SECTION 03 // HIGH-PERFORMANCE SCIENTIFIC COMPUTING

COMPUTATIONAL MACHINERY & OPEN-SOURCE JULIA

Open-source physics packages, real-time FCIQMC algorithms, Slurm HPC cluster pipelines, and numerical toolsets.

01 // SCIENTIFIC JULIA: RIMU.JL & REAL-TIME FCIQMC

[MERGED PR #19]

RimuRealTime.jl Real-time FCIQMC dynamics for Rimu.jl

JULIA 1.10+ GITHUB REPO ↗

Full Configuration Interaction Quantum Monte Carlo (FCIQMC) has revolutionized ground-state calculations of strongly interacting quantum systems. However, real-time quantum dynamics governed by $e^{-iHt}$ suffer from the dynamic phase problem. Within the Brand research group, we developed RimuRealTime.jl to enable numerically stable unitary propagation using symplectic algorithms.

LeapfrogComplex

Symplectic second-order integrator splitting real and imaginary walker components over staggered time grids.

InternalCoherence

Post-step annihilation strategy filtering high-frequency noise without violating total particle conservation.

SignCorrelator

Custom observable monitoring the decay of walker phase coherence to detect onset of the sign collapse.

src/strategies/internal_coherence.jl [JULIA KERNEL]

# Implementation of InternalCoherence Post-Step Strategy for Real-Time FCIQMC
# Joachim Brand Lab // Massey University (Auckland, NZ)

using Rimu
using Rimu.Hamiltonians
import Rimu.Interfaces: post_step

struct InternalCoherence{T<:AbstractFloat} <: PostStepStrategy
    threshold::T
    damping_factor::T
end

InternalCoherence(; threshold=0.05, damping_factor=0.98) = 
    InternalCoherence(promote(threshold, damping_factor)...)

@inline function post_step(strategy::InternalCoherence, step::Int, state::ComplexFciqmcState)
    walkers = state.walker_vector
    corr = compute_sign_correlator(walkers)
    
    # Check if stochastic phase oscillations have compromised signal-to-noise
    if abs(corr) < strategy.threshold
        # Symplectically damp high-frequency orthogonal phase fluctuations
        damp_orthogonal_phase!(walkers, strategy.damping_factor)
    end
    
    return state
end

function compute_sign_correlator(w::AbstractVector{Complex{T}}) where T
    real_sum = sum(real, w)
    imag_sum = sum(imag, w)
    norm_sq = sum(abs2, w)
    return (real_sum^2 + imag_sum^2) / (norm_sq + eps(T))
end

02 // ALGORITHMIC TOOLSETS & HAMILTONIAN SOLVERS

[TESTED SUITE]

FermiHubbard1D.jl EXACT DIAG.

High-performance Julia solver for 1D extended Fermi-Hubbard chains. Implements sparse Hamiltonian matrices, bitwise occupation basis generation, and Lanczos/Arnoldi iterations using KrylovKit.jl.

• CDW and SDW structure factor computation
• Non-Hermitian asymmetric hopping support
• Multithreaded sparse-matrix vector multiplication

DEPS: KrylovKit.jl, DataFrames.jl, JLD2.jl v0.4.2

QuantumGateSynthesis INRIA 2025

Algorithmic compiler synthesizing single-qubit unitaries $U \in SU(2)$ into exact and $\varepsilon$-approximate Clifford+T gate circuits. Developed during research at Inria Paris-Saclay.

• Algebraic factoring in cyclotomic rings $\mathbb{Z}[\frac{1}{\sqrt{2}}, i]$
• Canonical Matsumoto-Amano normal form verification
• T-count and ancilla minimization algorithms

STACK: Python, SymPy, Qiskit, Rust FFI v1.1.0

VQE-QAOA-Workbench OPTIMIZATION

Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA) benchmark suite comparing statevector backends against noisy shot simulation.

• PennyLane & PyTorch gradient descent backends
• Quantum natural gradient (QNG) optimizer
• Barren plateau avoidance strategies in deep ansatze

STACK: PennyLane, PyTorch, SciPy v0.8.0

GPE1D-Spectral SOLITONS

Split-step Fourier spectral method solver for 1D and quasi-1D Gross-Pitaevskii equations with contact and non-local interaction potentials.

• Symplectic 4th-order Yoshida time-stepping
• Imaginary time ground-state preparation
• Real-time soliton collision phase extraction

STACK: Julia (FFTW.jl, Plots.jl) v1.2.1

ARCHIVAL PLATE 03-C // 1D NON-HERMITIAN FERMI-HUBBARD SKIN EFFECT & BOUNDARY ACCUMULATION

LATTICE SPECTRUM

Non-Hermitian Skin Effect: Under open boundary conditions, non-reciprocal hoppings ($\gamma > 0$) force an extensive number of bulk eigenstates to collapse exponentially onto the boundary manifold, fundamentally altering the bulk-boundary correspondence.

03 // SLURM BATCH ORCHESTRATION & HPC ARTIFACT PIPELINES

PRODUCTION CLUSTER DEPLOYMENT

Large-scale FCIQMC and Gross-Pitaevskii simulations require parameter sweeps spanning hundreds of coupling strengths ($g_{1D}$) and interaction regimes ($U/t, V/t$). Below is the standard Slurm job array template used across our Massey University HPC cluster nodes:

slurm_fciqmc_array.sbatch [BASH SLURM SCRIPT]

#!/usr/bin/env bash
# ==============================================================================
# SLURM PRODUCTION SCRIPT // REAL-TIME FCIQMC DYNAMICS SWEEP
# Joachim Brand Lab // Massey University Auckland
# ==============================================================================
#SBATCH --job-name=fciqmc_sweep
#SBATCH --partition=parallel
#SBATCH --nodes=4
#SBATCH --ntasks-per-node=32
#SBATCH --cpus-per-task=1
#SBATCH --time=48:00:00
#SBATCH --mem=128G
#SBATCH --array=1-100%20
#SBATCH --output=/nesi/nobackup/massey_phys/logs/%x_%A_%a.out
#SBATCH --error=/nesi/nobackup/massey_phys/logs/%x_%A_%a.err

module purge
module load Julia/1.10.2-GCC-12.3.0
module load OpenMPI/4.1.5-GCC-12.3.0

export JULIA_NUM_THREADS=32
export OPENBLAS_NUM_THREADS=32

PARAM_FILE="config/sweep_parameters.csv"
LINE=$(sed -n "$((SLURM_ARRAY_TASK_ID + 1))p" "$PARAM_FILE")
IFS=',' read -r RUN_ID G_COUPLING N_WALKERS DT T_MAX <<< "$LINE"

echo "=========================================================="
echo "LAUNCHING TASK $SLURM_ARRAY_TASK_ID on $(hostname)"
echo "PARAMETERS: G=$G_COUPLING, WALKERS=$N_WALKERS, DT=$DT, T_MAX=$T_MAX"
echo "=========================================================="

srun julia --project=@. scripts/run_realtime_fciqmc.jl \
    --coupling "$G_COUPLING" \
    --walkers "$N_WALKERS" \
    --dt "$DT" \
    --tmax "$T_MAX" \
    --outdir "/nesi/nobackup/massey_phys/data/run_${SLURM_ARRAY_JOB_ID}_${SLURM_ARRAY_TASK_ID}"

echo "TASK $SLURM_ARRAY_TASK_ID COMPLETED AT $(date -u '+%Y-%m-%dT%H:%M:%SZ')"

AUTOMATED ARTIFACT CACHING VIA SSH JUMP PROXY:

To securely retrieve HDF5 / JLD2 simulation artifacts from remote Massey/NeSI supercomputers directly to local Neovim/Julia buffers without manual scp commands:

rsync -avz -e "ssh -J gateway.massey.ac.nz" node01:/nesi/nobackup/massey_phys/data/ ./scratch/artifacts/