Packaged Quantum States for Gauge-Invariant Quantum Computation and Communication
Rongchao Ma
TL;DR
The paper develops a gauge-invariant framework for quantum information processing by packaging all internal quantum numbers (IQNs) into inseparable blocks and restricting dynamics to fixed superselection sectors, thereby suppressing gauge-violating errors and enabling robust quantum computation and communication.It introduces necessary and sufficient conditions for single- and multi-particle packaged states, constructs pure-packaged qubits/qudits, packaged gates, and packaged circuits, and proves their gauge invariance and closure properties within a ($d imes D$)-dimensional hybrid-packaged space.By adapting standard quantum error-correction codes (Shor-like, Steane-like CSS, surface codes) to the packaged space and detailing fault-tolerant implementations, the work demonstrates universality (Clifford+Θ_r) and enhanced fault-tolerance due to restricted error types, with explicit methods for magic-state injection and leakage handling.The framework is then extended to high-dimensional hybrid-packaged qudits, Bell bases, MUBs, and resource states, and applied to re-express conventional algorithms (QFT, QPE) and coding strategies in the gauge-respecting setting, offering potential for native lattice-gauge theory simulations and more secure quantum communication.Overall, the packaged-space approach provides a principled path toward gauge-respecting, fault-tolerant quantum technologies with richer internal structure and improved resilience against gauge-violating noise.
Abstract
Packaged quantum states are gauge-invariant states in which all internal quantum numbers (IQNs) form an inseparable block. This feature gives rise to novel packaged entanglements that encompass all IQNs, which is important both for fundamental physics and for quantum technology. Here we develop a framework for gauge-invariant quantum information processing based on packaged quantum states. We propose the necessary and sufficient conditions for a valid packaged superposition state of a single particle and multi-particle. We then present the details of constructing gauge-invariant packaged qubits (or qudits), packaged gates, and packaged circuits (which commute with the total charge operator). These serve as alternative foundation for gauge-invariant quantum information science. We then adapt conventional quantum error-correction codes, quantum algorithms, and quantum communication protocols to the ($d \times D$)-dimensional hybrid-packaged subspace. This high-dimensional hybrid-packaged subspace is flexible for pruning and scaling to match available physics systems. Thus, packaged quantum information processing becomes feasible and testable. Our results show that the gauge-invariant packaged quantum states may provide a possible route toward robust, fault-tolerant, and secure quantum technologies.