TY - GEN
T1 - Overlapping qubits
AU - Chao, Rui
AU - Reichardt, Ben W.
AU - Sutherland, Chris
AU - Vidick, Thomas
N1 - R.C., B.R. and C.S. supported by NSF grant CCF-1254119 and ARO grant W911NF-12-1-0541. T.V. supported by NSF CAREER grant CCF-1553477, an AFOSR YIP award, and the IQIM, an NSF Physics Frontiers Center (NFS Grant PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-12500028).
PY - 2017/11/1
Y1 - 2017/11/1
N2 - 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 < € in nO(1/€2) 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.
AB - 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 < € in nO(1/€2) 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.
UR - http://www.scopus.com/inward/record.url?scp=85038591233&partnerID=8YFLogxK
U2 - https://doi.org/10.4230/LIPIcs.ITCS.2017.48
DO - https://doi.org/10.4230/LIPIcs.ITCS.2017.48
M3 - منشور من مؤتمر
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 8th Innovations in Theoretical Computer Science Conference, ITCS 2017
A2 - Papadimitriou, Christos H.
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 8th Innovations in Theoretical Computer Science Conference, ITCS 2017
Y2 - 9 January 2017 through 11 January 2017
ER -