diffqc: Differentiable Quantum Circuit Simulator for Quantum Machine Learning

1. Overview

Note
This project started as diffq, but because of accidental name conflict, we changed name to diffqc.

diffqc is a python package providing differentiable quantum circuit simulator. The main target is quantum machine learning.

diffqc is built on JAX, so that it is

• GPU friendly,
• easily vectorized,
• differentiable, but
• supported environments are limited. (Ref. "Installation" section at JAX README)

2. Features

diffqc provides 2 types of operations, dense and sparse. Both have same operations and only internal representations are different.

2.1 dense operation

In dense operation, complex coefficients of all possible 2**nqubits states are traced. This is simple matrix calculation but requires exponentially large memory when nqubits is large.

2.2 sparse operation

Warning
sparse module is under depelopment, and is not ready to use.

In sparse operation, only neccessary states are traced. This might reduce memory requirements at large nqubits system, but it can be computationally inefficient.

2.3 Builtin Algorithm lib

Builtin algorithms are implemented at diffqc.lib. To support both dense and sparse operation, operation module is passed to 1st argument.

• GHZ(op, c: jnp.ndarray, wires: Tuple[int])
  • Create Greenberger-Horne-Zeilinger state [2]
  • |00...0> -> (|00...0> + |11...1>)/sqrt(2)
• QFT(op, c: jnp.ndarray, wires: Tuple[int])
  • Quantum Fourier Transform (without last swap) [3]
• QPE(op, c: jnp.ndarray, wires: Tuple[int], U: jnp.ndarray, aux: Tuple[int])
  • Quantum Phase Estimation [4]
  • wires: Eigen Vector
  • U: Unitary Matrix
  • aux: Auxiliary qubits. These should be |00...0>.

2.4 PennyLane Plugin

Warning
PennyLane plugin is planned, but is still under development, and is not ready yet.

PennyLane is a quantum machine learning framework. By using PennyLane, we can choose machine learning framework (e.g. TensorFlow, PyTorch) and real/simulation quantum device independently, and can switch relatively easy.

3. Example Usage

• example/00-circuit-basics.py
  • Basic Usage of diffqc
• example/01-qcl-flax.py
  • QCL[1] Classification of Iris with Flax
• example/02-cnn-like-qcl-flax.py
  • CNN-like QCL[1] Classification of Digits with Flax
• example/03-pennylane.py
  • PennyLane Plugin
• example/04-builtin-variational-circuit-centric.py
  • Builtin Variational Circuit: Circuit Centric Block described at [5]
  • According to [6], this is one of the best circuit.
• example/05-builtin-variational-josephson-sampler.py
  • Builtin Variational Circuit: Josephson Sampler described at [7]
  • According to [6], this is one of the best circuit.

4. References

• JAX
  • Official Site
  • Repository at GitHub
• PennyLane
  • Official Site
  • Repository at GitHub
• TensorFlow
  • Official Site
  • Repository at GitHub
• PyTorch
  • Official Site
  • Repository at GitHub
• Flax
  • Official Site
  • Repository at GitHub
• [1] K. Mitarai et al. "Quantum Circuit Learning", Phys. Rev. A 98, 032309 (2018)
  • DOI: https://doi.org/10.1103/PhysRevA.98.032309
  • arXiv: https://arxiv.org/abs/1803.00745
• [2] D. M. Greenberger et al., "Going Beyond Bell's Theorem", arXiv:0712.0921
  • arXiv: https://arxiv.org/abs/0712.0921
• [3] D. Coppersmith, "An approximate Fourier transform useful in quantum factoring", IBM Research Report RC19642
  • arXiv: https://arxiv.org/abs/quant-ph/0201067
• [4] A. Kitaev, "Quantum measurements and the Abelian Stabilizer Problem", arXiv:quant-ph/9511026
  • arXiv: https://arxiv.org/abs/quant-ph/9511026
• [5] M. Schuld et al., "Circuit-centric quantum classifiers", Phys. Rev. A 101, 032308 (2020)
  • DOI: https://doi.org/10.1103/PhysRevA.101.032308
  • arXiv: https://arxiv.org/abs/1804.00633
• [6] S. Sim et al., "Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms", Adv. Quantum Technol. 2 (2019) 1900070
  • DOI: https://doi.org/10.1002/qute.201900070
  • arXiv: https://arxiv.org/abs/1905.10876
• [7] M. R. Geller, "Sampling and scrambling on a chain of superconducting qubits", Phys. Rev. Applied 10, 024052 (2018)
  • DOI: https://doi.org/10.1103/PhysRevApplied.10.024052
  • arXiv: https://arxiv.org/abs/1711.11026