Wormhole in a quantum computer

Adam R. Brown, Leonard Susskind

Susmita Bhattacharjee, Riddhima Sadhu, Deep Bhattacharjee +13 more

Adam Bouland, Bill Fefferman, Umesh V. Vazirani

A fundamental issue in the AdS/CFT correspondence is the wormhole growth paradox. Susskind's conjectured resolution of the paradox was to equate the volume of the wormhole with the circuit complexity of its dual quantum state in the CFT. We study the ramifications of this conjecture from a complexity-theoretic perspective. Specifically we give evidence for the existence of computationally pseudorandom states in the CFT, and argue that wormhole volume is measureable in a non-physical but computational sense, by amalgamating the experiences of multiple observers in the wormhole. In other words the conjecture equates a quantity which is difficult to compute with one which is easy to compute. The pseudorandomness argument further implies that this is a necessary feature of any resolution of the wormhole growth paradox, not just of Susskind's Complexity=Volume conjecture. As a corollary we conclude that either the AdS/CFT dictionary map must be exponentially complex, or the quantum Extended Church-Turing thesis must be false in quantum gravity.

Yingyu Yang

Abstract We compute the half-wormhole contribution in a complex SYK model with one time point by exact computations and saddle point analysis. The chemical potential significantly influences the computation and the relative magnitude of the half-wormhole. When the chemical potential is large compared to the random coupling, the disk dominates so that there is no wormhole and half-wormhole. When the chemical potential is relatively small we find out the wormhole and the half-wormhole contributions.

Daniel Louis Jafferis, Alexander Zlokapa, Joseph David Lykken +5 more

Yonghong Liu

In this article, we present wormholes cryptosystems (WCS). The first is the wormhole key distribution centre theorem, which asserts that the WCS is a public key group. The second is the security theorem, which asserts that the WCS are a one-way function. The third is new version of the definition for the WCS, and we introduce the notion of groups of WCS. The fourth ingredient is the encryption algorithm and decryption algorithm, and design principle. Here, we present a toy example to illustrate the computation of these encryptions and decryptions. The finally we present the unsymmetrical WCS theorem.