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Correct CDR and VNCDR acronyms in example (#2479)
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* Correct CDR and VNCDR acronyms

* Update vnCDR with correct capitalization
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bdg221 authored Aug 23, 2024
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In this tutorial, we employ ZNE, CDR, and VNCDR mitigation techniques to address errors in the simulation of the 1-D Transverse-Longitudinal Ising model using Mitiq. It is important to note that the results presented here are not original, but rather an attempt to reproduce some of the findings outlined in the paper available at {cite}`Sopena_2023_Quantum`.

One of the primary applications of quantum computers is simulating dynamics in many-body systems. This is particularly significant because as the system size increases, the number of parameters grows exponentially. As a result, classical computers struggle to efficiently simulate such dynamics. However, we are currently in the Noisy Intermediate-Scale Quantum (NISQ) era, which means we lack the necessary resources for fault-tolerant quantum computing. Nevertheless, Quantum Error Mitigation techniques have been developed to address noise using minimal qubit resources. These techniques harness the power of classical computers to handle and mitigate quantum noise. In quantum simulation, our main interest is usually finding the average value of an observable. However, NISQ hardware can only provide us with noisy results. In mitigation techniques, we combine these noisy results with the computational power of classical computers to combat the noise. In this tutorial, we specifically utilize Zero Noise Extrapolation (ZNE), Corrected Dynamical Reduction (CDR), and Variational Noise-Corrected Dynamical Reduction (VNCDR) techniques to mitigate errors in the simulation of a 1-D Ising Hamiltonian.
One of the primary applications of quantum computers is simulating dynamics in many-body systems. This is particularly significant because as the system size increases, the number of parameters grows exponentially. As a result, classical computers struggle to efficiently simulate such dynamics. However, we are currently in the Noisy Intermediate-Scale Quantum (NISQ) era, which means we lack the necessary resources for fault-tolerant quantum computing. Nevertheless, Quantum Error Mitigation techniques have been developed to address noise using minimal qubit resources. These techniques harness the power of classical computers to handle and mitigate quantum noise. In quantum simulation, our main interest is usually finding the average value of an observable. However, NISQ hardware can only provide us with noisy results. In mitigation techniques, we combine these noisy results with the computational power of classical computers to combat the noise. In this tutorial, we specifically utilize Zero Noise Extrapolation (ZNE), Clifford Data Regression (CDR), and Variable-Noise Clifford Data Regression (vnCDR) techniques to mitigate errors in the simulation of a 1-D Ising Hamiltonian.

The Hamiltonian for the quantum one-dimensional Ising model, with both transverse and longitudinal fields, can be expressed as follows:

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