Boolean simulation of a circuit, for testing and debugging purposes. Input a classical circuit, and output the corresponding boolean function. This will fail with an error if the circuit contains a gate not acting within the computational basis, or if some assertion is not met.

Unlike run_classical_unary, this can be applied to a circuit-generating function in curried form with n arguments, for any n ≥ 0. The resulting boolean function then will also have n arguments.

The type of this heavily overloaded function is difficult to read. In more readable form, it has all of the following types:

run_classical_generic :: (QCData qa) => Circ qa -> BType qa
run_classical_generic :: (QCData qa, QCData qb) => (qa -> Circ qb) -> BType qa -> BType qb
run_classical_generic :: (QCData qa, QCData qb, QCData qc) => (qa -> qb -> Circ qc) -> BType qa -> BType qb -> BType qc

and so forth.

Efficiently simulate a Quipper circuit that consists entirely of Clifford group operators, using the stabilizer formalism.

Inputs a quantum circuit, and outputs a corresponding probabilistic boolean function. The inputs to the quantum circuit are initialized according to the given boolean arguments. The outputs of the quantum circuit are measured, and the boolean measurement outcomes are returned. Because the measurement outcomes are probabilistic, this function takes place in the IO monad.

The type of this heavily overloaded function is difficult to read. In more readable form, it has all of the following types (for example):

run_clifford_generic :: (QCData qa) => Circ qa -> IO (BType qa)
run_clifford_generic :: (QCData qa, QCData qb) => (qa -> Circ qb) -> BType qa -> IO (BType qb)
run_clifford_generic :: (QCData qa, QCData qb, QCData qc) => (qa -> qb -> Circ qc) -> BType qa -> BType qb -> IO (BType qc)

and so forth.

Quantum simulation of a circuit, for testing and debugging purposes. Input a source of randomness, a real number, and a quantum circuit. Output a corresponding probabilistic boolean function.

The inputs to the quantum circuit are initialized according to the given boolean arguments. The outputs of the quantum circuit are measured, and the boolean measurement outcomes are returned.

The real number argument is a dummy and is never evaluated; its only purpose is to specify the type of real numbers that will be used during the simulation.

The type of this heavily overloaded function is difficult to read. In more readable form, it has all of the following types (for example):

run_generic :: (Floating r, Random r, Ord r, RandomGen g, QCData qa) => g -> r -> Circ qa -> BType qa
run_generic :: (Floating r, Random r, Ord r, RandomGen g, QCData qa, QCData qb) => g -> r -> (qa -> Circ qb) -> BType qa -> BType qb
run_generic :: (Floating r, Random r, Ord r, RandomGen g, QCData qa, QCData qb, QCData qc) => g -> r -> (qa -> qb -> Circ qc) -> BType qa -> BType qb -> BType qc

and so forth.

Like run_generic, but run in the IO monad instead of passing an explicit source of randomness.

Input a source of randomness, a quantum circuit, and an initial state (represented as a map from basis vectors to amplitudes). Simulate the circuit and return the final state. If the circuit includes measurements, the simulation will be probabilistic.

The type of this heavily overloaded function is difficult to read. It has, for example, the following types:

sim_amps :: StdGen -> (Qubit -> Circ Qubit) -> Map Bool (Cplx Double) -> Map Bool (Cplx Double)
sim_amps :: StdGen -> ((Qubit,Qubit) -> Circ Qubit) -> Map (Bool,Bool) (Cplx Double) -> Map Bool (Cplx Double)

and so forth. Note that instead of Double, another real number type, such as FixedPrec e, can be used.

A QuantumTrace is essentially a probability distribution for the current state of the qubits that have been traced. We can represent this using a Vector. The list of Booleans is in the same order as the list of Qubits that was being traced.

Like run_generic, but also output a trace of the states of the given list of qubits at each step during the evaluation.

Like run_generic_trace, but run in the IO monad instead of passing an explicit source of randomness.

The type of vectors with scalars in n over the basis a. A vector is simply a list of pairs.

A probability distribution gives each element a probability.

A generic function to simulate Quipper circuits, returning a probability distribution of the possible results.

The type of this heavily overloaded function is difficult to read. In more readable form, it has all of the following types (for example):

sim_generic :: (Floating r, Ord r, QCData qa) => r -> Circ qa -> ProbabilityDistribution r (BType qa)
sim_generic :: (Floating r, Ord r, QCData qa, QCData qb) => r -> (qa -> Circ qb) -> BType qa -> ProbabilityDistribution r (BType qb)
sim_generic :: (Floating r, Ord r, QCData qa, QCData qb, QCData qc) => r -> (qa -> qb -> Circ qc) -> BType qa -> BType qb -> ProbabilityDistribution r (BType qc)

and so forth.