tableau.jl

Gate

A gate in a stabiliser circuit.

Fields

• type::String: String describing the gate type.
• index::Int32: The index labelling the unique layer occurrences of the gate in a circuit.
• targets::Vector{Int16}: The qubit target or targets of the gate.

Supported gates

• H: Hadamard gate.
• S: Phase gate.
• CX or CNOT: Controlled-X gate; the first qubit is the control and the second qubit is the target.
• CZ: Controlled-Z gate.
• I: Identity gate.
• Z: Pauli Z gate.
• X: Pauli X gate.
• Y: Pauli Y gate.
• II: Two-qubit identity gate.
• AB: Two-qubit Pauli gate, where A and B are Paulis Z, X, or Y.
• SQRT_AB: Two-qubit Pauli rotation, where A and B are Paulis Z, X, or Y.
• SQRT_AB_DAG : Two-qubit Pauli rotation, where A and B are Paulis Z, X, or Y.
• PZ+: Prepare the Pauli +Z eigenstate.
• PZ-: Prepare the Pauli -Z eigenstate.
• PX+: Prepare the Pauli +X eigenstate.
• PX-: Prepare the Pauli -X eigenstate.
• PY+: Prepare the Pauli +Y eigenstate.
• PY-: Prepare the Pauli -Y eigenstate.
• M or MZ: Measure in the computational Pauli Z basis.
• MX: Measure in the Pauli X basis.
• MY: Measure in the Pauli Y basis.
• R: Reset to the computational Z basis.

Layer

A layer of gates in a stabiliser circuit. Gates in a layer are simultaneously implemented by the device, and act on disjoint sets of qubits such that they trivially commute with each other.

Fields

• layer::Vector{Gate}: The gates in the layer.
• qubit_num::Int16: The number of qubits in the circuit.

Tableau

A tableau representation of a stabiliser state.

Stabiliser circuit simulations follow Improved simulation of stabilizer circuits by S. Aaronson and D. Gottesman (2004).

Fields

• tableau::Matrix{Bool}: The tableau representation of the stabiliser state.
• qubit_num::Int16: The number of qubits in the stabiliser state.

apply!(t::Tableau, l::Layer; return_measurements::Bool = false)

Perform on the tableau t all gates in the layer l, and return the list of measurement outcomes if return_measurements is true.

make_layer(gate_type::String, range::Vector{Int}, n::Int)

Returns a layer of single-qubit gate_type gates acting on the qubits in range, where the layer acts on n qubits.

make_layer(gate_type::String, range_set::Vector{Vector{Int}}, n::Int)

Returns a layer of gate_type gates, each acting on the qubits in range_set, where the layer acts on n qubits.

make_layer(gate_types::Vector{String}, ranges::Vector{Vector{Int}}, n::Int)

Returns a layer of single-qubit gates, with gate types specified by gate_types and the qubits upon which they act specified by ranges, where the layer acts on n qubits.

pad_layer(l::Layer)

Returns a copy of the layer l padded by single-qubit identity gates that act on each of the qubits not already acted upon by some gate in the layer.

cx!(t::Tableau, control::Integer, target::Integer)

Perform a controlled-X gate on the tableau t with control qubit control and target qubit target.

cz!(t::Tableau, control::Integer, target::Integer)

Perform a controlled-Z gate on the tableau t with control qubit control and target qubit target. The gate is symmetric, so the control and target qubits can be swapped.

hadamard!(t::Tableau,target::Integer)

Perform a Hadamard gate on the tableau t with target qubit target.

measure!(t::Tableau, target::Integer)

Measure the tableau t at the target qubit target, and return the measurement outcome.

phase!(t::Tableau,target::Integer)

Perform a phase gate on the tableau t with target qubit target.

reset!(t::Tableau, target::Integer)

Reset the tableau t at the target qubit target by measuring in the computational basis and flipping the phase if the measurement outcome is -1.

row_phase(x₁::Bool, z₁::Bool, x₂::Bool, z₂::Bool)

Calculate a phase for row_sum!.

row_sum!(t::Tableau, target::Integer, control::Integer)

In the tableau t, add the control row control to the target row target, while tracking the phase bit of the target row.

sqrt_zz!(t::Tableau, control::Integer, target::Integer)

Perform a π/2 ZZ Pauli rotation gate on the tableau t with control qubit control and target qubit target. The gate is symmetric, so the control and target qubits can be swapped.

sqrt_zz_dag!(t::Tableau, control::Integer, target::Integer)

Perform a -π/2 ZZ Pauli rotation gate on the tableau t with control qubit control and target qubit target. The gate is symmetric, so the control and target qubits can be swapped.

x!(t::Tableau,target::Integer)

Perform a Pauli X gate on the tableau t with target qubit target, noting that $X = H S^2 H$.

y!(t::Tableau,target::Integer)

Perform a Pauli Z gate on the tableau t with target qubit target, noting that $Y = S H S^2 H S^3$.

z!(t::Tableau,target::Integer)

Perform a Pauli Z gate on the tableau t with target qubit target, noting that $Z = S^2$.