Unitary Partitioning Approach to the Measurement Problem in the Variational Quantum Eigensolver Method.

Area of Science:

• Quantum Computing
• Computational Chemistry
• Quantum Algorithms

Background:

• The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm used for estimating electronic energies.
• Current VQE implementations are limited by quantum hardware's inability to perform simultaneous measurements of non-commuting Hamiltonian terms.
• The number of measurement groups scales as N^4, restricting the size of quantum systems that can be studied.

Purpose of the Study:

• To develop a more efficient measurement strategy for the VQE algorithm.
• To overcome the limitations imposed by qubit-wise commuting groups in Hamiltonian partitioning.
• To enable the study of larger and more complex molecular systems using quantum computation.

Main Methods:

• A novel circuit formulation for VQE was developed using a partitioning of the system Hamiltonian into a linear combination of unitary operators.
• This approach allows for the simultaneous measurement of fully anticommuting terms within a single series of single-qubit measurements.
• The proposed method was numerically compared against traditional qubit-wise commutativity grouping strategies.

Main Results:

• The new unitary partitioning method enables the measurement of anticommuting Hamiltonian terms in a single circuit.
• Numerical simulations demonstrated an N-fold reduction in the number of measurable groups compared to previous methods.
• This significantly alleviates the measurement overhead in VQE calculations.

Conclusions:

• The proposed unitary partitioning offers a more efficient approach to Hamiltonian measurement in VQE.
• This advancement is expected to enhance the scalability of quantum algorithms for electronic structure calculations.
• The findings pave the way for tackling larger quantum chemistry problems on near-term quantum hardware.