TY - JOUR

T1 - Universality of black hole quantum computing

AU - Dvali, Gia

AU - Gomez, Cesar

AU - Lüst, Dieter

AU - Omar, Yasser

AU - Richter, Benedikt

N1 - Funding Information:
The work of G.D. was supported by Humboldt Foundation under Alexander von Humboldt Professorship, by European Commission under ERC Advanced Grant 339169 ?Selfcompletion? and by TRR 33 ?The DarkUniverse?. The work of C.G. was supported in part by Humboldt Foundation and by Grants: FPA 2009-07908, CPAN (CSD2007-00042) and by the ERC Advanced Grant 339169 ?Selfcompletion?. The work of D.L. was supported by the ERC Advanced Grant 32004 ?Strings and Gravity? and also by TRR 33. The work of Y.O. and B.R. was supported by Funda??o para a Ci?ncia e a Tecnologia (Portugal), namely through programmes PTDC/POPH/POCH and projects UID/EEA/50008/2013, IT/QuSim, IT/QuNet, ProQuNet, partially funded by EU FEDER, and from the EU FP7 project PAPETS (GA 323901). B.R. acknowledges the support from the DP-PMI and FCT through scholarship SFRH/BD/52651/2014. Furthermore, B.R. would like to thank the Arnold Sommerfeld Center for Theoretical Physics at LMU Munich for hospitality and support.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - By analyzing the key properties of black holes from the point of view of quantum information, we derive a model-independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with quantum critical condensates, allowing the use of a common language to describe quantum computing in both systems. We analyze such quantum computing by allowing coupling to external modes, under the condition that the external influence must be soft-enough in order not to offset the basic properties of the system. We derive model-independent bounds on some crucial time-scales, such as the times of gate operation, decoherence, maximal entanglement and total scrambling. We show that for black hole type quantum computers all these time-scales are of the order of the black hole half-life time. Furthermore, we construct explicitly a set of Hamiltonians that generates a universal set of quantum gates for the black hole type computer. We find that the gates work at maximal energy efficiency. Furthermore, we establish a fundamental bound on the complexity of quantum circuits encoded on these systems, and characterize the unitary operations that are implementable. It becomes apparent that the computational power is very limited due to the fact that the black hole life-time is of the same order of the gate operation time. As a consequence, it is impossible to retrieve its information, within the life-time of a black hole, by externally coupling to the black hole qubits. However, we show that, in principle, coupling to some of the internal degrees of freedom allows acquiring knowledge about the micro-state. Still, due to the trivial complexity of operations that can be performed, there is no time advantage over the collection of Hawking radiation and subsequent decoding.

AB - By analyzing the key properties of black holes from the point of view of quantum information, we derive a model-independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with quantum critical condensates, allowing the use of a common language to describe quantum computing in both systems. We analyze such quantum computing by allowing coupling to external modes, under the condition that the external influence must be soft-enough in order not to offset the basic properties of the system. We derive model-independent bounds on some crucial time-scales, such as the times of gate operation, decoherence, maximal entanglement and total scrambling. We show that for black hole type quantum computers all these time-scales are of the order of the black hole half-life time. Furthermore, we construct explicitly a set of Hamiltonians that generates a universal set of quantum gates for the black hole type computer. We find that the gates work at maximal energy efficiency. Furthermore, we establish a fundamental bound on the complexity of quantum circuits encoded on these systems, and characterize the unitary operations that are implementable. It becomes apparent that the computational power is very limited due to the fact that the black hole life-time is of the same order of the gate operation time. As a consequence, it is impossible to retrieve its information, within the life-time of a black hole, by externally coupling to the black hole qubits. However, we show that, in principle, coupling to some of the internal degrees of freedom allows acquiring knowledge about the micro-state. Still, due to the trivial complexity of operations that can be performed, there is no time advantage over the collection of Hawking radiation and subsequent decoding.

KW - Black hole

KW - Quantum computing

UR - http://www.scopus.com/inward/record.url?scp=85007376684&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007376684&partnerID=8YFLogxK

U2 - 10.1002/prop.201600111

DO - 10.1002/prop.201600111

M3 - Article

AN - SCOPUS:85007376684

VL - 65

JO - Fortschritte der Physik

JF - Fortschritte der Physik

SN - 0015-8208

IS - 1

M1 - 1600111

ER -