Ground State Energy of He molecule Using a Four-Qubit Photonic Processor with the Variational Quantum Eigensolver (2504.07568v2)

Abstract: To understand the properties and interactions of materials, and determining the ground state energies is one of the important challenges in quantum chemistry, materials science, and quantum mechanics, where quantum computing can play an important role for studying the properties of materials. In this study, we have explored the quantum processor application to compute the He molecule ground state energy which utilizes the Variational Quantum Eigensolver (VQE) algorithm. In here, we have implemented VQE on a state-of-the-art quantum processor, optimizing a parameterized quantum circuit to minimize the energy expectation value of the He molecule's Hamiltonian on the four qubits processor. The obtained results of this work show a significant improvement in accuracy compared to classical computational methods, such as Hartree-Fock and density functional theory, which demonstrate the compute potential of quantum algorithms in quantum many-body problems. Thus, these results demonstrate the advantages of quantum computing in achieving high accuracy in simulations of molecular and material properties, and pave the way for future applications in more complex systems. This work highlights the potential of quantum processors in the fields of quantum chemistry, computational physics, and data science.

Overview of Quantum Computing Strategies for Helium Ground State Energy Calculation

This paper presents an important milestone in quantum computing, specifically focusing on computational quantum chemistry of the helium molecule ground state energy. Using a four-qubit photonic processor, the authors employ the Variational Quantum Eigensolver (VQE) algorithm—a hybrid quantum-classical approach known for efficiently tackling quantum many-body problems. The research highlights improvements in accuracy compared to classical computational methods, such as Hartree-Fock and Density Functional Theory (DFT).

Within the domain of quantum chemistry, the calculation of ground state energies is a critical task. Traditional methods used for these calculations face limitations, particularly in terms of computational cost and accuracy as the complexity of the target systems increases. The advent of quantum computing, with algorithms like VQE, offers promising solutions by leveraging the inherent quantum properties of processors.

Methodological Insights

The paper meticulously describes the transformation and representation of the helium molecule's Hamiltonian. Starting from the first-quantized Hamiltonian, which defines the system by electron positions and momenta, the authors translate this into a second-quantized form using creation and annihilation operators. Further, the Jordan-Wigner transformation maps these operators into spin (Pauli) operators, rendering them suitable for implementation on quantum computers.

For computation, the research proposes using specific quantum circuits involving Hadamard gates, CNOT gates, and complex Mach-Zehnder interferometers. These configurations are robust for generating superposition, ensuring entanglement between qubits, and facilitating phase adjustments necessary for photonic quantum processors. The unitary matrix and R_z gate discussed are vital for astronautical manipulations within the circuit.

Results and Implications

The implementation of the proposed quantum circuit on a photonic processor demonstrates notable efficacy, achieving convergence of energy values across iterations, as evidenced by computational simulations. Fidelity metrics, along with probability density functions of measured energies, underscore the reliability and precision of the approach.

One highlighted aspect is the theoretical foundation and computation of matrix permanents essential for simulating quantum photonic processors. Accurate calculations of these permanents, efficiently approached by Ryser's method, enable predictions of Fock state output probabilities—a critical component in quantum optic systems.

Comparison and Evaluation

The research compares its findings with prior studies focusing on superconducting and trapped-ion qubit systems, underscoring distinctions created by using photonic quantum processors. The custom RealAmplitudes and photonic circuits employed demonstrate significant advancements over traditional ansatzes, exhibiting superior scalability and efficiency.

Conclusion and Future Prospects

This work substantially advances the use of quantum computing in solving quantum chemistry problems, establishing quantum processors as potent tools for precise molecular simulations. The insights gained point towards future applications in increasingly complex systems. With further technological refinement, quantum computing could become integral in various academic and practical domains, confronting challenges that classical computing struggles to surmount.

Given these encouraging findings, ongoing research could explore extensions of quantum algorithms and enhancements in processor capabilities to tackle larger systems, potentially accelerating developments across computational physics and data science. Furthermore, considering quantum advantage in molecular simulations, integrating quantum computing strategies with existing frameworks in material sciences may catalyze transformative advancements beyond current computational limitations.