Researchers Leverage Phase Estimation to Find Ground States and Energies of Strongly-correlated Systems

Preparing quantum states for complex calculations remains a significant challenge in the field, and researchers are continually seeking more efficient methods. Michal Krompiec, Josh J. M. Kirsopp, and Antonio Márquez Romero, all from Fujitsu Research of Europe Ltd., alongside Vicente Perez Soloviev, present a streamlined approach to creating initial quantum states necessary for algorithms like Phase Estimation. Their work addresses a key limitation of these algorithms, the need for complex preparation of states with sufficient overlap with the desired ground state, particularly for strongly-correlated systems where quantum computers are expected to excel. By drawing a connection between established classical methods for modelling molecular structures and a simplified quantum framework, the team demonstrates the ability to prepare high-fidelity quantum states using surprisingly shallow circuits, potentially unlocking more efficient quantum simulations of complex chemical and material systems.

However, this requires starting from an initial state that closely resembles the ground state of the system. For strongly correlated states, where Quantum Phase Estimation (QPE) is expected to outperform classical methods, preparing such initial states often demands deep quantum circuits and/or computationally expensive hybrid quantum-classical optimization. The team addressed this by leveraging insights from orbital-optimized paired Coupled Cluster Doubles (oo-pCCD) theory, a classical method known for accurately describing static correlation in many strongly-correlated singlet states. Scientists demonstrate that oo-pCCD and UpCCD become equivalent under specific conditions, allowing them to substitute leading oo-pCCD amplitudes directly into the UpCCD framework. This innovative approach enables the preparation of high-fidelity singlet states using remarkably shallow quantum circuits, circumventing the need for computationally expensive full Configuration Interaction calculations or complex circuit encoding methods.

The method avoids the optimization challenges inherent in Variational Quantum Eigensolver (VQE) approaches, offering a potentially more efficient route to accurate quantum simulations. Experiments focused on models of multiple-bond dissociation in ethene, ethyne, and dinitrogen, as well as one-dimensional Hubbard models at half-filling, demonstrating the versatility of the technique. Researchers successfully prepared states with high fidelity, significantly reducing the number of quantum gates required compared to existing methods. The team highlights that oo-pCCD scales favorably with system size, possessing O(N 2 ) amplitudes and O(N 3 ) time complexity, making it a potentially scalable solution for tackling increasingly complex quantum simulations. This approach promises to be a valuable tool for approximate preparation of singlet states, enhancing the capabilities of QPE and related quantum algorithms.

Unitary Coupled Cluster Simplifies Quantum State Preparation

Researchers have developed a novel method for preparing initial states for quantum computations, achieving high fidelity with significantly reduced computational cost. The team’s approach leverages the connection between orbital-optimized paired Coupled Cluster Doubles (oo-pCCD) theory and its unitary counterpart, Unitary pCCD (UpCCD), to create compact quantum circuits. The core of this advancement lies in recognizing that, under specific conditions, oo-pCCD and UpCCD become equivalent. By substituting leading oo-pCCD amplitudes into the UpCCD framework, scientists can efficiently prepare high-fidelity singlet states, essential for modeling electronic structures, using remarkably shallow quantum circuits.

Demonstrating the utility of this method, the researchers successfully determined the ground state energy of a stretched ethene molecule using Quantum Phase Estimation. Experiments reveal that this new technique surpasses existing methods in terms of efficiency and scalability. For instance, the team achieved the same state fidelity for a 14-atom hydrogen chain as achieved by more complex methods, but with a reduction of over 1000 times in the number of quantum gates required. This reduction in gate count is crucial for minimizing errors and enabling computations on near-term quantum devices. The findings demonstrate that the method is broadly applicable to various systems, including models of multiple-bond dissociation in ethene, ethyne, and dinitrogen, as well as one-dimensional Hubbard models. This innovative approach promises to accelerate progress in quantum chemistry and materials science by providing a practical and efficient means of preparing initial states for quantum algorithms. The ability to generate high-fidelity states with minimal resources opens new avenues for exploring complex quantum systems and designing novel materials with tailored properties.

Accurate QPE Initial States via Coupled Cluster

This research introduces a novel approach to preparing initial states for quantum algorithms, specifically Quantum Phase Estimation (QPE). The team demonstrates that by leveraging the orbital-optimized paired Coupled Cluster Doubles (oo-pCCD) method, and then transforming the resulting data into a Unitary Coupled Cluster Doubles (UpCCD) format, they can generate highly accurate initial states using relatively simple quantum circuits. The key finding is that the oo-pCCD and UpCCD approaches yield remarkably similar states, particularly when focusing on the most significant correlations within the system. This allows researchers to use the computationally efficient oo-pCCD method to generate data that can then be readily implemented in a quantum circuit via UpCCD, significantly reducing the complexity of state preparation.

The method was successfully tested on model systems representing multiple-bond dissociation in ethene, ethyne, and dinitrogen, as well as one-dimensional Hubbard models, demonstrating its broad applicability. Importantly, the team showed that using these UpCCD-prepared states as input for QPE algorithms leads to faster convergence and more accurate results compared to using more traditional initial states, such as Hartree-Fock approximations. Future work will likely focus on extending this approach to larger and more complex systems, and on exploring ways to improve the accuracy of the initial pCCD calculations. The team suggests that this method could be broadly applicable to approximate preparation of singlet states for QPE and related quantum algorithms, offering a pathway towards more efficient and accurate simulations of complex chemical and materials systems.