Hamiltonian-Driven Shadow Tomography of Quantum States

02/19/2021
by   Hong-Ye Hu, et al.
0

Classical shadow tomography provides an efficient method for predicting functions of an unknown quantum state from a few measurements of the state. It relies on a unitary channel that efficiently scrambles the quantum information of the state to the measurement basis. Facing the challenge of realizing deep unitary circuits on near-term quantum devices, we explore the scenario in which the unitary channel can be shallow and is generated by a quantum chaotic Hamiltonian via time evolution. We provide an unbiased estimator of the density matrix for all ranges of the evolution time. We analyze the sample complexity of the Hamiltonian-driven shadow tomography. We find that it can be more efficient than the unitary-2-design-based shadow tomography in a sequence of intermediate time windows that range from an order-1 scrambling time to a time scale of D^1/6, given the Hilbert space dimension D. In particular, the efficiency of predicting diagonal observables is improved by a factor of D without sacrificing the efficiency of predicting off-diagonal observables.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/12/2019

Bell Diagonal and Werner state generation: entanglement, non-locality, steering and discord on the IBM quantum computer

We shortly review Bell-diagonal and Werner states of two quantum bits an...
research
05/30/2022

TimeEvolver: A Program for Time Evolution With Improved Error Bound

We present TimeEvolver, a program for computing time evolution in a gene...
research
06/08/2023

Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltonian

We consider the prediction of the Hamiltonian matrix, which finds use in...
research
09/07/2022

Learning Distributions over Quantum Measurement Outcomes

Shadow tomography for quantum states provides a sample efficient approac...
research
07/29/2022

Fermionic tomography and learning

Shadow tomography via classical shadows is a state-of-the-art approach f...
research
08/08/2019

Hiddenly Hermitian quantum models: The concept of perturbations

In conventional Schrödinger representation the unitarity of the evolutio...
research
09/01/2018

The Optimization Problem of Quantum Discord In the Language of Correlated Observables

The general zero discord condition is asymmetric in the way that it allo...

Please sign up or login with your details

Forgot password? Click here to reset