statevectorsim 0.1.0

Simple quantum statevector simulator

Quantum Simulator

A lightweight, quantum state-vector simulator, written in Python. This package includes a backend that switches between dense (NumPy) and sparse (SciPy CSR) matrix representations, optimised circuit compilation, noise modelling via Monte Carlo methods, and built-in implementations of major quantum algorithms. Generally, it can efficiently handle up to 26-qubit circuits, though this is dependent on the memory you have available and circuit sparsity. After this memory scaling becomes too large.

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Features

• Dual Storage matrix representation of $2^N$ amplitudes:

  • Dense (NumPy) storage.
  • Sparse (SciPy) storage.

  This project relies on the C-based efficiency of both packages to do most of the heavy memory lifting.

• Circuit Compilation: Options for optimising.

  • V1: Adjacent gate 'fusion' and clutter removal.
  • V2: Uses gate-commutativity rules to swap gates and fuse them, reducing circuit depth.

• Smart Backend: Auto-selects optimisation and storage method by estimating sparsity. Some heuristics gained from testing are used here.

• Noise Modelling: Support for Monte Carlo noisy simulations (Depolarizing, Bit-Flip, Phase-Flip channels).

• Visualisation: Tools for Bloch sphere representation, ASCII circuit drawing, and measurement histograms.

• Circuit&Gate Library: pre-built implementations of Shor's Algorithm, Grover's search, QPE, QFT, and Quantum Addition (mod N). as well as most common gates.

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Project Structure

statevectorsim package:

• QuantumState: State manager supporting dense and sparse statevector representations. Handles initialisation, basis-state preparation, and measurement collapse.
• QuantumGate: Comprehensive library of standard, rotational, controlled, and multi-controlled gates. Gate application logic using Tensor Slicing (dense) and Bitmasking (sparse).
• QuantumCircuit: Build, optimise, and run circuits. Includes:
  • Compiler: Basic gate fusion (V1) and commutative 'lookahead' gate fusion (V2).
  • Algorithm Library: Pre-built circuits for Shor's Algorithm, Grover's Search, QPE, QFT, and Quantum Adders.
• QuantumNoise: Monte-Carlo noise simulation with Depolarizing, Bit-Flip, and Phase-Flip error channels.
• QuantumBackend: Dispatcher that auto-selects the optimal execution strategy based on circuit topology and qubit count.
• utils: Visualisation tools including 3D Bloch Sphere plotter, ASCII circuit drawing, Pandas dataframe export, and measurement probability histograms.

Bonus tools:

• test_suite: Dedicated file for testing all implemented circuits and gates.
• benchmark: Dedicated file for benchmarking gate-application and optimiser methods. Includes qiskit circuit transpiler.

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Benchmarking

The simulator is benchmarked against IBM's Qiskit Statevector simulator (v2.2). Statevectorsim generally keeps up with or out-performs Qiskit. Though this is largely down to the fact that Qiskit breaks down the circuit into something parsable by hardware (Qiskit has a very quick C-foundation). Advantage is amplified when benchmarking for a large number of qubits and dense circuits such as Grover's algorithm. Largest source of cost predictably comes from scaling qubits - compiling has some weight-saving on circuit depth, but it wavers in comparison to improving memory usage.

Below is the benchmark for 100 50-gate random n-qubit circuits. More benchmarks can be found in \benchmark.

Usage

1. Basic Circuit & Measurement

from statevectorsim.quantum_circuit import QuantumCircuit
from statevectorsim.quantum_gate import QuantumGate
from statevectorsim.quantum_backend import QuantumBackend
from statevectorsim.utils import plot_histogram

# 1. Initialize Backend
backend = QuantumBackend()

# 2. Create a Bell State Circuit
qr = QuantumState(2)
qc = QuantumCircuit(2)
qc.add_gate(QuantumGate.h(0))
qc.add_gate(QuantumGate.cx(0, 1))

# 3. Execute (Smart Backend automagically handles Mode)
# Runs 1024 shots
results = backend.run(qc, qr, shots=1024)

# 4. Visualize
print(f"Counts: {results}")
plot_histogram(results, shots=1024)

2. Optimiser

qc = QuantumCircuit(3)
# ... add complex sequence of gates ...

print("Original Gate Count:", len(qc.gates))

# Apply V2 Optimization (Commutativity-Aware Fusion)
qc.optimise(method='v2')

print("Optimized Gate Count:", len(qc.gates))

3. Pre-built Algorithms

# Generate Grover's Search for a 4-qubit space, searching for state |13>
grover_circuit = QuantumCircuit.grover_search(n_qubits=4, marked_state_index=13)

backend = QuantumBackend()
final_state = backend.run(grover_circuit, shots=1) # Get statevector

# Print probabilities
print(final_state.get_probabilities())

4. Noise

from statevectorsim.quantum_noise import NoiseModel

# Create a noise model with 1% Depolarizing noise
noise_model = NoiseModel(default_error_rate=0.01)

# Run circuit with noise injection
results = backend.run(qc, shots=1000, noise_model=noise_model)

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Installation

To set-up, follow the steps:

1. Clone the repository:

git clone https://github.com/jonesdwill/Quantum-Simulator.git
cd Quantum-Simulator

2. Set up a virtual environment (recommended): If you don't have it already, install venv:

py -m pip install venv

Navigate to project directory. Create and activate virtual environment.

py -m venv venv
venv\Scripts\activate

3. Install Required Packages

pip install -r requirements.txt

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Gate Look-up (QuantumGate)

Static methods available in the QuantumGate class.

Category	Gate	Method Signature	Description
Standard	Pauli-X (NOT)	x(targets)	Bit flip.
	Pauli-Y	y(targets)	Phase and bit flip.
	Pauli-Z	z(targets)	Phase flip on $
	Hadamard	h(targets)	Creates superposition.
	Identity	i(targets)	No change.
Phase	Phase (S)	s(targets)	$Z$ rotation by $\pi/2$.
	Inverse Phase ($S^\dagger$)	sdg(targets)	$Z$ rotation by $-\pi/2$.
	$\pi/8$ (T)	t(targets)	$Z$ rotation by $\pi/4$.
	Inverse $\pi/8$ ($T^\dagger$)	tdg(targets)	$Z$ rotation by $-\pi/4$.
Rotation	$R_x(\theta)$	rx(targets, theta)	Rotation about X-axis.
	$R_y(\theta)$	ry(targets, theta)	Rotation about Y-axis.
	$R_z(\theta)$	rz(targets, theta)	Rotation about Z-axis.
Controlled	CNOT (CX)	cx(control, target)	Controlled-X.
	Controlled-Y (CY)	cy(control, target)	Controlled-Y.
	Controlled-Z (CZ)	cz(control, target)	Controlled-Z.
	SWAP	swap(q1, q2)	Swaps two qubit states.
	Controlled- $R_x(\theta)$ (CRX)	crx(c, t, theta)	Controlled-Rotation-X.
	Controlled- $R_y(\theta)$ (CRY)	cry(c, t, theta)	Controlled-Rotation-Y.
	Controlled- $R_z(\theta)$ (CRZ)	crz(c, t, theta)	Controlled-Rotation-Z.
	Controlled-Phase (CRP)	crp(c, t, theta)	Controlled-Phase rotation.
	Controlled-U	cu(c, targets, U, k)	Applies $U^k$ controlled by c.
Multi-Controlled	Toffoli (CCX/MCX)	mcx(controls, target)	Multi-Controlled X.
	MCY	mcy(controls, target)	Multi-Controlled Y.
	MCZ	mcz(controls, target)	Multi-Controlled Z.

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Circuit Look-up (QuantumCircuit)

The QuantumCircuit class includes static methods to quickly generate common n-qubit circuits.

Circuit Name	Method Signature	Qubit Count	Description
Bell State	QuantumCircuit.bell()	2	Creates the Bell state $(\vert 00 \rangle + \vert 11 \rangle)/ \sqrt{2}$.
GHZ State	QuantumCircuit.ghz(n_qubits: int)	$n$	Creates the $n$-qubit Greenberger–Horne–Zeilinger state $(\vert 0...0 \rangle + \vert 1...1 \rangle)/ \sqrt{2}$.
Grover Search	QuantumCircuit.grover_search(n_qubits: int, marked_state_index: int)	$n$	Full Grover's algorithm circuit (Oracle + Diffuser) to find the marked index.
QFT	QuantumCircuit.qft(n_qubits: int, swap_endian: bool = False)	$n$	Performs Quantum Fourier Transform (QFT).
IQFT	QuantumCircuit.qft(n_qubits: int, inverse=True)	$n$	Performs Inverse Quantum Fourier Transform (IQFT).
QFT Adder	QuantumCircuit.qft_adder(n_qubits: int)	$2n$	Performs addition: $\vert A \rangle \vert B \rangle \to \vert A \rangle \vert B+A \pmod{2^n} \rangle$.
QPE	QuantumCircuit.qpe(t_qubits: int, unitary_matrix, m_qubits: int)	$t+m$	Quantum Phase Estimation to estimate the phase of a unitary operator $U$.
Shor's Algo	QuantumCircuit.shors(N: int, a: int)	$\approx 3 \log N$	Quantum subroutine for Shor's Algorithm (factoring $N$).

License

This project is licensed under the MIT License. See the LICENSE file for full details.

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Version

Current version: 0.1.0