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.
• S_DAG: Conjugate 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.
• PX: Prepare the Pauli X 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 in 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.

get_one_qubit_gates()

Returns a list of the supported single-qubit gate types.

get_two_qubit_gates(; stim_supported::Bool = false)

Returns a list of the supported two-qubit gate types, restricting to those also supported by Stim if stim_supported is true.

is_additive(g::Gate; strict::Bool = false)

Returns true if the noise associated with the gate g can only be estimated to additive precision, and false otherwise. If strict is true, this is true only for state preparation and measurement noise, as is proper, otherwise it is also true for mid-circuit measurement and reset noise, and measurement idle noise.

is_meas_idle(g::Gate)

Returns true if the gate g is a measurement idle gate, and false otherwise.

is_mid_meas(g::Gate)

Returns true if the gate g is a mid-circuit measurement gate, and false otherwise.

is_mid_meas_reset(g::Gate)

Returns true if the gate g is a mid-circuit measurement or reset gate, and false otherwise.

is_mid_reset(g::Gate)

Returns true if the gate g is a mid-circuit reset gate, and false otherwise.

is_one_qubit(g::Gate)

Returns true if the gate g is a supported single-qubit gate, and false otherwise.

is_pauli(g::Gate)

Returns true if the gate g is a Pauli gate, and false otherwise.

is_spam(g::Gate)

Returns true if the gate g is a state preparation or measurement gate, and false otherwise.

is_state_meas(g::Gate)

Returns true if the gate g is a state measurement gate, and false otherwise.

is_state_prep(g::Gate)

Returns true if the gate g is a state preparation gate, and false otherwise.

is_two_qubit(g::Gate; stim_supported::Bool = false)

Returns true if the gate g is a supported two-qubit gate, and false otherwise. If stim_supported is true, restrict to those gates also supported by Stim.

make_layer(gate_type::String, range::Vector{Int}, n::Integer; index::Integer = 0)

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

make_layer(gate_type::String, range_set::Vector{Vector{Int}}, n::Integer; index::Integer = 0)

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

make_layer(gate_types::Vector{String}, ranges::Vector{Vector{Int}}, n::Integer; index::Integer = 0)

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, optionally specifying the gate index index.

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(x_1::Bool, z_1::Bool, x_2::Bool, z_2::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 $Z = S^2$.