Ground-state energy estimation of the water molecule on a trapped ion quantum computer (1902.10171v2)

Abstract: Quantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure, simulating strongly-interacting electron systems, and modeling aspects of material function. While substantial theoretical advances have been made in mapping these problems to quantum algorithms, there remains a large gap between the resource requirements for solving such problems and the capabilities of currently available quantum hardware. Bridging this gap will require a co-design approach, where the expression of algorithms is developed in conjunction with the hardware itself to optimize execution. Here, we describe a scalable co-design framework for solving chemistry problems on a trapped ion quantum computer, and apply it to compute the ground-state energy of the water molecule. The robust operation of the trapped ion quantum computer yields energy estimates with errors approaching the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics.

• The paper achieves ground-state energy estimation of water using a trapped-ion quantum computer and a VQE algorithm with a UCC ansatz.
• The methodology integrates hardware and algorithm co-design, leveraging all-to-all connectivity to minimize error overhead.
• Results demonstrate energy accuracy within approximately 1.6e-3 Hartree, paving the way for practical quantum chemistry applications.

Ground-State Energy Estimation of the Water Molecule on a Trapped Ion Quantum Computer

The paper "Ground-state energy estimation of the water molecule on a trapped ion quantum computer" presents an experiment leveraging a trapped-ion quantum computer to estimate the ground-state energy of a water molecule ($\text{H}_2 \text{O}$). This research bridges the gap between theoretical advances in quantum algorithms and the practical limitations of current quantum hardware, particularly in the field of quantum chemistry simulations, which require high accuracy that classical methods struggle to achieve due to exponential scaling in computational resources.

Methodology

The paper employs a co-design framework optimized for trapped-ion quantum hardware. Optimization strategies encompass both algorithmic and hardware considerations to minimize error while conserving computational resources. A particular focus is on quantum chemistry's variational quantum eigensolver (VQE) methods, utilizing a unitary coupled-cluster (UCC) ansatz with first-order Trotterization. The choice of the trapped-ion system capitalizes on its inherent characteristics, such as all-to-all connectivity, which eliminates the overhead common in other architectures requiring additional quantum gates for qubit reordering and connectivity limitations.

Key Numerical Results

The research demonstrated practical quantum circuits for computing the ground-state energy of water with accuracy approaching chemical precision (within approximately 1.6e-3 Hartree). The trapped-ion quantum computer achieved a close approximation of the desired energy level without employing complex error mitigation techniques. This performance marks a significant achievement in NISQ-era computers, demonstrating near-term applicability of quantum systems for real-world computational chemistry problems.

Implications and Future Directions

The implications of this paper are multi-faceted. Practically, this work paves the way for more accurate computational methods in chemical and materials engineering, potentially replacing costly experimental procedures with simulations. Theoretically, the co-design principles demonstrated could be adapted across different quantum computer architectures as they evolve.

Looking forward, increasing the number of qubits and improving their fidelity will enable the simulation of more complex molecular systems. Additionally, refining error correction techniques and exploring algorithmic co-design further will push the envelope of what current and near-future quantum computers can achieve. As trapped-ion and other quantum technologies advance, they promise to release their full potential, solving problems beyond the reach of even the most powerful classical computers available today.

The paper structurally executes an insightful blend of cutting-edge quantum technology application and theoretical optimization that anticipates pushing forward the practical boundaries of quantum computing in chemical applications. These developments underscore the necessity for continuous co-design approaches, tailored to harness the unique capabilities of existing quantum computing technologies effectively.