QQuantLib.PE

classical_qpe

This module contains the necessary functions and classes to implement the classical Quantum Phase Estimation with the inverse of the Quantum Fourier Transform. The following references were used:

Brassard, G., Hoyer, P., Mosca, M., & Tapp, A. (2000). Quantum amplitude amplification and estimation. AMS Contemporary Mathematics Series, 305. https://arxiv.org/abs/quant-ph/0005055v1

NEASQC deliverable: D5.1: Review of state-of-the-art for Pricing and Computation of VaR

Author: Gonzalo Ferro Costas & Alberto Manzano Herrero

class tnbs.BTC_02_AE.QQuantLib.PE.classical_qpe.CQPE(**kwargs)

Bases: object

Class for using classical Quantum Phase Estimation, with inverse of Quantum Fourier Transformation.

Parameters:

kwars (dictionary) –

dictionary that allows the configuration of the CQPE algorithm: Implemented keys:

initial_stateQLM Program

QLM Program with the initial Psi state over the Grover-like operator will be applied Only used if oracle is None

unitary_operatorQLM gate or routine

Grover-like operator which autovalues want to be calculated Only used if oracle is None

cbits_numberint

number of classical bits for phase estimation

qpuQLM solver

solver for simulating the resulting circuits

shotsint

number of shots for quantum job. If 0 exact probabilities will be computed.

run()

Creates the quantum phase estimation routine

iterative_quantum_pe

This module contains necessary functions and classes to implement Iterative Quantum Phase Estimation (IQPE). The implementation is based on following paper:

Dobšíček, Miroslav and Johansson, Göran and Shumeiko, Vitaly and Wendin, Göran*. Arbitrary accuracy iterative quantum phase estimation algorithm using a single ancillary qubit: A two-qubit benchmark. Physical Review A 3(76), 2007. https://arxiv.org/abs/quant-ph/0610214

Author: Gonzalo Ferro Costas & Alberto Manzano Herrero

class tnbs.BTC_02_AE.QQuantLib.PE.iterative_quantum_pe.IQPE(**kwargs)

Bases: object

Class for using Iterative Quantum Phase Estimation (IQPE) algorithm

Parameters:

kwars (dictionary) –

dictionary that allows the configuration of the ML-QPE algorithm. Implemented keys:

initial_stateQLM Program

QLM Program withe the initial Psi state over the Grover-like operator will be applied Only used if oracle is None

unitary_operatorQLM gate or routine

Grover-like operator whose autovalues want to be calculated Only used if oracle is None

cbits_numberint

number of classical bits for phase estimation

qpuQLM solver

solver for simulating the resulting circuits

shotsint

number of shots for quantum job. If 0 exact probabilities will be computed.

easybool

If True step_iqpe_easy will be used for each step of the algorithm If False step_iqpe will be used for each step.

apply_iqpe()

Apply a complete IQPE algorithm

property cbits_number

creating cbits_number property

init_iqpe()

Initialize several properties

iqpe(number_of_cbits=None, shots=None)

This method apply a workflow for executing a complete IQPE algorithm

Parameters:

• number_of_cbits (int (overwrite correspondent property)) – Number of classical bits for storing the phase estimation

• shots (int (overwrite correspondent property)) – Number of shots for executing the QLM job

static measure_classical_bits(result)

Post-process intermediate measurements from a QLM result.

Parameters:

result (list list with QLM results)

Returns:

pdf – contains extracted information from intermediate_measurements from a qlm result. Columns:

BitStringstr.

String with the bits of the measurements done during simulation of the circuit

BitIntint.

Integer representation of the BitString

Phifloat.

Angle representation of the BitString between [0,1].

Probabilityfloat.

Probability of the measurement of the classical bits.

Return type:

pandas DataFrame

static post_proccess(input_pdf)

This function uses the results property and add it additional columns that are useful for Amplitude Amplification procedure

Parameters:

input_pdf (Pandas DataFrame.)

Returns:

final_results – DataFrame with complete information about the results

Return type:

Pandas DataFrame

restart()

Reinitialize several properties for restart purposes

static run_qprogram(q_prog, q_aux, shots, linalg_qpu)

Executes a complete simulation

Parameters:

• q_prog (QLM Program)

• q_aux (QLM qbit) – auxiliary qubit for measuring during all ipe steps

• shots (int) – number of shots for simulation

• linalg_qpu (QLM solver)

Returns:

• result (QLM result object)

• circuit (QLM circuit)

• pdf_time (pandas DataFrame) – DataFrame with elapsed time of different parts of the simulation

static step_iqpe(q_prog, q_gate, q_aux, c_bits, l)

Implements a iterative step of the Iterative Phase Estimation (IPE) algorithm.

Parameters:

• q_prog (QLM program) – QLM Program where the unitary operator will be applied

• q_gate (QLM AbstractGate) – QLM implementation of the unitary operator. We want estimate the autovalue theta of this operator

• q_aux (QLM qbit) – auxiliary qubit for IPE. This qbit will be the control for application of the unitary operator to the principal bits of the program. Additionally will be the target qubit for the classical bit controlled rotation. This qubit will be reset at the end of the step.

• c_bits (list) – list with the classical bits allocated for phase estimation

• l (int) – iteration step of the IPE algorithm

static sumarize(input_pdf, columns=None)

This method summarize the results.

Parameters:

• input_pdf (Pandas DataFrame.)

• columns (list) – list with the names of the input DataFrame for summarize

Returns:

final_results – DataFrame with summary results

Return type:

Pandas DataFrame

windows_pe

This module contains different window functions. Based on:

Effects of cosine tapering window on quantum phase estimation. Rendon, Gumaro and Izubuchi, Taku and Kikuchi, Yuta Phys. Rev. D, 106. 2022

Author: Gonzalo Ferro Costas

tnbs.BTC_02_AE.QQuantLib.PE.windows_pe.cosine_window(number_qubits: int)

Creates a QLM AbstractGate for loading a Cosine Window Function into a quantum state.

Parameters:

number_qubits (int) – Number of qubits for the quantum AbstractGate

Returns:

window_state – AbstractGate for loading a cosine

Return type:

AbstractGate

tnbs.BTC_02_AE.QQuantLib.PE.windows_pe.kaiser_array(number_qubits, alpha=1e-05)

Creates the probability discretization of a Kaiser window function for a given input of number of qubits and a alpha :param number_qubits: Number of qubits for building the Kaiser window function :type number_qubits: int :param alpha: Parameter for modified Bessel function or order 0. :type alpha: float

Returns:

pdf – pandas DF with the probability discretization of the Kaiser window function

Return type:

pandas DataFrame

tnbs.BTC_02_AE.QQuantLib.PE.windows_pe.kaiser_window(number_qubits, alpha=1e-05)

Creates a QLM AbstractGate for loading a Kaiser Window Function into a quantum state. Uses load_probability function for loading the discretization of the probability of the Kaiser window function.

Parameters:

• number_qubits (int) – Number of qubits for the quantum AbstractGate

• alpha (float) – Parameter for modified Bessel function or order 0.

Returns:

kaiser_state – AbstractGate for loading a Kaiser Window

Return type:

AbstractGate

tnbs.BTC_02_AE.QQuantLib.PE.windows_pe.sine_window(number_qubits: int)

Creates a QLM AbstractGate for loading a Sine Window Function into a quantum state.

Parameters:

number_qubits (int) – Number of qubits for the quantum AbstractGate

Returns:

window_state – AbstractGate for loading a sine

Return type:

AbstractGate

tnbs.BTC_02_AE.QQuantLib.PE.windows_pe.window_selector(window_type, **kwargs)

Selector funcion for window functions

Parameters:

• window_type (str) – String with the desired Window function

• kwargs (keyword arguments) – Keyword arguments for configuring window functions. Mandatory: auxiliar_qbits_number. For Kaiser window it is mandatory to provide kaiser_alpha

Returns:

• window gate (AbstractGate) – AbstractGate with the desired window function

• last_control_change (Bool) – last_control_change value