Efficient Quantum Readout Error Mitigation for Sparse Measurement Outcomes of Near-term Quantum Devices

libs_qrem is a Python package which executes efficient quantum readout error mitigation (QREM) written in C++/Cython. This package mitigates the readout errors in the 65-qubit measurement result of the GHZ state from ibmq_brooklyn in a few seconds.

• Time Complexity: $O(ns^2)$
• Space Complexity: $O(s^2)$ ( Can be reduced into $O(ns)$ )

Quick access to the usage: demonstration.ipynb

Raw histogram	Mitigated histogram

Installation

Requirements

• C++/Eigen: This can be done by downloading the Eigen package and allocating it as eigen folder under libs_qrem.
• Cython

Install via pip

pip install git+https://github.com/BOBO1997/libs_qrem

c.f.) Reinstall via pip

pip install --upgrade --force-reinstall git+https://github.com/BOBO1997/libs_qrem

Install manually

git clone https://github.com/BOBO1997/libs_qrem.git
cd libs_qrem
python setup.py install --record install_record.txt

Uninstall via pip

pip uninstall libs_qrem

Inplace build and clean

• build

python setup.py build_ext --inplace

• clean

rm -rf dist/ build/ libs_qrem.egg-info/ libs_qrem.cpython-38-darwin.so libs_qrem/*.cpp

Usage

Classes

There are four different classes that support four different QREM methods, respectively.

1. DeltaFilter: Apply inverse matrix for the vector elements in subspace + correct the vector by adding a correction vector "delta" which is approximated through the solution of Lagrange multiplier + apply SGS algorithm.
2. LeastNormFilter: Apply inverse matrix for the vector elements in subspace + apply the solution of the least norm problem to compute the closest vector that meets all elements are summed up to 1 + apply the SGS algorithm.
3. MooneyEtalFilter: Method by Mooney, White, Hill, Hollenberg, 2021 + apply SGS algorithm.
4. NationEtalFilter: Method by Nation, Kang, Sundaresan, Gambetta, 2021 + apply SGS algorithm.
5. IgnisFilter: Apply full inverse matrix under tensor product noise model (such as TensoredFilter in qiskit.ignis) + apply SGS algorithm.

where SGS algorithm is the algorithm proposed by Smolin, Gambetta, Smith, 2012.

Each class inherits the base class BaseFilter, which has the following methods in order to get access to the internal information.

• Matrices
  • reduced_A(): returns a list of list with double elements
  • normalized_reduced_A(): returns a list of list with double elements
  • reduced_inv_A(): returns a list of list with double elements
  • exact_one_norm_of_inv_reduced_A(): returns a double value
  • iterative_one_norm_of_inv_reduced_A(): returns a double value
  • exact_one_norm_of_reduced_inv_A(): returns a double value
• Mitigated vectors and vectors under the procedure
  • mitigated_hist(): returns a dict with str keys and double values
  • x_s(): returns a list with double elements
  • x_hat(): returns a list with double elements
  • x_tilde(): returns a list with double elements
• Sum of vectors
  • sum_of_x(): returns a double value
  • sum_of_x_hat(): returns a double value
  • sum_of_x_tilde(): returns a double value
• Other information
  • indices_to_keys_vector(): returns a list with str elements
  • times(): returns a dict with str keys and double values
  • expval(): returns a double value
  • mitigation_stddev(norm_type = "exact"): returns a double value

Examples

Each QREM filter in libs_qrem takes the number of qubits and calibration matrices in the following way.

from libs_qrem import LeastNormFilter
meas_filter = LeastNormFilter(n, meas_fitter.cal_matrices)

Passing a dictionary typed noisy probability distribution or noisy histogram to LeastNormFilter.apply() method, it returns a mitigated probability distribution.

mitigated_hist = meas_filter.apply(noisy_hist)

This apply function can also take as input qiskit.result.Result, qiskit.result.Counts, and their lists.

A simple example code can be found in demonstration.ipynb

from qiskit.circuit import QuantumRegister
# prepare calibration circuit (same as qiskit tutorial)

num_qubits = 4
qr = QuantumRegister(num_qubits)
mit_pattern = [[0], [1], [2], [3]] ### This indicates which sets of qubits to mitigate taking the correlated error into account.
### mit_pattern = [[0], [1], [2, 3]] ### correlated error is currently not supported (bug found).

# create quantum circuits for calibrating readout errors
from libs_qrem import tensored_meas_cal
qcs_qrem, _ = tensored_meas_cal(mit_pattern=mit_pattern, qr=qr, circlabel='mcal')

# run calibration circuit (same as qiskit tutorial) using the simulated fake backend
results_qrem = simulator_noisy.run(circuits=qcs_qrem,
                                   shots=5000).result()

from libs_qrem import TensoredMeasFitter
meas_fitter = TensoredMeasFitter(results_qrem, mit_pattern=mit_pattern)

# Create mitigator instance (corresponds to meas_fitter.filter in the tutorial code.)
# this is very similar to the usage of qiskit.ignis.mitigation modules 
# meas_filter = meas_fitter.filter
from libs_qrem import LeastNormFilter
meas_filter = LeastNormFilter(num_qubits, meas_fitter.cal_matrices)

# apply mitigation
# Let `noisy_hist` be a dict variable representing a noisy histogram obtained from `.get_counts()` method in `qiskit.result.Result` instance.
# e.g. `noisy_hist = {"000": 50, "101": 20, "111": 30}`
# Then you can mitigate it as follows.
mitigated_hist = meas_filter.apply(noisy_hist)

Publications

Paper

This package is based on the paper: Efficient Quantum Readout Error Mitigation for Sparse Measurement Outcomes of Near-term Quantum Devices by Bo Yang, Rudy Raymond, and Shumpei Uno.

Demonstrations in the paper are also stored here.

International Conferences

• Efficient Readout Error Mitigation Heuristic for Measurement Outcomes with Few States (Bo Yang, Rudy Raymond and Shumpei Uno) AQIS2021, Poster Session B22

Cite This Package

Please cite our paper when you use this package.

@article{PhysRevA.106.012423,
  title = {Efficient quantum readout-error mitigation for sparse measurement outcomes of near-term quantum devices},
  author = {Yang, Bo and Raymond, Rudy and Uno, Shumpei},
  journal = {Phys. Rev. A},
  volume = {106},
  issue = {1},
  pages = {012423},
  numpages = {14},
  year = {2022},
  month = {Jul},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.106.012423},
  url = {https://link.aps.org/doi/10.1103/PhysRevA.106.012423}
}

Package Contributors

• Bo Yang
• Dongjia Zhang