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Efficient Local Classical Shadow Tomography with Number Conservation.

Sumner N Hearth1, Michael O Flynn1, Anushya Chandran1

  • 1Department of Physics, <a href="https://ror.org/05qwgg493">Boston University</a>, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA.

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|August 23, 2024
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This summary is machine-generated.

We developed a new All-Pairs shadow protocol for quantum tomography in systems with number conservation laws, like ultracold atoms. This method efficiently reconstructs few-body observables using two-body gates and a linear-time algorithm.

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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.