NCU module

The NCU module enables the implementation of an $n$-qubit controlled unitary gate. In this instances, we have chosen to work primarily with $n$CX and $n$CZ gates, though others may also be used.

Implementation

The general principle follows the work of Barenco et al., Phys. Rev. A 52, 3457, (1995). All higher-order controlled quantum gates can be decomposed into 1 and 2 qubit gate calls, with varying degrees of optimisation. We implement the default quadratic gate decomposition strategy, alongside the 3CU optimised, and auxiliary register optimised variants.

API

QXZoo.NCU.apply_ncu! — Method

apply_ncu!(cct::Circuit.Circ, q_ctrl::Vector, q_aux::Vector, q_tgt, U::GateOps.GateSymbol)

Apply an n-qubit controlled gate operation on the given target qubit. Ensure the 2-qubit gate corresponding with symbol c_U is registered with GateMap.gates before use. Appends the GateCall operations to circuit

Arguments

cct::Circuit.Circ
ctrls::Vector:
aux::Vector:
tgt::Int:
U::GateOps.GateSymbol: symbol for 2-qubit gate to extend (cx, cz, etc)

source

QXZoo.NCU.get_intermed_gate — Method

get_intermed_gate(U::GateOps.GateSymbol)

Generate sqrt U and adjoint sqrt U, given a previously cached gate U.

source

Example

To use the NCU module, we provide example code below to apply an n-controlled Pauli Z gate using either the unoptimised (quadratic) or optimised (linear) decomposition routines.

Default NCU with 3CU optimisation

using QXZoo

# Set 10-qubit limit on circuit
num_qubits = 10

# Create Pauli-Z gate-label for application
gate_z = QXZoo.DefaultGates.GateSymbols.c_z

# Create empty circuit with qiven qubit count
cct = QXZoo.Circuit.Circ(num_qubits)

ctrl = collect(range(1, length=num_qubits  ) )
aux = []
tgt = num_qubits

for i in ctrl
    QXZoo.Circuit.add_gatecall!(cct, QXZoo.DefaultGates.x(i) )
end

QXZoo.NCU.apply_ncu!(cct, ctrl, aux, tgt, gate_z)

# Number of generation gate-call operations
println(cct)

10 qubits with 11079 gate-calls using 34 unique gates.

Auxiliary optimised NCU

# Auxiliary-assisted NCU

using QXZoo

# 19 qubit aux-optimised matches 10 qubit unoptimised.
num_qubits = 19

cct = QXZoo.Circuit.Circ(num_qubits)

ctrl = collect(1:10)
tgt = 11
aux =  collect(11:19)

for i in ctrl
    cct << QXZoo.DefaultGates.x(i)
end

QXZoo.NCU.apply_ncu!(cct, ctrl, aux, tgt, DefaultGates.GateSymbols.c_z)

println(cct)

19 qubits with 172 gate-calls using 5 unique gates.