Reconstructing Quantum States Using Basis-Enhanced Born Machines
- URL: http://arxiv.org/abs/2206.01273v1
- Date: Thu, 2 Jun 2022 19:52:38 GMT
- Title: Reconstructing Quantum States Using Basis-Enhanced Born Machines
- Authors: Abigail McClain Gomez, Susanne F. Yelin, Khadijeh Najafi
- Abstract summary: We show that a Born machine can reconstruct pure quantum states using projective measurements from only two Pauli measurement bases.
We implement the basis-enhanced Born machine to learn the ground states across the phase diagram of a 1D chain of Rydberg atoms.
The model accurately predicts quantum correlations and different observables, and system sizes as large as 37 qubits are considered.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Rapid improvement in quantum hardware has opened the door to complex
problems, but the precise characterization of quantum systems itself remains a
challenge. To address this obstacle, novel tomography schemes have been
developed that employ generative machine learning models, enabling quantum
state reconstruction from limited classical data. In particular,
quantum-inspired Born machines provide a natural way to encode measured data
into a model of a quantum state. Born machines have shown great success in
learning from classical data; however, the full potential of a Born machine in
learning from quantum measurement has thus far been unrealized. To this end, we
devise a complex-valued basis-enhanced Born machine and show that it can
reconstruct pure quantum states using projective measurements from only two
Pauli measurement bases. We implement the basis-enhanced Born machine to learn
the ground states across the phase diagram of a 1D chain of Rydberg atoms,
reconstructing quantum states deep in ordered phases and even at critical
points with quantum fidelities surpassing 99%. The model accurately predicts
quantum correlations and different observables, and system sizes as large as 37
qubits are considered. Quantum states across the phase diagram of a 1D XY spin
chain are also successfully reconstructed using this scheme. Our method only
requires simple Pauli measurements with a sample complexity that scales
quadratically with system size, making it amenable to experimental
implementation.
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