Overlapping qubits

• DOI: 10.48550/arxiv.1701.01062
• Publication Date: 2017-01-01
• Authors: Rui Chao; Ben W. Reichardt; Chris Sutherland; Thomas Vidick
• Keywords: Quantum Physics; Dimension test; FOS: Physical sciences; 0102 computer and information sciences; ddc:004; Quantum computing; Quantum Physics (quant-ph); 530; Qubits; 01 natural sciences; 004

An ideal system of $n$ qubits has $2^n$ dimensions. This exponential grants power, but also hinders characterizing the system's state and dynamics. We study a new problem: in physical might not be independent. They can "overlap," sense that an operation on one qubit slightly affects others. show allowing for slight overlaps, fit just polynomially many (Defined natural way, all pairwise overlaps $\leq ε$ $n^{O(1/ε^2)}$ dimensions.) Thus, even before considering issues like noise, real inherently lack any potential power. On other hand, we provide efficient test to certify dimensionality. Unfortunately, is sensitive noise. It important devise more robust tests arrangements quantum devices.