hard-core-boson-quantum-circuit-synthesis

name	hard-core-boson-quantum-circuit-synthesis
category	quantum-computing
description	Hard-core boson algebra for efficient quantum circuit simulation and synthesis. Provides natural representation of multi-qubit systems without sign corrections, with substantially improved execution times over IBM Qiskit, combined with genetic algorithms for circuit synthesis.
trigger_words	hard-core boson, quantum circuit simulation, circuit synthesis, genetic algorithm, qubit representation, bosonic algebra, quantum circuit optimization
arxiv	2606.28004
authors	David Emmanuel-Costa, Michael Epping
published	2026-06-26

Hard-Core Boson Quantum Circuit Synthesis

Overview

Hard-core bosons (HCBs) provide an algebraic framework for representing and simulating multi-qubit quantum systems. Unlike fermionic representations that require sign corrections (Jordan-Wigner strings), HCBs offer a natural representation without sign overhead, leading to substantially improved execution times.

Core Concepts

1. Hard-Core Boson Algebra: Bosonic operators with the constraint that each mode can hold at most one particle (n_i ∈ {0, 1})
2. No Sign Problem: Unlike fermions, HCBs do not require anti-commutation sign corrections
3. Natural Multi-Qubit Mapping: Direct correspondence between HCB occupation numbers and qubit computational basis states

Key Steps for Circuit Simulation

1. Map qubit states to HCB occupation numbers: |0⟩ ↔ |vacuum⟩, |1⟩ ↔ |occupied⟩
2. Express quantum gates as HCB operator products
3. Apply HCB operators to state vectors using algebraic rules
4. Extract measurement probabilities from resulting state amplitudes

Key Steps for Circuit Synthesis (with Genetic Algorithms)

1. Define target unitary or state to be synthesized
2. Initialize population of random HCB gate sequences
3. Evaluate fitness: fidelity between synthesized and target unitary
4. Apply genetic operators: crossover (combine gate sequences), mutation (add/remove/modify gates)
5. Select best candidates for next generation
6. Iterate until convergence or maximum generations

Performance Benefits

• Substantially faster execution than IBM Qiskit for equivalent simulations
• No sign correction overhead compared to fermionic approaches
• Natural parallelization potential due to simplified algebraic structure

When to Use

• Quantum circuit simulation on classical hardware
• Quantum circuit optimization and synthesis
• Multi-qubit system simulation where fermionic sign overhead is prohibitive
• Genetic algorithm-based circuit design pipelines

Implementation Notes

• HCB creation operator: b†_i creates a particle at site i if site is empty, annihilates if occupied
• HCB annihilation operator: b_i annihilates a particle at site i if occupied, annihilates if empty
• On-site constraint: (b†_i)² = 0, (b_i)² = 0 (hard-core constraint)
• Commutation: [b_i, b†_j] = 0 for i ≠ j, {b_i, b†_i} = 1

Pitfalls

• HCB representation is limited to qubit-like (two-level) systems
• Mapping to fermionic problems may still require Jordan-Wigner transformation
• Genetic algorithm convergence depends heavily on fitness function design
• Gate sequence length grows with circuit complexity — consider depth constraints in GA fitness