This Python package is a toolkit that can help with the analysis of multi-qubit magic states (e.g. their rank and related decompositions). The code originated to support the research for my Master's Thesis at UT Austin: CCZ Magic.
Universal quantum computation can be achieved with a gate set that includes a generating set of Clifford gates and at least one non-Clifford gate. When it comes to classically simulating quantum computation, Clifford gates generate an important class of circuits known as stabilizer circuits, which are efficiently simulable. Stabilizer simulators can be extended to support universal quantum computation by using magic state injection gadgets and magic state decomposition. The computational scaling directly relates to the exact stabilizer rank, χ, of the magic state, which is the minimum number of stabilizer states in superposition that are necessary to represent the state.
We show that decompositions of Clifford magic states of the form |D⟩ = D|+⟩^{⊗n}, where D is a diagonal circuit composed of Z, CZ, and CCZ gates, have χ = 2 for n ≤ 5. We also establish that all CCZ circuits of n ≤ 5 qubits are Clifford equivalent to k ≤ 2 CCZ circuits. These results provide a new lower-bound for the complexity of simulating Clifford+CCZ circuits in general. We suggest the use of a state-injection gadget of |D⟩ in contrast to the naïve approach of multiple state-injection gadgets of individual |CCZ⟩ states. Since extended stabilizer simulators have a gadget-based method of simulation, this approach can improve classical simulation of quantum computation when using a Clifford+CCZ gate set.
from stabilizer_states import StabilizerStates
from stabilizer_toolkit.decompositions import rank2, validate_decompositions
from stabilizer_toolkit.magic_states import enumerate_ccz
S3 = StabilizerStates(3)
_, CCZ, _, _ = next(enumerate_ccz(3))
decompositions, coeffs = rank2.search_all_stabilizer_states(CCZ, S3)
validate_decompositions(CCZ, decompositions, coeffs)For more usage take a look at the example notebooks.
The package is available on pypi and installable via pip:
pip install stabilizer-toolkit You may also want to install the optional stabilizer-states package,
which provides the stabilizer datasets for n <= 6, then you can install with the states extras:
pip install "stabilizer-toolkit[states]" There are also additional helpers that require the use of additional libraries, so you may also want to install those:
pip install "stabilizer-toolkit[states,helpers]" If you'd like to work with a development copy, then clone this repository and install via
poetry:
poetry install -vvv --with dev --all-extras