Quantum Simulator

I wanted to undertsand more about Quantum Computing. Quantum computing is a huge topic, and I felt that just using a ready-made library wasn't enough for me to really 'get' it. I decided to write this simulator from scratch to see what happens behind the scenes

Features

• In-place computation: Memory-efficient bitwise operations.
• Multithreading: Optimized with OpenMP for multicore CPUs.
• CLI Interface: Accepts qubit count and shots as arguments.

Mathematical Model

This simulator models a quantum system of $N$ qubits. The global state of the system is represented by a complex state vector $\left| \psi \right\rangle$ of size $2^N$:

$$\left| \psi \right\rangle = \sum_{i=0}^{2^N-1} \alpha_i \left| i \right\rangle$$

where $\alpha_i \in \mathbb{C}$ represents the probability amplitude of the basis state $\left| i \right\rangle$. The simulation enforces the normalization condition $\sum_{i} |\alpha_i|^2 = 1$.

Quantum gates (X, H, Z, CNOT) are applied not via naive matrix multiplication (which would require sparse matrices of size $2^N \times 2^N$), but through in-place bitwise operations that directly manipulate the pairs of probability amplitudes involved.

Memory Complexity Warning

Simulating quantum systems on classical hardware requires exponential memory $\mathcal{O}(2^N)$. Each state amplitude uses a std::complex<double> (16 bytes).

• 10 qubits $\approx$ 16 KB
• 20 qubits $\approx$ 16 MB
• 30 qubits $\approx$ 16 GB of RAM

Do not simulate more than 28-30 qubits unless you have sufficient physical RAM, or your system will trigger the OOM (Out-Of-Memory) killer.

Compilation

g++ main.cpp QuantumSimulator.cpp -o qsim -O3 -fopenmp

USAGE

./qsim <number_of_qubits> <number_of_shots>