Sparse Quantum State Preparation for Strongly Correlated Systems

TL;DR

The paper tackles the challenge of preparing high-quality initial states for ground-state quantum chemistry simulations in strongly correlated systems. It compares variational and non-variational sparse quantum state preparation approaches applied to CIPSI-selected SCI targets encoded by Jordan-Wigner, up to 28 qubits. Key findings include that CVO-QRAM can perform exact state preparation with cost scaling as $O(M log M + nM)$ and gate counts governed by a determinant-based relation with coefficients (8t-4) minus t_max, while the Overlap-ADAPT-VQE with suitable operator pools delivers high fidelity (F > 0.95) with substantially smaller circuits for near-term use. The Hyperion-1 emulator enables these large-scale QSP studies, highlighting the trade-offs between exact and variational initialization for post-treatment methods like QPE and informing scalable quantum chemistry on near-term hardware.

Abstract

Quantum Computing allows, in principle, the encoding of the exponentially scaling many-electron wave function onto a linearly scaling qubit register, offering a promising solution to overcome the limitations of traditional quantum chemistry methods. An essential requirement for ground state quantum algorithms to be practical is the initialisation of the qubits to a high-quality approximation of the sought-after ground state. Quantum State Preparation (QSP) allows the preparation of approximate eigenstates obtained from classical calculations, but it is frequently treated as an oracle in quantum information. In this study, we conduct QSP on the ground state of prototypical strongly correlated systems, up to 28 qubits, using the Hyperion GPU-accelerated state-vector emulator. Various variational and non-variational methods are compared in terms of their circuit depth and classical complexity. Our results indicate that the recently developed Overlap-ADAPT-VQE algorithm offers the most advantageous performance for near-term applications.

Figures (6)

• Figure 1: Determinants count (a) and circuit size (b) in the SCI representation of linear H$_n$ chains. The circuit size has been established using CVO-QRAM loader and ESP Ansatz as state preparation method.
• Figure 2: (a) Absolute CI coefficient of each Slater determinant in the Selected-CI expansion of linear H$_{14}$ ground state wave function. (b) Associated absolute sum of CI squared coefficients.
• Figure 3: (a) Gate-count for approximate state preparation of ground state wave function of linear H$_{14}$ displayed in \ref{['fig:main']}. The CVO-QRAM algorithm generated states from CIPSI iterates as well as states derived from truncations of the ground state (TGS). The Overlap-ADAPT-VQE approximates the ground state using the QEB- and the Qubit-pool of operators. (b) Fidelity of the Overlap-ADAPT-VQE ansatz over the iterations for the same target.
• Figure 4: Gate-count for approximate state preparation of ground state wave function of linear H$_{10}$ in (a) and H$_{12}$ in (b). The CVO-QRAM algorithm generated states derived from truncations of the CIPSI ground state (TGS). The Overlap-ADAPT-VQE approximates the CIPSI ground state using the QEB- and the Qubit-pool of operators, iterating over 500 steps for each system. The solid lines represent the CNOT counts, while the dashed lines indicate the single-qubit gate counts.
• Figure 5: A quantum circuit performing a generic single-qubit excitation yordanov2020efficient.