Efficient Local Classical Shadow Tomography with Number Conservation

Area of Science:

• Quantum information science
• Condensed matter physics
• Ultracold atomic systems

Background:

• Shadow tomography classically describes quantum states using random measurements.
• Existing single-body shadow protocols are efficient but fail for systems with number conservation.

Purpose of the Study:

• To propose and analyze a novel local shadow protocol for quantum systems with number conservation laws.
• To enable efficient reconstruction of few-body observables in such systems.

Main Methods:

• Developed the All-Pairs protocol using one layer of two-body gates.
• Derived a linear-time postprocessing algorithm exploiting permutation symmetry.
• Applied the protocol to hardcore bosons and spinless fermions in any spatial dimension.

Main Results:

• The All-Pairs protocol reconstructs arbitrary few-body observables with poly(V) samples.
• Demonstrated proof-of-principle reconstruction of two- and four-point functions.
• Successfully applied to a paired Luttinger liquid of hardcore bosons.

Conclusions:

• The All-Pairs protocol overcomes limitations of single-body shadow methods for conserved systems.
• This work provides a practical tool for quantum state characterization in ultracold atoms.
• The developed algorithm offers efficient postprocessing for quantum tomography.