Value of the VQE

H.G.H. Dixon

Chenfeng Cao, Hiroshi Yano, Yuya O. Nakagawa

The variational quantum eigensolver (VQE) stands as a prominent quantum-classical hybrid algorithm for near-term quantum computers to obtain the ground states of molecular Hamiltonians in quantum chemistry. However, due to the noncommutativity of the Pauli operators in the Hamiltonian, the number of measurements required on quantum computers increases significantly as the system size grows, which may hinder practical applications of VQE. In this work, we present a protocol termed (JBM-VQE) to reduce the number of measurements and speed up the VQE algorithm. Our method employs joint Bell measurements, enabling the simultaneous measurement of the absolute values of all expectation values of Pauli operators present in the Hamiltonian. In the course of the optimization, JBM-VQE estimates the absolute values of the expectation values of the Pauli operators for each iteration by the joint Bell measurement, while the signs of them are measured less frequently by the conventional method to measure the expectation values. Our approach is based on the empirical observation that the signs do not often change during optimization. We illustrate the speed-up of JBM-VQE compared to conventional VQE by numerical simulations for finding the ground states of molecular Hamiltonians of small molecules, and the speed-up of JBM-VQE at the early stage of the optimization becomes increasingly pronounced in larger systems. Our approach based on the joint Bell measurement is not limited to VQE and can be utilized in various quantum algorithms whose cost functions are expectation values of many Pauli operators. Published by the American Physical Society 2024

Qingfeng Wang, Ming Li, Christopher R. Monroe +1 more

Akshay Uttarkar, Vidya Niranjan

Abstract Quantum computing in biology is one of the most rapidly evolving field of technology. Protein folding is one of the key challenges which requires accurate and efficient algorithms with a quick computational time. Structural conformations of proteins with disordered regions need colossal amount of computational resource to map its least energy conformation state. In this regard, quantum algorithms like Variational quantum eigensolver (VQE) are applied in the current research work to predict the lowest energy value of 50 peptides of 7 amino acids each. VQE is initially used to calculate the energy values over which Variational Quantum Optimization is applied via Conditional Value at Risk (CVaR) over 100 iterations of 500000 shots each to obtain least ground state energy value. This is compared to the molecular dynamics-based simulations of 50 nanoseconds each to calculate the energy values along with the folding pattern. The results suggest efficient folding outcomes from CvaR-VQE compared to MD based simulations. With the ever-expanding quantum hardware and improving algorithms the problem of protein folding can be resolved to obtain in depth insights on the biological process and drug design.

Alex Jason Martin, J. W. Martin

Abstract An exciting application of quantum computers is the simulation of physical systems. The goal of the variational quantum eigensolver (VQE) is to approximate the ground state of a quantum system. This is done by applying the variational principle, finding the expectation value of the Hamiltonian in an ansatz quantum state, then minimizing this expectation value with respect to the parameters of the ansatz. In the VQE, the calculation of the expectation value in the ansatz state is done on a quantum computer, while the adjustment of the parameters of the ansatz to find the minimum energy is done classically. In this article we study the spin–spin coupling H = A S → 1 · S → 2 . This coupling appears in the hyperfine interaction of atomic systems, resulting from the interaction of the electronic spin with the nuclear spin. The form of the interaction satisfies the requirements of the VQE, that the Hamiltonian must be expressed as sums of products of Pauli matrices, making it an interesting trial system for a quantum computer. In our calculation technique, the expectation value is implemented using two qubits on a quantum computer. The ansatz state is simplified to a single free parameter, which is then optimized classically. The algorithm converges rapidly, and the correct ground state is deduced. This serves as a useful example of implementing the VQE to solve a physically realizable problem in quantum mechanics.

Mikita Vostry