2017/01/01 by Rui Chao, Ben W. Reichardt, Chris Sutherland +5 · 1 voice · 3 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #quant-ph
paper · pdf · doi:10.4230/lipics.itcs.2017.48
22 pages, 3 figures
arxiv created 2017/01/04 · arxiv updated 2018/10/19
An ideal system of n qubits has 2n dimensions. This exponential grants power, but also hinders characterizing the system's state and dynamics. We study a new problem: the qubits in a physical system might not be independent. They can "overlap," in the sense that an operation on one qubit slightly affects the others. We show that allowing for slight overlaps, n qubits can fit in just polynomially many dimensions. (Defined in a natural way, all pairwise overlaps can be ≤ ε in nO(1/ε2) dimensions.) Thus, even before considering issues like noise, a real system of n qubits might inherently lack any potential for exponential power. On the other hand, we also provide an efficient test to certify exponential dimensionality. Unfortunately, the test is sensitive to noise. It is important to devise more robust tests on the arrangements of qubits in quantum devices.