Quantum Walks & GPU-Accelerated Quantum Simulation

An open research project exploring quantum algorithms — from classical Markov chains to GPU-accelerated quantum circuit simulation on AMD Instinct MI300X.

What is this?

This repository documents a hands-on learning journey through quantum computing fundamentals, implemented entirely in Julia. It starts with classical random walks, transitions to quantum walks, and builds up to a custom GPU-accelerated state-vector quantum circuit simulator running on AMD hardware.

The code is heavily commented — each file is designed to be read as a tutorial, not just executed.

Why Julia on AMD GPUs?

There is currently no ready-made Julia quantum simulation package with an AMD GPU backend. Existing frameworks like Yao.jl offer CUDA-only GPU support (CuYao.jl), while AMDGPU.jl provides the low-level GPU programming interface but no quantum-specific tooling. This project bridges that gap by building quantum simulation primitives directly on top of AMDGPU.jl with custom ROCm kernels.

Current capabilities

• Classical Markov chains — transition matrices, stationary distributions, eigenvalue analysis
• Discrete-time quantum walks — Hadamard coin, conditional shift, boundary reflection, unitarity verification
• GPU quantum circuit simulator — custom @roc kernels for single-qubit gates (H, X, Z) and CNOT, Bell state generation, multi-shot measurement, benchmarked up to 28 qubits (4 GiB state vector) achieving ~66% of MI300X peak HBM3 bandwidth

Hardware

GPU simulation runs on an AMD Instinct MI300X (192 GiB HBM3, 5.3 TB/s bandwidth, CDNA 3 architecture) provisioned via DigitalOcean GPU Droplets. The AMD Developer Cloud programme offers complimentary MI300X hours for qualified developers — a practical way to experiment with high-end GPU hardware at zero cost.

Roadmap

• Push simulation to 30+ qubits (16–128 GiB state vectors)
• Add parameterised rotation gates (Rx, Ry, Rz) for variational circuits
• Implement Grover's search algorithm on GPU
• Benchmark against Yao.jl CPU baseline
• Explore Yao.jl + ROCArray integration (experimental)
• Variational quantum circuits (VQE, QAOA) targeting IonQ cloud simulators
• Quantum kernel methods for classification

References

• Scott Aaronson, Quantum Computing Since Democritus — complexity theory and conceptual foundations
• John Watrous, The Theory of Quantum Information — rigorous mathematical treatment
• Maria Schuld, Supervised Learning with Quantum Computers — quantum ML algorithms

Requirements

• Julia 1.12+ (MI300X/gfx942 requires Julia 1.12 for LLVM support)
• ROCm 6.x
• AMDGPU.jl, LinearAlgebra.jl, HTTP.jl, JSON3.jl

Licence

MIT