QOLE

The Quantum Operations Lazy Evaluator is an easy-to-use Software Development Kit for executing quantum circuits in JavaScript. Behind its simplistic, Qiskit-like interface, lies a simulation backend based on Quantum Multiple-Valued Decision Diagrams (QMDDs).

Whether you need to incorporate reversible/quantum algorithmic functionality to your JS project, or you want to benchmark the performance of QMDDs, QOLE is the tool for you.

Usage

As previously stated, QOLE's interface employs a pattern very similar to Qiskit:

```JavaScript const qc = new QuantumCircuit(5);

qc.initialize('01111');
qc.h(0);
qc.cx(0, 1);
qc.cswap(3, 2, 1, '0');

```

The declarative style and index-based qubit logic remains intact, while also introducing new compact, quality-of-life syntactic sugars, like method-chaining:

JavaScript const qc = new QuantumCircuit(3) .h(0) .cx(0, 1) .cx(1, 2);

QOLE currently supports the following gate set: X, Y, Z, H, S, T, CX, CY, CZ, CH, CS, CCX, CCS, SWAP, CSWAP, MCX

notably allowing for both reversible and universal quantum computation. More gates to come.

Output can be extracted in two ways; the full statevector can be parsed iteratively through a lazy Generator object:

```JavaScript // lazy parsing for (const { state, re, im } of qc.statevector()) ...

// can also be force-loaded in memory
const sv = [...qc.statevector()];

```

which circumvents the exponential overhead of representing a full statevector in-memory. A shot-based method returning counts by sampling the internal QMDD diagram is also offered:

JavaScript const counts = qc.sample(10_000); console.log(counts.get('11010')?.occurrences); // counts for |11010> console.log(counts.get('11010')?.re); // also the amplitude of |11010> console.log(counts.get('11010')?.im); // received for free

Shot-based sampling also yields the theoretical amplitudes of the occurred basis states "for free".

Installation (NOTE: Not yet operational)

You can install QOLE as a standalone package through NPM:

npm install qole From here, you can access the QuantumCircuit class directly and get to work

JavaScript import { QuantumCircuit } from 'qole';

or you can peer into the implementation details through the modules 'qole.gates', 'qole.qmdd' and 'qole.complex'.

QMDD Backend

The actual simulation is done through these Decision Diagrams. For an initial introduction to QMDDs, please refer to Zulehner and Wille, arXiv:1707.00865 (2017).

This project acts as a mini-review of the topic, merging together implementation details scattered throughout the literature. Specifically, the main sources followed are:

• A. Zulehner and R. Wille. "Advanced Simulation of Quantum Computations". arXiv:1707.00865 (2017)
• R. Wille et al. "Decision Diagrams for Quantum Computing". In: Topaloglu, R.O. (eds) Design Automation of Quantum Computers. Springer, Cham. https://doi.org/10.1007/978-3-031-15699-1_1
• A. Sander et al. "Stripping Quantum Decision Diagrams of their Identity". arXiv:2406.11959 (2024)
• D. M. Miller et al. "A Decision Diagram Package for Reversible and Quantum Circuit Simulation". 2006 IEEE International Conference on Evolutionary Computation, Vancouver, BC, Canada, 2006, pp. 2428-2435, doi: 10.1109/CEC.2006.1688610
• P. Niemann et al. “Efficient Construction of QMDDs for Irreversible, Reversible, and Quantum Functions”. International Workshop on Reversible Computation (2017)
• P. Niemann et al. "On the “Q” in QMDDs: Efficient Representation of Quantum Functionality in the QMDD Data-Structure". In: Dueck, G.W., Miller, D.M. (eds) Reversible Computation. RC 2013. Lecture Notes in Computer Science, vol 7948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38986-3_11
• S. Hillmich et al. "Just Like the Real Thing: Fast Weak Simulation of Quantum Computation". 2020 57th ACM/IEEE Design Automation Conference (DAC), San Francisco, CA, USA, 2020, pp. 1-6, doi: 10.1109/DAC18072.2020.9218555
• D. Goodman et al. "Quantum logic circuit simulation based on the QMDD data structure." Int’l Reed-Muller Workshop (2007)
• A. Zulehner et al. "Accuracy and Compactness in Decision Diagrams for Quantum Computation". 2019 Design, Automation & Test in Europe Conference & Exhibition (DATE), Florence, Italy, 2019, pp. 280-283, doi: 10.23919/DATE.2019.8715040

while also consulting the rest of the bibliography, as well as the implementation in MQT, for further optimization techniques. A full documentation explaining the entire QMDD implementation is in the works.

Contributing

Please refer to CONTRIBUTING.md.

Citation

If you use this project in your research, kindly consider citing it as:

Asimakis Kydros. (2025). QOLE: A QMDD-based Quantum Circuit Simulator (Version 2.0.0) [Computer software]. https://github.com/asimakiskydros/QOLE

Licence

This project is licensed under the Mozilla Public License 2.0. You are free to use, modify, and distribute this code as long as any modifications to MPL-licensed files are also distributed under the same license.