Quantum chemistry calculations on a trapped-ion quantum simulator (1803.10238v2)

Abstract: Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report on the experimental implementation of such an algorithm to solve a quantum chemistry problem, using a digital quantum simulator based on trapped ions. Specifically, we implement the variational quantum eigensolver algorithm to calculate the molecular ground state energies of two simple molecules and experimentally demonstrate and compare different encoding methods using up to four qubits. Furthermore, we discuss the impact of measurement noise as well as mitigation strategies and indicate the potential for adaptive implementations focused on reaching chemical accuracy, which may serve as a cross-platform benchmark for multi-qubit quantum simulators.

• The paper demonstrates a hybrid quantum-classical approach using the VQE algorithm on a trapped-ion platform to solve quantum chemistry problems.
• It compares JW and BK encoding methods applied to H2 and LiH simulations, noting practical trade-offs in Hamiltonian locality and error mitigation.
• The experimental results validate the simulator's potential while highlighting challenges like decoherence and gate fidelity for achieving chemical accuracy.

Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator

The paper "Quantum chemistry calculations on a trapped-ion quantum simulator" presents an experimental implementation of the Variational Quantum Eigensolver (VQE) algorithm to solve quantum chemistry problems, specifically focusing on calculating molecular ground state energies using a digital quantum simulator based on trapped ions. The authors explore this implementation by examining two simple molecules, emphasizing different encoding methods using up to four qubits.

The research is structured around the central idea that quantum-classical hybrid algorithms, such as the VQE, hold significant promise for near-term quantum computing applications. The authors detail the experimental setup, which employs a trapped-ion system capable of executing digital quantum simulations. In this setup, the VQE algorithm is deployed to calculate the ground state energies of molecular hydrogen (H2) and lithium hydride (LiH).

Key Methodologies:

1. Variational Quantum Eigensolver (VQE): VQE is a hybrid quantum-classical algorithm that combines quantum state preparation with classical optimization. It iteratively prepares a parameterized quantum state and adjusts parameters using a classical optimizer to minimize the expected energy concerning a given Hamiltonian.
2. Encoding Methods: The paper discusses two primary fermion-to-qubit mappings: Jordan-Wigner (JW) and Bravyi-Kitaev (BK), each with distinct advantages and computational overheads. The JW transformation results in $N$-local Hamiltonians, while the BK transformation yields $\log(N)$-local Hamiltonians.
3. Trapped-Ion Quantum Simulator: The experiment leverages a linear array of trapped ions with qubits encoded in electronic states. Quantum gates are implemented through laser manipulations to simulate the evolution of molecular quantum states.

Results and Discussion:

• H₂ and LiH Simulations: The authors successfully simulate the ground state energy of H₂ using both JW and BK encodings and LiH using the BK mapping. Measurement results are compared with theoretical predictions for validation.
• Decoherence and Error Mitigation: The paper evaluates the effects of decoherence, specifically focusing on measurement noise and suggests strategies for improvement. Adaptive error mitigation and encoding strategies in decoherence-free subspaces are employed to increase accuracy.
• Scalability and Practicality: The work highlights the potential for scalability of the VQE algorithm using trapped-ion platforms, given their intrinsic all-to-all qubit connectivity. However, challenges such as decoherence, gate fidelity, and measurement precision remain to be addressed for reaching chemical accuracy.

Implications and Future Directions:

The successful implementation of the VQE algorithm for quantum chemistry points to the growing potential of quantum technologies in computational chemistry. The research exemplifies how quantum simulators could tackle classically intractable problems by leveraging quantum mechanisms. Future research can focus on scaling these simulations to more complex systems, integrating error correction methods, and enhancing the algorithmic framework for better resource efficiency. Advanced techniques in quantum hardware and error mitigation, along with improvements in quantum algorithms, are expected to push the boundaries of what can be practically simulated using quantum computers in chemistry and material science.

Finally, this work provides a foundational demonstration for using quantum processors as tools for scientific research, setting a precedent for cross-platform benchmarks for multi-qubit quantum simulators that target practical chemical accuracy. The evolution of these techniques and devices promises substantial contributions to fundamental science, particularly in areas requiring detailed quantum mechanical simulation.