Grover Search and the No-Signaling Principle

• Main Authors: Bao, Ning (Author), Jordan, Stephen P. (Author), Bouland, Adam Michael (Contributor)
• Other Authors: Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory (Contributor), Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor)
• Format: Article
• Language: English
• Published: American Physical Society, 2016-12-20T14:45:50Z.
• Subjects: Article
• Online Access: Get fulltext

Two of the key properties of quantum physics are the no-signaling principle and the Grover search lower bound. That is, despite admitting stronger-than-classical correlations, quantum mechanics does not imply superluminal signaling, and despite a form of exponential parallelism, quantum mechanics does not imply polynomial-time brute force solution of NP-complete problems. Here, we investigate the degree to which these two properties are connected. We examine four classes of deviations from quantum mechanics, for which we draw inspiration from the literature on the black hole information paradox. We show that in these models, the physical resources required to send a superluminal signal scale polynomially with the resources needed to speed up Grover's algorithm. Hence the no-signaling principle is equivalent to the inability to solve NP-hard problems efficiently by brute force within the classes of theories analyzed.
National Science Foundation (U.S.) (Alan T. Waterman Award Grant 1249349)
DuBridge Postdoctoral Fellowship
National Science Foundation (U.S.) (Physics Frontiers Center, Institute for Quantum Information and Matter. Grant PHY-1125565)
Gordon and Betty Moore Foundation (Grant GBMF-12500028)
United States. Dept. of Energy. Office of High Energy Physics (Award DE-SC0011632)
National Science Foundation (U.S.). Graduate Research Fellowship Program (Grant 1122374)