Tangent Space Excitation Ansatz for Quantum Circuits

Area of Science:

• Quantum Computing
• Quantum Many-Body Physics

Background:

• Computing excitation spectra is key for demonstrating quantum device utility.
• Current noisy quantum devices are advancing towards the 'megaquop' regime.

Purpose of the Study:

• Introduce a novel tangent space excitation ansatz for quantum circuits.
• Improve the accuracy and number of excited states computed compared to existing algorithms.

Main Methods:

• Developed a tangent space excitation ansatz inspired by quasiparticle picture and tensor networks.
• Increased circuit depth by one layer to construct tangent space around variational optimum.
• Implemented using the Hadamard test.

Main Results:

• Captured massive low-energy single-particle states.
• Significantly improved number of excited states and accuracy with similar computational cost.
• Demonstrated ansatz in both one and two dimensions.

Conclusions:

• The tangent space excitation ansatz is a scalable and suitable approach for current quantum processors.
• This method offers a distinct mechanism from existing excitation ansatz, avoiding their limitations.