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NumQI

WARNING: no backward compatiblity until version 1.0.0 (TODO roadmap). Right now, feel free to ask questions on GitHub issue page.

numqi (pronounce: num-q-i) is a numpy-based quantum information package that makes quantum computing more accessible and fun for everyone. Whether you're just getting started or you're already deep into quantum computing, numqi has something for you. It's like a Swiss Army knife for quantum computing, packed with tools and features that help you simulate quantum systems, play around with quantum gates, and even tackle complex quantum information challenges. From creating and manipulating quantum states to exploring the mysteries of entanglement and beyond, numqi is your go-to resource for diving into the quantum world. And the best part? You don't need to be a quantum physicist to get started. So, let's embark on this quantum journey together with numqi at your side!

Quickstart

pip install numqi

Detect whether Bell state wiki is entangled or not using positive partial transpose (PPT) criteria.

import numqi
bell_state = numqi.state.Werner(d=2, alpha=1)
print(bell_state)
# [[ 0.   0.   0.   0. ]
#  [ 0.   0.5 -0.5  0. ]
#  [ 0.  -0.5  0.5  0. ]
#  [ 0.   0.   0.   0. ]]
print(numqi.entangle.is_ppt(bell_state, (2,2))) #True if seperable, False if entangled
# False

Let's try a "non-trival" quantum circuit (Five-qubit error correcting code)

import numpy as np
import numqi
circ = numqi.sim.Circuit()
for x in range(4):
    circ.H(x)
circ.cz(3, 4)
circ.cy(2, 3)
circ.cz(2, 4)
circ.cx(1, 2)
circ.cz(1, 3)
circ.cx(1, 4)
circ.cy(0, 2)
circ.cx(0, 3)
circ.cx(0, 4)

q0 = np.zeros(2**5, dtype=np.complex128)
q0[0] = 1
q1 = circ.apply_state(q0)

Module structure

project-structure

Core modules

  1. numqi.sim: numpy based quantum simulator wiki/quantum-simulator, support gradient back-propagation and variational quantum circuits, Clifford circuit simulator
  2. numqi.dicke: Dicke basis, bosonic states
  3. numqi.random: sample random quantum states, matrices, channels, etc.
  4. numqi.state: various quantum states, like Werner state, Bell state, etc. and their properties like entanglement measure, etc.
  5. numqi.gate: various quantum gate wiki/quantum-logic-gate, like Pauli gate (various representation), Clifford gate, etc.
  6. numqi.gellmann: convert matrix into gellmann basis and reversally wiki/gellmann wiki/generalized-gellmann
  7. numqi.channel: utilities related to quantum channel, like conversion between different representations of a quantum channel (Kraus operator, super-operator, Choi state, etc.) wiki/quantum-channel
  8. numqi.manifold: trivialzation of various smooth manifolds and quantum objects
    • smooth manifold: sphere, positive semi-definite matrix, special orthogonal / unitary group, Stiefel manifold etc.
    • quantum object: denotes quantum state, quantum gate, Hamiltonian, quantum channel etc.
  9. numqi.group: some basic utility for group theory wiki/group, like irreducible representation, symmetric group, Symplectic group over finite field Sp(2n, F2), etc.
  10. numqi.optimize: wrapper of scipy.optimize and SGD/Adam optimizers for manifold optimization
  11. numqi.matrix_space: Numerical range, linear space of matrices, geometric measure, hierarchical method, etc.
    • Quantifying Subspace Entanglement with Geometric Measures arxiv-link
  12. numqi.utils: some utility functions, like, calculate fidelity, purity, entropy etc.

Application modules

  1. numqi.entangle: detect entanglement wiki/quantum-entanglement
    • PPT (positive partial transpose)
    • convex hull approximation
    • Pure Bosonic extension arxiv-link
    • irreducible representation of symmetric extension doi-link
    • unextendible product state, bound extangled state, etc.
  2. numqi.maximum_entropy: relation between Hamiltonian, groud state, and marginal problem
    • Maximum entropy methods for quantum state compatibility problems arxiv-link
  3. numqi.qec: quantum error correction code (QECC) wiki
    • Variational learning for quantum error-correcting codes doi-link
    • circuits to encode some well-known QECC, like ((5,2,3)), ((8,8,3))
  4. numqi.unique_determine: unique determinedness in quantum state tomography
    • Variational Approach to Unique Determinedness in Pure-state Tomography arxiv-link
  5. numqi.query: quantum query
    • Variational learning algorithms for quantum query complexity arxiv-link
  6. numqi.optimal_control: optimal control for quantum system, e.g. finding the optimal control pulse to implement a quantum gate
    • Gradient ascent pulse engineering algorithm (GRAPE) (gradient ascent pulse engineering)

Generally, the application modules are implemented based on the core modules. For example, the numqi.entangle module use quite a lots of the module numqi.group and numqi.optimize. For those who are more interested in quantum information problems, you may directly dive into these specific modules. For those who are more interested in the underlying algorithms or math concepts, you may start from the core modules.

  1. QETLAB documentation github a matlab toolbox designed for quantum entanglement detection
  2. GeoTorch github
  3. geoopt github
  4. google/quantumlib google/quantumAI github openfermion stim
  5. pennylane documentation
  6. github/qustop github/toqito
  7. github/qutip
  8. github/pymanopt Python toolbox for optimization on Riemannian manifolds with support for automatic differentiation
  9. github/QGopt Riemannian optimization for quantum technologies
  10. qctrl
  11. github/cvxquad
  12. github/qiskit
  13. github/torchquantum
  14. github/pysme
  15. github/quantumgroup
  16. github/qibo
  17. github/quimb
  18. libcreme doi-link
  19. github/quantum-tomography