QuL

QuL is a python package to generate, analyze and test quantum circuits for various computational cooling protocols.

Installation

The package can be installed via pip:

python3 -m pip install qubitcooling

Cooling Unitary

A Cooling Unitary is a generalized permutation matrix which can perform an arbitrary number of permutations of arbitrary lengths on the quantum states. The class CoolingUnitary efficently stores the matrix using a scipy.sparse.csr_array, the matrix can be accessed by the method getCoolingUnitary(). The class can calculate the work cost of the Unitary with the method calculateWorkCost().

Generate a Cooling Unitary using a protocol

It is possibile to generate a Cooling Unitary using one of the three protocols provided by QuL which are the Partner Pairing Algorithm, Minimal Work and the Mirror Protocol. The only required argument is the number of qubits, optionally the user can provide the probability of the excited state for each qubit.

In this example a Cooling unitary is generated using the Mirror Protocol:

from qubitcooling import MirrorProtocol

number_of_qubits = 5
unitary = MirrorProtocol(number_of_qubits)

#Print the unitary
print(unitary.coolingUnitary.toarray())

A Cooling Unitary generated using the Minimal Work using the optional probability of the excited state:

from qubitcooling import MinimalWorkProtocol

number_of_qubits = 5
probability_excited_state = 0.2
unitary = MinimalWorkProtocol(number_of_qubits,probability_excited_state)

Generate a Cooling Unitary using the Partner Pairing Algorithm using a different probability of the excited state for each qubit:

from qubitcooling import PartnerPairingAlgorithm

number_of_qubits = 5
probability_excited_state = [0.1,0.2,0.05,0.2,0.1]
unitary = PartnerPairingAlgorithm(number_of_qubits,probability_excited_state)

Generate a Cooling Unitary using a list of permutations

It is possible to generate a Cooling Unitary using a list of permutations using the class CoolingUnitary. The required arguments are the number of qubits and the list of permutations. An example where the state 000 is swapped with the state 001:

from qubitcooling import CoolingUnitary

number_of_qubits = 3
#1 Swaps: 000 <-> 001
permutations = [["000","001"]] 
unitary = CoolingUnitary(number_of_qubits,permutations)

It is possible to create cycles with length greater than 2:

from qubitcooling import CoolingUnitary

number_of_qubits = 3
#1 Cycle is 000 -> 001 -> 100 -> 000
#2 Cycle is 010 <-> 011
permutations = [[0,1,"100"],["010","011"]] 
unitary = CoolingUnitary(number_of_qubits,permutations)

Generate a Cooling Circuit

Given a Cooling Unitary, QuL provides four classes to create a Cooling Circuit. In each class the method getCircuit() returns a QuantumCircuit by the package Qiskit.

Dynamic Cooling

Dynamic Cooling is implemented using the class DynamicCooling, the only required argument is a Cooling Unitary. An example:

from qubitcooling import DynamicCooling
from qubitcooling import MinimalWorkProtocol

number_of_qubits = 5
unitary = MinimalWorkProtocol(number_of_qubits)
#The True as the second argument is to show the barriers in the QuantumCircuit
circuit = DynamicCooling(unitary,True)

#Print the circuit
print(circuit.getCircuit().draw())

Heat-Bath Algorithmic Cooling

Heat-Bath Algorithmic Cooling is implemented using the class HeatBathCooling, the required arguments are a Cooling Unitary and the number of rounds.

Sub-Optimal Dynamic Cooling

Sub-Optimal Dynamic Cooling is implemented using the class SubOptimalCooling, the required arguments are a Cooling Unitary and the number of rounds.

Semi-Open Dynamic Cooling

Semi-Open Dynamic Cooling is implemented using the class SemiOpenCooling, the required arguments are a Cooling Unitary and the number of rounds.

Example:

from qubitcooling import HeatBathCooling
from qubitcooling import MinimalWorkProtocol

number_of_qubits = 5
unitary = MinimalWorkProtocol(number_of_qubits)
rounds = 3
circuit = HeatBathCooling(unitary,rounds,False)

Calculate work cost and final temperature

After generating a quantum circuit with the method calculateFinalTemperature() it is possible to calculate the theorical final temperature of the target qubit. The work cost is calculated with the method calculateWorkCost().