Resource-Efficient Quantum Circuit Synthesis

Overview

**OVERVIEW** A quantum computing research architecture developed to reduce logical qubit requirements, expensive gate operations, and computational resource costs through joint mathematical and circuit optimization. The work combines three computational implementations: reversible inverse-square-root arithmetic, finite-field decoding, and representation-aware quantum chemistry. Its central finding is that the mathematical representation of a computation can substantially influence its implementation cost. Equivalent formulations may require different numbers of quantum operations, even when they describe the same underlying mathematical result. **TECHNICAL CHALLENGE** Quantum algorithms can require significant resources because of their arithmetic, numerical precision, temporary storage, and reversible cleanup requirements. Conventional circuit optimization often begins after the mathematical formulation has been selected. This research also investigates whether a better formulation can reduce the necessary computation before circuit synthesis. **CORE INNOVATION** The approach jointly optimizes mathematical representations, reversible algorithms, numerical precision, and circuit construction. In quantum chemistry, the optimizer searches mathematically equivalent factorization coordinates with different resource-related normalization costs. In reversible arithmetic and decoding, it uses structured numerical and algebraic methods to reduce expensive operations and workspace requirements. **SYSTEM ARCHITECTURE** **Reversible Numerical Arithmetic:** Segmented quadratic approximation, centered radix-4 Booth arithmetic, optimized coefficient lookup, and measurement-based uncomputation. **Finite-Field Decoding:** Composite-field arithmetic, reversible Reed–Solomon decoding, structured polynomial operations, and optimized temporary-register management. **Quantum Chemistry:** Double-factorized Hamiltonian representations, orthogonal coordinate optimization, numerical compression, quantized rotations, and compact reversible data preparation. **PERFORMANCE** The recorded implementations achieved modeled reference-cost improvements of 9.0917× for inverse-square-root arithmetic, 8.4008× for finite-field decoding, and 1.2700× for quantum chemistry. Their combined geometric mean is 4.5947× across three distinct computational evaluations. **VALIDATION** All three implementations have recorded circuit-level verification results satisfying their respective computational requirements. The measurements concern logical quantum circuit resource models. Physical quantum hardware execution and hardware-level acceleration have not been demonstrated.

Technical Specifications

• Arithmetic Circuit: 108 logical qubits
• Arithmetic Operations: 1,877 Toffoli-like
• Arithmetic Verification: 200,540,928 trials
• Decoder Field: GF(2¹²)
• Decoder Circuit: 1,929 logical qubits
• Decoder Operations: 652,567 Toffoli-like
• Chemistry Model: 76 orbitals
• Factorization Dimensions: 65 × 60 × 29
• Chemistry Circuit Width: 123 qubits per angle circuit
• Chemistry Operations: 72,222 Toffoli-like
• Chemistry Accuracy Errors: ≤ 0.020 hartree
• Evaluation Stage: Computational verification

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