Quantum Circuit Simulation Framework

This project focuses on building a simulation framework for quantum circuits from scratch, emphasizing Clifford dynamics. The implementation relies exclusively on Python standard libraries, prioritizing efficiency and correctness. Some of the algorithms implemented in this project are based on the following paper: https://www.scottaaronson.com/papers/chp6.pdf

Objectives

1. Initialization of $n$-qubit states:

   • Implement $n$-qubit initialization using a $2^n$ state vector.
   • Develop a tableau-based representation of $n$-qubit states.

2. Application of Clifford gates:

   • Implement key Clifford gates, including CNOT, Hadamard (H), and Phase (S) gates.
   • Enable the application of gates to $n$-qubit states.

3. Measurement of $n$-qubit states:

   • Support deterministic and random measurements on single qubits.
   • Efficiently simulate measurement outcomes.

By simulating a quantum computer with:

• A full $2^n$-state vector (referred to as the vector simulator),
• And a tableau-based Clifford simulator,

The project compares the performance and scalability of these two approaches.

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Results

1. Validation of Implementations

Both simulators were validated using randomly generated Clifford circuits. Measurement outcomes and probability amplitudes were compared between the two implementations.

• Key Observation: Both simulators showed consistent results across all tests, with no discrepancies in measured states.
• Probability Amplitudes: Consistent computation of amplitudes across both approaches confirmed their accuracy.

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2. Performance Comparison

The efficiency of the simulators was compared by evaluating runtime and memory usage across 1,000 runs of $n$-qubit circuits.

• Runtime Analysis:
  The Clifford simulator exhibited significantly faster execution times for larger $n$-qubit circuits compared to the vector simulator.

• Memory Usage:
  The vector simulator performed competitively in memory usage for circuits up to 6 qubits but was outperformed by the Clifford simulator for larger systems.

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3. Key Observations

1. The Clifford simulator excels in scalability, efficiently handling large $n$-qubit circuits, making it ideal for Clifford dynamics.
2. The state vector simulator is valuable for verifying correctness but is limited in performance for larger systems.
3. Both simulators produced consistent results, validating their implementation for state evolution and measurements.

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Summary

This framework demonstrates the strengths of both simulation approaches:

• The Clifford simulator is highly efficient and scalable, optimized for Clifford circuits.
• The state vector simulator provides a reliable tool for validation and small-scale circuit analysis.

By comparing these methods, the project offers insights into the trade-offs between correctness and efficiency in quantum circuit simulation.

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More Results

The results shown above are just a comparative example at the efficiency boundary of both quantum computing frameworks. The following Images showcase the same relations but for a random 8 qubit circuit.