Implementation of the Projective Quantum Eigensolver on a Quantum Computer.

Area of Science:

• Quantum computing
• Computational chemistry
• Condensed matter physics

Background:

• Quantum algorithms are essential for simulating complex quantum systems.
• Near-term quantum devices suffer from noise and errors, limiting their accuracy.
• Error mitigation techniques are vital for extracting reliable results from noisy quantum hardware.

Purpose of the Study:

• To evaluate the performance of the projective quantum eigensolver (PQE) on IBM quantum hardware.
• To assess the effectiveness of error mitigation techniques in improving PQE accuracy.
• To investigate PQE's capability in solving molecular and condensed matter problems.

Main Methods:

• Implementation of the projective quantum eigensolver (PQE) on IBM quantum processors.
• Application of error mitigation techniques, including error extrapolation, qubit tapering, and postselection.
• Utilized direct inversion of the iterative subspace algorithm for parameter optimization.

Main Results:

• Achieved molecular energies within 4 millihartree of exact values for a single-qubit H2 model.
• Recovered 99% of correlation energy for the 4-site transverse-field Ising model at its critical point.
• Identified stochastic noise and device inconsistencies as key limitations to accuracy.

Conclusions:

• PQE demonstrates potential for accurate quantum simulations on current hardware with error mitigation.
• Optimization algorithms can converge swiftly, but noise necessitates careful parameter update handling.
• Error extrapolation and qubit tapering are recommended for enhancing PQE experimental reliability.