Running Quantum Fourier Transform on NVIDIA H100 GPU using cuQuantum appliance

Copyright: Sanjay Basu

The Quantum Fourier Transform (QFT) is the quantum counterpart of the classical Fast Fourier Transform (FFT), crucial in quantum algorithms like Shor’s algorithm and quantum phase estimation. QFT, offering exponential speed-up on quantum computers, changes the basis from computational to Fourier. It’s distinct from classical Fourier transform in that QFT operates on qubits in superposition and is reversible, unlike the classical version where some information is irretrievably lost. Now, let’s proceed with generating code for implementing QFT on NVIDIA H100 using cuQuantum appliance.

Creating a code for the Quantum Fourier Transform (QFT) implementation using NVIDIA’s H100 GPU and cuQuantum appliance involves several steps. cuQuantum is a suite of software tools and libraries for accelerating quantum computing workflows on GPUs.

Copyright: Sanjay Basu

Please refer to these links for cuQuantum appliance setup:

https://github.com/NVIDIA/cuQuantum

Below is a high-level Python pseudocode outline for implementing QFT using cuQuantum and qiskit:

# Import necessary libraries
from qiskit import QuantumCircuit
import cuquantum

# Define the quantum circuit for QFT
def create_qft_circuit(num_qubits):
    circuit = QuantumCircuit(num_qubits)
    # Apply Hadamard and controlled rotation gates
    # [Add QFT algorithm implementation here]
    return circuit

# Create QFT circuit
num_qubits = 4  # example number of qubits
qft_circuit = create_qft_circuit(num_qubits)

# Optimize circuit for NVIDIA H100 GPU using cuQuantum
optimized_circuit = cuquantum.optimize(qft_circuit)

# Execute the circuit on the GPU
result = cuquantum.execute(optimized_circuit)

# Process the results
# [Add code to interpret results here]

# Validate and test the implementation
# [Add code for testing and validation]

This pseudocode provides a framework for implementing QFT on the NVIDIA H100 GPU using cuQuantum. The implementation will involve detailed coding, especially in defining the QFT algorithm within the quantum circuit and handling the results.

Processing the results from a Quantum Fourier Transform (QFT) on a quantum computer involves interpreting the quantum states (qubits) after the computation. The sample code below demonstrates how to analyze these results:

# Assuming 'result' contains the output from the QFT execution

# Convert the result to a probability distribution
probabilities = result.get_probabilities()

# Display the probabilities of each state
for state in probabilities:
    print(f"State {state}: Probability = {probabilities[state]:.2f}")

# Optionally, find the state with the highest probability
most_probable_state = max(probabilities, key=probabilities.get)
print(f"The most probable state is: {most_probable_state}")

This code snippet displays the probability of each quantum state resulting from the QFT. It also identifies the state with the highest probability, which can be crucial in many quantum computing applications like quantum algorithms and simulations.

Validating and testing the implementation of the Quantum Fourier Transform (QFT) involves comparing the output of your quantum circuit with the expected theoretical results. Here’s a sample code snippet for this purpose:

# Function to calculate the expected QFT result for a given input state
def expected_qft_result(input_state):
    # [Add the theoretical QFT calculation here]
    return expected_result

# Testing the QFT implementation
input_state = '0001'  # Example input state
expected_result = expected_qft_result(input_state)

# Execute the QFT circuit with the input state
qft_output = cuquantum.execute(qft_circuit, input_state)

# Validate the output
if qft_output == expected_result:
    print("Test Passed: QFT implementation is correct.")
else:
    print("Test Failed: QFT implementation needs review.")

This code tests the QFT implementation by comparing its output for a given input state against the expected theoretical result. Adjust the expected_qft_result function to compute the theoretical outcome of QFT for any input state. This approach helps ensure the correctness of your QFT implementation.

The quantum Fourier Transform (QFT) represents a significant advancement in quantum computing, offering exponential speedups over classical counterparts. This article elucidates the foundational aspects of QFT and also bridges the gap between theory and practical application by providing guidance to implement QFT on NVIDIA’s cutting-edge H100 GPU using the cuQuantum appliance. The sample code snippets for processing results and validating the implementation underscore the practicality of this approach. This seamless integration of theory and practice in quantum computing paves the way for future breakthroughs in the field, heralding a new era of computational capabilities.