Analysing the accumulation of Renyi-2 entropy density due to noise in quantum circuits.
Classical simulation of the Renyi-2 entropy density evolution of a 3-qubit hardware-efficient ansatz circuit under local depolarizing noise using the classical shadows protocol for entropy estimation.
This is the code used in relation to the article Entropy Density Benchmarking of Near-Term Quantum Circuits by Marine Demarty, James Mills, Kenza Hammam and Raul Garcia-Patron.
This repository provides some basic toolkit for analysing the accumulation of Renyi-2 entropy density in a noisy quantum circuit as a function of circuit depth (number of layers of gates) and system size (number of qubits). It is suitable for both quantum circuits run on classical simulations of noisy quantum computers, and those run on actual quantum hardware.
As a work example, we have implemented specific classes of quantum circuits and noise models for the classical simulator, however generalization is possible. For estimating the entropy, two protocols are implemented: a single-copy NISQ-friendly protocol and a two-copy scalable protocol.
More details about specific implementations can be found in the next subsections.
Quantum hardware
- Superconducting qubits
- Trapped ions
Classical simulator
- Hardware-efficient parameterized quantum circuit with RX, RY, CZ gates (superconducting)
- Hardware-efficient parameterized quantum circuit with GPI, GPI2, MS gates (ion traps)
- Local depolarizing noise with single-qubit and two-qubit gate error probabilities
$p_{\text{DP},1}$ and$p_{\text{DP},2}$ respectively - Amplitude damping noise with single-qubit and two-qubit gate error probabilities
$p_{\text{AD},1}$ and$p_{\text{AD},2}$ respectively - Readout error
$p_{\text{meas}}$
Renyi-2 entropy density/Purity estimation protocols that are implemented:
- Shadows: Pauli-basis classical shadows protocol REF. This protocol should be preferred for small system sizes, and for devices with low connectivity.
- SWAP: SWAP-test-based protocol REF. This protocol should be preferred for devices with sufficient connectivity (ideally all-to-all), and is suitable for systems of any sizes. However, note that the measurement circuit of this protocol introduces a higher systematic error in the entropy estimate than the classical shadows protocol due to the presence of two-qubit gates.
In addition to those protocols, it is possible to run a density matrix simulation of the quantum circuit and obtain the exact Renyi-2 entropy density or purity evolution of its output under a specified noise model:
- DensMat: exact density matrix simulation.
myqiskitenv.yml contains all necessary dependencies for running this code.
To obtain the Renyi-2 entopy density evolution using a specific protocol as a function of circuit depth, one needs to run 3 scripts for Shadows or SWAP from the Code folder:
get_entropy_[protocol]-PROCESS-measurements.pyis used to prepare the output of the target quantum circuit, add the measurement circuit of the specified protocol, and collect measurement outcomes. Those are stored in a csv file.get_entropy_[protocol]-PROCESS-metrics.pyloads the csv file, then implements the classical post-processing of the specified protocol to obtain a Renyi-2 entropy density estimate. This is stored in a json file.get_entropy_[protocol]-PLOT.pyloads the json file, then plots the corresponding entropy density evolution as a function of circuit depth and saves plots in the chosen results folder.
and only 2 scripts for DensMat:
get_entropy_[protocol]-PROCESS-metrics.pyis used to prepare the output of the target quantum circuit under some noise model, and obtain its exact Renyi-2 entropy density. This is stored in a json file.get_entropy_[protocol]-PLOT.pyloads the json file, then plots the corresponding entropy density evolution as a function of circuit depth and saves plots in the chosen results folder.