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libs_qrem is a python package written in C++/Cython that executes quantum readout error mitigation (QREM) efficiently even for large measurement results.

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# 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](https://github.com/BOBO1997/libs_qrem/blob/main/demonstration.ipynb)

Raw histogram             |  Mitigated histogram
:-------------------------:|:-------------------------:
![raw histogram](https://github.com/BOBO1997/libs_qrem/blob/main/figures/fig_hist_ghz4_raw.png)  |  ![mitigated histogram](https://github.com/BOBO1997/libs_qrem/blob/main/figures/fig_hist_ghz4_mitigated.png)

# Installation

## Requirements
- [C++/Eigen](https://eigen.tuxfamily.org/index.php?title=Main_Page): This can be done by downloading the Eigen package and allocating it as `eigen` folder under `libs_qrem`.
- [Cython](https://cython.org/)

## Install via pip
```sh
pip install git+https://github.com/BOBO1997/libs_qrem
```

c.f.) Reinstall via pip
```sh
pip install --upgrade --force-reinstall git+https://github.com/BOBO1997/libs_qrem
```

## Install manually
```sh
git clone https://github.com/BOBO1997/libs_qrem.git
cd libs_qrem
python setup.py install --record install_record.txt
```

## Uninstall via pip

```sh
pip uninstall libs_qrem
```

## Inplace build and clean

- build
```sh
python setup.py build_ext --inplace
```

- clean
```sh
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](https://arxiv.org/abs/2101.08946) + apply SGS algorithm.
4. `NationEtalFilter`: Method by [Nation, Kang, Sundaresan, Gambetta, 2021](https://arxiv.org/abs/2108.12518) + apply SGS algorithm.
5. `IgnisFilter`: Apply full inverse matrix under tensor product noise model (such as `TensoredFilter` in [qiskit.ignis](https://github.com/Qiskit/qiskit-ignis)) + apply SGS algorithm.

where SGS algorithm is the algorithm proposed by [Smolin, Gambetta, Smith, 2012](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.070502).

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.
```py
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.
```py
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](https://github.com/BOBO1997/libs_qrem/blob/main/demonstration.ipynb)

```py
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](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.106.012423) by Bo Yang, Rudy Raymond, and Shumpei Uno.

Demonstrations in the paper are also stored [here](https://github.com/BOBO1997/master_thesis/tree/main/test_libs_qrem).

## International Conferences

- Efficient Readout Error Mitigation Heuristic for Measurement Outcomes with Few
States (Bo Yang, Rudy Raymond and Shumpei Uno) [AQIS2021, Poster Session B22, September 2021](http://aqis-conf.org/2021/)
([Best student poster award](https://aqis-conf.org/2021/best-student-poster-award-winner/))

## Cite This Package

Please cite [our paper](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.106.012423) 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](https://github.com/BOBO1997)
- [Dongjia Zhang](https://github.com/tokatoka)

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