Circuit compilation and hybrid computation using Pauli-based computation

In this repository we can find the Python code used to produce the results presented in our paper [https://quantum-journal.org/papers/q-2023-10-03-1126/].

This code uses different modules, each equipped with different classes, methods and functions to make things more readable and user friendly. Each module is suitably documented at the start for clarity. In principle, users need only open and make changes to Main.py.

Contact: fcrperes@onsager.ugr.es

Prerequisites: This code was written using the following versions:

• Python 3.7.10;
• numpy 1.20.1;
• matplotlib 3.3.4;
• 'qiskit-terra': '0.17.4', 'qiskit-aer': '0.8.2', 'qiskit-ignis': '0.6.0', 'qiskit-ibmq-provider': '0.13.1', 'qiskit-aqua': '0.9.1', 'qiskit': '0.26.2', 'qiskit-nature': None, 'qiskit-finance': None, 'qiskit-optimization': None, 'qiskit-machine-learning': None

Brief description: The modules supplied allow us to execute two different tasks (as described in our paper [https://quantum-journal.org/papers/q-2023-10-03-1126/]):

• Task 1: Efficient circuit compilation and weak simulation; to carry out this task one should open the Main.py module, change the number of virtual qubits, vq, to 0 and adjust the parameters of the function cc.run_pbc as desired;
• Task 2: Hybrid computation using virtual qubits and approximate strong simu- lation with maximum relative error ϵ; to perform this task one should open the Main.py module, change the number of virtual qubits, vq, to a number greater than 0, and adjust the parameters of the function cc.hybrid_pbc as desired.

Use instructions:

1. Make sure that the four Python modules (Main.py, input_prep_t1.py, input_prep_t2.py, and c_and_c.py) are all in the same directory in your computer;
2. Copy the input (.qasm) toy files supplied in this repository into a folder in your computer (or make your own files with suitable Clifford+T quantum circuits);
3. The files output by the code will be saved to a folder named "output" which will be found inside the folder where you have placed the input file or files;
4. In the Main.py file change the location of the input files to point to the correct location in your computer; change also the name of the input file(s) appropriately, and choose the desired name for the different output files. Adjust the parameters of cc.run_pbc or cc.hybrid_pbc depending on the simulation you want to run;
5. Open a terminal window in the directory where you have placed the Python modules and run the command: python Main.py;
6. Check the output files at the location that you have selected.

Tracking code versions:

1. First commit: the original version of the code.
2. Second commit: no changes to the original code, simple inclusion of the e-print no. in this file and in the string documentation of the python files.
3. Third commit: an improvement was made to the sampling complexity of the hybrid computation task (the theoretical explanation of this improvement can be seen in the final version of our article).
4. Fourth commit: an improvement was made in the algorithm for assessing the (in)dependence of the Paulis; this lead to an improvement of the overall complexity of our code as seen in the new version of our article.
5. Fifth commit: included the greedy algorithm proposed in our new paper [https://journals.aps.org/pra/abstract/10.1103/d3x5-cgky].
6. Sixth commit: minor bug fix in the greedy algorithm.
7. Seventh commit: postselecting classically decidable gadget measurements to 0.
8. Eighth commit: updating this document (inc. contact info).
9. Ninth commit: small fix of the postselection introduced in 7.
10. Tenth commit: small bug fix in method RPQproduct(self, P, Q) and in the sign correlation of dependent Paulis.

Copyright: Copyright (C) 2022 Filipa C. R. Peres

MIT License

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.