quantum Circuits and High Accuracy [6.81054341190257]
  We develop an enhanced Variational Quantum Eigensolver (VQE) ansatz based on the Qubit Coupled Cluster (QCC) approach. We evaluate our enhanced QCC ansatz on two distinct quantum hardware, IBM Kolkata and Quantinuum H1-1.
  arXiv  Detail & Related papers  (2024-02-21T17:45:03Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Blockwise Stochastic Variance-Reduced Methods with Parallel Speedup for Multi-Block Bilevel Optimization [43.74656748515853]
  Non-stationary multi-block bilevel optimization problems involve $mgg 1$ lower level problems and have important applications in machine learning. We aim to achieve three properties for our algorithm: a) matching the state-of-the-art complexity of standard BO problems with a single block; (b) achieving parallel speedup by sampling $I$ samples for each sampled block per-iteration; and (c) avoiding the computation of the inverse of a high-dimensional Hessian matrix estimator.
  arXiv  Detail & Related papers  (2023-05-30T04:10:11Z)
• Tensor Factorized Recursive Hamiltonian Downfolding To Optimize The Scaling Complexity Of The Electronic Correlations Problem on Classical and Quantum Computers [0.15833270109954137]
  We present a new variant of post-Hartree-Fock Hamiltonian downfolding-based quantum chemistry methods with optimized scaling for high-cost simulations. We demonstrate super-quadratic speedups of expensive quantum chemistry algorithms on both classical and quantum computers.
  arXiv  Detail & Related papers  (2023-03-13T12:15:54Z)
• Quantum Goemans-Williamson Algorithm with the Hadamard Test and Approximate Amplitude Constraints [62.72309460291971]
  We introduce a variational quantum algorithm for Goemans-Williamson algorithm that uses only $n+1$ qubits. Efficient optimization is achieved by encoding the objective matrix as a properly parameterized unitary conditioned on an auxilary qubit. We demonstrate the effectiveness of our protocol by devising an efficient quantum implementation of the Goemans-Williamson algorithm for various NP-hard problems.
  arXiv  Detail & Related papers  (2022-06-30T03:15:23Z)
• Unimon qubit [42.83899285555746]
  Superconducting qubits are one of the most promising candidates to implement quantum computers. Here, we introduce and demonstrate a superconducting-qubit type, the unimon, which combines the desired properties of high non-linearity, full insensitivity to dc charge noise, insensitivity to flux noise, and a simple structure consisting only of a single Josephson junction in a resonator.
  arXiv  Detail & Related papers  (2022-03-11T12:57:43Z)
• K-sparse Pure State Tomography with Phase Estimation [1.2183405753834557]
  Quantum state tomography (QST) for reconstructing pure states requires exponentially increasing resources and measurements with the number of qubits. QST reconstruction for any pure state composed of the superposition of $K$ different computational basis states of $n$bits in a specific measurement set-up is presented.
  arXiv  Detail & Related papers  (2021-11-08T09:43:12Z)
• Halving the cost of quantum multiplexed rotations [0.0]
  We improve the number of $T$ gates needed for a $b$-bit approximation of a multiplexed quantum gate with $c$ controls. Our results roughly halve the cost of state-of-art electronic structure simulations based on qubitization of double-factorized or tensor-hypercontracted representations.
  arXiv  Detail & Related papers  (2021-10-26T06:49:44Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Preparation of excited states for nuclear dynamics on a quantum computer [117.44028458220427]
  We study two different methods to prepare excited states on a quantum computer. We benchmark these techniques on emulated and real quantum devices. These findings show that quantum techniques designed to achieve good scaling on fault tolerant devices might also provide practical benefits on devices with limited connectivity and gate fidelity.
  arXiv  Detail & Related papers  (2020-09-28T17:21:25Z)

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.