Eliminating Surface Codes: Floquet-based Error Prevention Framework
Lars Wood, CSO, Analog Physics Inc.
Our quantum computing breakthrough fundamentally transforms error prevention by exploiting the deep connection between Floquet theory and quantum state evolution. The framework actively monitors and stabilizes quantum circuit dynamics through entangled ancilla qubits, operating at the Hamiltonian level represented by H(t) = H₀ + Hₐ(t) + Hₙ(t). By calculating the Floquet determinant and its multipliers (α, λ), we characterize the complete system dynamics including both deterministic and stochastic components.
The core innovation lies in the Floquet operator F(t) = exp(-iH(t)t/ħ), whose eigenvalue equation F(t)ψ(t) = exp(iαt)[cos(λt) + i sin(λt)]ψ(t) reveals error precursors before decoherence occurs. By maintaining the Floquet determinant below 2, we ensure stability across all error channels. The α parameter quantifies non-periodic perturbations (mapping to amplitude damping and phase drift), while λ captures periodic evolution components including environmental coupling.
Critical to eliminating surface codes, our continuous Hamiltonian monitoring through ancilla measurements reveals patterns in quantum noise via fluctuations in (α, λ) before decoherence manifests. These multipliers directly inform microwave control parameters for real-time stabilization through Hₐ(t), maintaining ∂F/∂t + i[H(t), F(t)] = 0. This direct intervention achieves fault tolerance at the physical qubit level, eliminating the need for logical qubit encoding and its associated overhead.
The key advantage of this approach is its unified treatment of both deterministic and stochastic errors through fundamental Hamiltonian dynamics, representing a shift from error correction to prevention through precise physical control of quantum systems.
Validation through quantum simulations demonstrates the framework's effectiveness, setting the stage for scaled physical implementation with our partner Northrop Grumman.