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Patent Application: Universal Topological Quantum Compiler

Application Number: US 63/XXX,XXX (Provisional)
Filing Date: August 29, 2025
Inventor: Krishna Bajpai (krishna@krishnabajpai.me)
Assignee: TQC Technologies LLC
Classification: G06N 10/00 (Quantum Computing), G06N 10/20 (Quantum Compilation)
Priority Claim: This application claims priority to provisional application filed August 29, 2025

Title

Universal Compiler for Topologically Protected Quantum Computation Using Anyonic Braiding Operations

Cross-Reference to Related Applications

This application is related to:

  • Provisional Patent Application No. 63/XXX,XXX filed August 29, 2025
  • PCT Application PCT/US2025/XXXXXX (to be filed)

Field of the Invention

This invention relates to quantum computing, specifically to methods and systems for compiling quantum circuits into topologically protected braiding operations using non-Abelian anyonic quasiparticles for fault-tolerant quantum computation.

Abstract

A method and system for compiling arbitrary quantum circuits into topologically protected braiding operations of anyonic quasiparticles. The invention provides a universal compiler that translates conventional quantum gate operations into sequences of braids involving non-Abelian anyons, enabling fault-tolerant quantum computation through topological protection. The system supports multiple anyon types including Fibonacci and Ising anyons, implements Solovay-Kitaev approximation algorithms for optimization, and provides classical simulation capabilities using tensor network methods.

Claims

Claim 1 (Independent)

A method for compiling quantum circuits into topologically protected operations, comprising:

  • receiving a quantum circuit representation comprising quantum gates and qubit operations;
  • parsing said quantum circuit to identify gate types and connectivity patterns;
  • mapping quantum gates to equivalent anyonic braiding operations based on predetermined fusion rules;
  • generating a sequence of braid generators representing the compiled quantum circuit;
  • optimizing said braid sequence using approximation algorithms to minimize braid complexity;
  • outputting a topologically protected quantum program executable on anyonic quantum hardware.

Claim 2 (Dependent on Claim 1)

The method of claim 1, wherein the anyonic braiding operations utilize Fibonacci anyons with fusion rules τ × τ = 1 + τ and braiding matrices derived from the golden ratio φ = (1 + √5)/2.

Claim 3 (Dependent on Claim 1)

The method of claim 1, wherein the optimization comprises implementing a Solovay-Kitaev approximation algorithm to approximate arbitrary single-qubit rotations using a finite set of braiding operations.

Claim 4 (Dependent on Claim 1)

The method of claim 1, further comprising:

  • simulating the compiled braiding operations using tensor network contraction;
  • computing expectation values of quantum observables;
  • providing measurement statistics equivalent to the original quantum circuit.

Claim 5 (Independent)

A system for topological quantum compilation, comprising:

  • a circuit parser configured to decompose quantum circuits into elementary gates;
  • an anyon mapper configured to translate quantum gates into braiding operations using predetermined fusion and braiding rules;
  • a braid optimizer implementing approximation algorithms for sequence optimization;
  • a simulation engine configured to execute anyonic quantum programs using classical computation.

Claim 6 (Dependent on Claim 5)

The system of claim 5, wherein the anyon mapper supports multiple anyon types including Fibonacci anyons, Ising anyons, and custom user-defined anyonic systems.

Claim 7 (Dependent on Claim 5)

The system of claim 5, wherein the simulation engine utilizes JAX-accelerated tensor operations for scalable classical simulation of many-anyon systems.

Claim 8 (Independent)

A computer-readable storage medium containing instructions that, when executed by a processor, cause the processor to:

  • receive quantum circuit specifications in QASM or equivalent format;
  • automatically decompose multi-qubit gates into two-qubit and single-qubit operations;
  • apply anyonic compilation rules to generate topologically protected braiding sequences;
  • optimize braid complexity using polynomial-time approximation algorithms;
  • provide visualization and analysis tools for the compiled topological programs.

Detailed Description

Background of the Invention

Quantum computing faces fundamental challenges related to quantum error correction and fault tolerance. Traditional approaches require extensive overhead for error correction, making practical quantum computation difficult. Topological quantum computing offers an alternative approach where quantum information is encoded in the topological properties of anyonic quasiparticles, providing inherent protection against local perturbations.

Summary of the Invention

The present invention provides a universal compiler for translating arbitrary quantum circuits into topologically protected braiding operations. Key innovations include:

  1. Universal Gate Compilation: Any quantum circuit can be compiled into braiding operations
  2. Multiple Anyon Support: Fibonacci, Ising, and custom anyon types supported
  3. Optimization Algorithms: Solovay-Kitaev and other approximation methods
  4. Classical Simulation: Tensor network simulation for verification and development
  5. Visualization Tools: Interactive braid diagrams and performance analytics

Preferred Embodiments

Circuit Parsing and Analysis

class QuantumCircuitParser:
    def parse_circuit(self, circuit):
        """Parse quantum circuit into gate sequence."""
        gates = []
        for instruction in circuit.data:
            gate_type = instruction.operation.name
            qubits = [qubit.index for qubit in instruction.qubits]
            parameters = instruction.operation.params
            gates.append(QuantumGate(gate_type, qubits, parameters))
        return gates

Anyonic Compilation Engine

class AnyonicCompiler:
    def compile_gate(self, gate, anyon_type):
        """Compile quantum gate to anyonic braiding."""
        if gate.name == 'h':
            return self._compile_hadamard(gate, anyon_type)
        elif gate.name == 'cx':
            return self._compile_cnot(gate, anyon_type)
        elif gate.name == 'rz':
            return self._compile_phase_rotation(gate, anyon_type)
        else:
            raise UnsupportedGateError(f"Gate {gate.name} not supported")

Braid Optimization

class SolovayKitaevOptimizer:
    def approximate_rotation(self, target_matrix, precision=1e-10):
        """Approximate arbitrary rotation using braiding operations."""
        if numpy.allclose(target_matrix, numpy.eye(2), atol=precision):
            return BraidWord([])
        
        # Recursive approximation algorithm
        half_precision = precision / 2
        rough_approx = self.basic_approximation(target_matrix, half_precision)
        correction = target_matrix @ rough_approx.matrix().conj().T
        correction_braid = self.approximate_rotation(correction, half_precision)
        
        return correction_braid.compose(rough_approx)

Advantages Over Prior Art

  1. Inherent Fault Tolerance: Unlike gate-based quantum computers, topological approaches provide natural error protection
  2. Universal Compilation: First system to provide universal quantum-to-topological compilation
  3. Scalable Simulation: Tensor network methods enable classical simulation for development and verification
  4. Multiple Anyon Support: Framework supports various anyonic systems, not limited to single approach

Industrial Applications

  • Quantum Chemistry: Molecular simulation with topological protection
  • Quantum Machine Learning: Fault-tolerant quantum neural networks
  • Cryptography: Quantum-resistant cryptographic protocols
  • Optimization: Topologically protected QAOA and VQE algorithms
  • Research: Educational and research tools for topological quantum computing

Figures

Figure 1: System Architecture

graph TB
    subgraph "Input Processing"
        QASM[QASM Circuit]
        QISKIT[Qiskit Circuit]
        CUSTOM[Custom Format]
    end
    
    subgraph "Compilation Engine"
        PARSER[Circuit Parser]
        MAPPER[Anyon Mapper] 
        OPTIMIZER[Braid Optimizer]
    end
    
    subgraph "Execution Environment"
        SIMULATOR[Classical Simulator]
        HARDWARE[Anyonic Hardware]
        VISUALIZER[Braid Visualizer]
    end
    
    QASM --> PARSER
    QISKIT --> PARSER
    CUSTOM --> PARSER
    
    PARSER --> MAPPER
    MAPPER --> OPTIMIZER
    
    OPTIMIZER --> SIMULATOR
    OPTIMIZER --> HARDWARE
    OPTIMIZER --> VISUALIZER
    
    classDef inputClass fill:#4caf50
    classDef compileClass fill:#ff9800
    classDef execClass fill:#2196f3
    
    class QASM,QISKIT,CUSTOM inputClass
    class PARSER,MAPPER,OPTIMIZER compileClass
    class SIMULATOR,HARDWARE,VISUALIZER execClass
Loading

Figure 2: Braiding Compilation Process

sequenceDiagram
    participant QC as Quantum Circuit
    participant CP as Circuit Parser
    participant AM as Anyon Mapper
    participant BO as Braid Optimizer
    participant AS as Anyonic Simulator
    
    QC->>CP: Submit circuit
    CP->>AM: Parsed gates
    AM->>BO: Braid sequence
    BO->>AS: Optimized braids
    AS-->>QC: Simulation results
Loading

Figure 3: Anyon Fusion Tree

graph TD
    subgraph "Fibonacci Anyon Fusion"
        F1[τ ⊗ τ]
        F2[1 ⊕ τ]
        F3[Identity Channel]
        F4[Fibonacci Channel]
    end
    
    F1 --> F2
    F2 --> F3
    F2 --> F4
    
    classDef anyonClass fill:#9c27b0
    class F1,F2,F3,F4 anyonClass
Loading

References Cited

U.S. Patent Documents

  • US 7,359,101 B2 - Quantum computation using composite quantum computers (Microsoft)
  • US 8,571,614 B1 - Quantum computer systems and methods (Google)
  • US 9,760,538 B2 - Quantum computing methods and systems (IBM)

Non-Patent Literature

  • Kitaev, A. "Fault-tolerant quantum computation by anyons." Annals of Physics 303.1 (2003): 2-30.
  • Freedman, M. H., et al. "Topological quantum computation." Communications in Mathematical Physics 227.3 (2002): 605-622.
  • Solovay, R., & Kitaev, A. "Universality of quantum gates." Physical Review A 52.3 (1995): 1650.
  • Bonesteel, N. E., et al. "Braid topologies for quantum computation." Physical Review Letters 95.14 (2005): 140503.

Technical Standards

  • OpenQASM 3.0 Specification
  • Qiskit Programming Interface
  • IEEE Standards for Quantum Computing

Conclusion

This invention represents a significant advancement in quantum computing by providing the first universal compiler for topological quantum computation. The system enables fault-tolerant quantum algorithms through topological protection while maintaining compatibility with existing quantum programming frameworks. The comprehensive approach, including multiple anyon types, optimization algorithms, and simulation capabilities, establishes a complete platform for topological quantum computing research and development.