This package efficiently simulates quantum circuits that don't generate a lot of superposition in the computational basis. In other words, they are few basis states to keep track of. Many common quantum gates, such as X, Z, S, CX, CZ along with several non-Clifford gates such as T or CCZ map each computational state to a single computational state, i.e. they are not branching. If there are few branching gates, such as the Hadamard gate H, the final state can be computed efficiently, since the state is effectively very sparse. Computationally, the complexity grows exponentially with the number of H gates, both in time and space.
SparseStates is a 
pkg> add <local_path>
where <local_path> is the path to the downloaded repository.
To generate a quantum register with two qubits initialized in the |00⟩ state, we just have do the following
using SparseStates
state_initial = SparseState(2)SparseStates are concrete types of AbstractDict, but should behave like AbstractArrays for basic algebraic manipulations.
We can then generate a quantum circuit
circuit = H(1) * CX(1, 2)Gates can be defined to act on multiple qubits simultaneously, such as CX([(1, 2), (3, 4)] or equivalently CX([1, 3], [2, 4]).
Let's now apply it to the state
state_final = circuit(state_initial)We can also use Julia's built-in pipe operator |> to write the more suggestive
state_final = state_initial |> circuitA variety of common gates are supported as well as quantum channels such as Measure and Reset.
Notice that in these cases a measurement outcome is chosen stochastically, so the result may differ between simulations.
In such cases one has to take over multiple simulations, for example
using LinearAlgebra
shots = 100
outcomes = [abs2(dot(state_initial, Reset(2), state_final)) for _ in 1:shots]
sum(outcomes) / shotsThis package is compatible with Julia 1.10 and above.