Optimizing Quantum Circuits with Real Similarity in Qiskit

Introduction

Quantum computing has been a buzzword in the tech industry for some time now, with many companies investing heavily in this new technology. One of the key frameworks for developing quantum applications is Qiskit, an open-source Python library developed by IBM.
One of the challenges when working with quantum circuits is their complexity and sensitivity to noise. As such, optimizing these circuits becomes essential for achieving reliable results. Real similarity, a feature within Qiskit’s optimization toolbox, offers a method to reduce this complexity while maintaining the integrity of the computation.

What is Real Similarity?

Real similarity in Qiskit refers to a process that transforms quantum circuits into simpler forms by reducing their depth and width without compromising their overall functionality. This transformation relies on the concept that certain quantum gates can be substituted with equivalent but simpler ones, leading to more efficient circuit execution.
The real similarity feature takes as input a quantum circuit and attempts to reduce it to an equivalent but simpler form through several steps:

  1. Gate Transformation: Qiskit’s real similarity algorithm performs a series of gate transformations that simplify the circuit without altering its outcome. This includes replacing certain gates with their equivalents, which are less resource-intensive.
  2. Circuit Reduction: After transformation, the real similarity feature reduces the depth and width of the circuit where possible, further simplifying it.
  3. Optimization: The final step involves an optimization process to ensure that the resulting circuit is as efficient as possible.

Practical Example

To see how real similarity works in practice, let’s consider a simple example. Suppose we have a quantum circuit that performs a Hadamard gate followed by a controlled-NOT (CNOT) operation on two qubits:

from qiskit import QuantumCircuit, execute
# Define the initial circuit
qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)
# Visualize the initial circuit
print(qc.draw())
# Apply real similarity to simplify the circuit
simplified_qc = qc.simplify()
# Compare the original and simplified circuits
original_depth = qc.depth()
simplified_depth = simplified_qc.depth()
# Print the results
print(f"Original depth: {original_depth}")
print(f"Simplified depth: {simplified_depth}")

In this example, the simplify method is used to apply real similarity to the initial circuit. The resulting simplified circuit is then compared with the original in terms of depth.

Conclusion

Real similarity is a powerful feature within Qiskit that helps optimize quantum circuits by reducing their complexity without compromising their functionality. Through gate transformation, circuit reduction, and optimization, this feature can significantly improve the efficiency of quantum computations. As the field of quantum computing continues to evolve, tools like real similarity will play an increasingly important role in unlocking its potential.

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