Internal APIs for developers

conv_ast(ast::MainProgram, state_vector::StateVector, num_qubits::Int64)::MainProgram

Converts a non-unitary quantum circuit so it can be tested for equality with its equivalent a unitary circuit

conv_prog(a::Any, state_vector::StateVector, num_qubits::Int, section::Int)::Any

Pattern matches a Prog element and returns it with the new address, based on the conversion from the StateVector

conv_qop(cx::CXGate, state_vector::StateVector, section::Int)::CXGate

Converts the adresses of a CXGate based on the state vector and section in the dynamic circuit.

conv_qop(inst::Instruction, state_vector::StateVector, section::Int)::Instruction

Converts the adresses of a quantum operation based on the state vector and section in the dynamic circuit.

conv_qop(m::Measure, state_vector::StateVector, section::Int)::Measure

Converts the adresses of a Meausment Operation based on the state vector and section in the dynamic circuit.

conv_qop(r::Reset, state_vector::StateVector, section::Int)::Reset

Return the Reset Operation unchanged

FIXME check if this is according to specifaction

conv_regdecl(reg::RegDecl, num_qubits::Integer)::RegDecl

Sets num_qubits bits as the number of bits in a quantum RegDecl

create_bit(state_vector::StateVector, i::Bit)::Bit

Create a Bit from a the state vector and the old bit adress

remove_measurements(ast::MainProgram)::MainProgram

Removes all measurements from a quantum circuit

remove_resets(ast::MainProgram)::MainProgram

Removes all resets from a quantum circuit

zip_prog_section(progs::Vector{Any})

Zip the index of each section with a prog element. Increment index after each Measure

calulate_indices(state_vector::StateVector)::Array{Int}

Create indices for reordering based

Example

julia> calulate_indices(StateVector([1,0], [2]))
Int8[0, 1, 4, 5, 2, 3, 6, 7]

create_bit_matrix(n::Int)::Matrix{Int}

Create matrix for all possible n bit combinations

matrix_row_to_bit(x::Vector{Int})::Int

parses an array of ints as a bit

Example

julia> matrix_row_to_bit([0,1,0])
2

reorder_columns(matrix::Matrix{Any}, column_indices::Vector{Int})::Matrix

Reorder matrix based on column_indices

Example

julia> n = 3  # Number of bits
julia> m = create_bit_matrix(n)
julia> m_reordered = reorder_columns(original_matrix, column_indices)

reorder_operator(operator::Matrix{ComplexF64})::Matrix{ComplexF64}

Calculate the new indices and peform the reordering of an operator

reorder_rows(operator, indices)::Matrix

Reorder the rows of a matrix based on the indices

density_matrix(matrix)::Matrix

Calculate the density matrix assuming phi is the first quantum state in Z Basis

Definition

\[M |ϕ⟩ ⟨ϕ| M^\dagger\]

fidelity(U1, U2)::Float64

Fidelity is a measure of distance between quantum states ϕ and ρ

Definition

The fidelity of two quantum state for qudits is defined as:

\[F(ϕ, σ) = tr(\sqrt{\sqrt{ϕ}ρ\sqrt{ρ}})\]

inner_product(x, y)::Vector

Calculate the inner product

Examples

The product is written as a bra standing on the left and a ket standing on the right, for example,

\[ ⟨β|α⟩= (⟨β|) ⋅(|α⟩)\]

TODO Doctest

Source

(1.46) Quantum Mechanics Book

outer_product(x, y)::Matrix

Definition

\[(|β⟩) ⋅ (⟨α|) = |β⟩⟨α|\]

$|β⟩⟨α|$ is known as the outer product of $|β⟩$ and $⟨α|$. We will emphasize in a moment that |β⟩⟨α| is to be regarded as an operator; hence it is fundamentally different from the inner product ⟨β|α⟩, which is just a number.

There are also “illegal products.” We have already mentioned that an operator must stand on the left of a ket or on the right of a bra.

Examples

TODO Doctest

Source

(1.46) Quantum Mechanics Book

equality(M, M_prime)::Float64

Test the equality of two matrices by converting them to density matrices and calculating their trace distance

tracedist(A::Matrix, B::Matrix)::Float64

Return the trace distance of register1 and register2.

Definition

Trace distance is defined as following:

\[\frac{1}{2} || A - B ||_{\rm tr}\]

Examples

TODO Doctest

References

• https://en.wikipedia.org/wiki/Trace_distance

verify_equivalence(traditional_circuit, dynamic_circuit, use_zx::Bool, transform_dynamic_circuit::Bool)::Float64

Verify the equality of a traditional_circuit and a reconstruced circuit, returning the trace distance and fidelity as a tuple

TODO change api to differentiate between exact and similar qc

combine(s::StateVector)::Array{Int}

Return the combined states of the state vector

convert_address(state::State, section::Int, address::Int)::Int64

Replaces the address of a qubit based on the state vector, section and position using a lookup table

Objective

This function converts old addresses into new addresses required for the ideal unitary circuit

drop_gate_of_type(arr, gate_type::Type)

Filters any gate which matches the gate type

get_controls(ast :: MainProgram)::Array{CXGate}

Return all control operations of the quantum circuit

get_measurements(ast :: MainProgram)::Array{Measure}

Return all measurement operations of the quantum circuit

get_num_of_qubits(ast :: MainProgram)::Int

Returns the number of qubits, which have been specified in the first quantum register

prepare_for_ZXCalculus(ast::MainProgram)

preparre for import in the ZXCalculus by removing measurements, barriers and #TODO applying custom gates

read_qasm_from_file(filename)::String

Read the qasm from a file

state_vector(ast::MainProgram)::StateVector

Creates the reordered StateVector based on the ast of a quantum circuit

acts_on?(operation::Any, qubit::Bit)

Does the operation act on the qubit

create_bit(state_vector::StateVector, i::Bit)::Bit

Create a Bit from a the state vector and the old bit adress

defeer_measurements(prog::Vector{Any})::Vector{Any}

Delay all meausrements to the end and replace phase roations controlled by meausrement outcomes with phase gates controlled by the respective circuits

overcome_resets(ast::MainProgram, state_vector::StateVector, num_qubits::Int64)::Vector{Any}

overcomes resets operations by eliminating qubit reuse

This transforms a n qubit circuit circuit containing r reset operations into a n+r qubit quantum circuits

Algorithm

Overcome resets by interpreting a reset as measuring a qubit and applying an X operation on the measurement being |1⟩ and discarding the measurement result. To overcome the resets replace by introducing a new qubit and applying subsequent operations involving the qubit to the new qubit

remove_measurements(ast::MainProgram)::MainProgram

Removes all measurements from a quantum circuit

remove_resets(ast::MainProgram)::MainProgram

Removes all resets from a quantum circuit

trans_ast(ast::MainProgram, state_vector::StateVector, num_qubits::Int64)::MainProgram

transform the dynamic primitives to unveil the underlying unitary functionality

How

1. Overcome resets
2. Apply the /defered measurement principle/

trans_if_stmt(stmt, state_vector, section)

transforms the qargs of a IfStmt

trans_prog(a::Any, state_vector::StateVector, num_qubits::Int, section::Int)::Any

Pattern matches a Prog element and returns it with the new address, based on the transformation from the StateVector

trans_qop(cx::CXGate, state_vector::StateVector, section::Int)::CXGate

transforms the adresses of a CXGate based on the state vector and section in the dynamic circuit.

trans_qop(inst::Instruction, state_vector::StateVector, section::Int)::Instruction

transforms the adresses of a quantum operation based on the state vector and section in the dynamic circuit.

trans_qop(m::Measure, state_vector::StateVector, section::Int)::Measure

transforms the adresses of a Meausment Operation based on the state vector and section in the dynamic circuit.

trans_qop(r::Reset, state_vector::StateVector, section::Int)::Reset

Return the Reset Operation unchanged

FIXME check if this is according to specifaction

trans_regdecl(reg::RegDecl, num_qubits::Integer)::RegDecl

Sets num_qubits bits as the number of bits in a quantum RegDecl

zip_prog_section(progs::Vector{Any})

Zip the index of each section with a prog element. Increment index after each Measure