Category: Uncategorized

THE END OF COMPLEXITY. “If the circuit continues to run, the complexity will continue to increase until it reaches a maximum. The existence of a maximum follows from the fact that any unitary can be implemented by a circuit with no more than an exponential number of gates.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201500092?casa_token=8OO3b1OY4e4AAAAA%3ARqriAgTwtxnvsxl09CqnNy79m7l4ye7ZrkZxcLtObB9kHsTwYgzBuIV2X-xXQ7ezoR6VQPfQLCS-vnI View in LinkedIn

LIMITS OF COMPLEXITY. “I will assume that over some range of time the complexity does increase linearly. The range cannot be infinite, since as we will see, complexity is bounded, but the time for saturating the bound is exponentially large. On even larger time scales the complexity is quasi‐periodic with an average period equal to the doubly exponential quantum recurrence time.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201500092?casa_token=8OO3b1OY4e4AAAAA%3ARqriAgTwtxnvsxl09CqnNy79m7l4ye7ZrkZxcLtObB9kHsTwYgzBuIV2X-xXQ7ezoR6VQPfQLCS-vnI View in LinkedIn

THE ILLUSION OF LINEARITY. “But that does not necessarily mean that the complexity of the output increases linearly. The complexity is defined as the minimum number of gates needed to do a job; not the number of gates in some particular setup.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201500092?casa_token=8OO3b1OY4e4AAAAA%3ARqriAgTwtxnvsxl09CqnNy79m7l4ye7ZrkZxcLtObB9kHsTwYgzBuIV2X-xXQ7ezoR6VQPfQLCS-vnI View in LinkedIn

LINEAR COMPLEXITY. “In the case of the parallel circuit the number of gates is the product of the width and the depth. By definition it increases linearly with time; i.e., with the depth of the circuit.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201500092?casa_token=8OO3b1OY4e4AAAAA%3ARqriAgTwtxnvsxl09CqnNy79m7l4ye7ZrkZxcLtObB9kHsTwYgzBuIV2X-xXQ7ezoR6VQPfQLCS-vnI View in LinkedIn

DEFINITION. “A quantum computation consists of applying a given unitary operator to a K‐qubit system. The complexity of the task, called , can be simply defined as the minimum number of gates that it takes to implement the unitary operator.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201500092?casa_token=8OO3b1OY4e4AAAAA%3ARqriAgTwtxnvsxl09CqnNy79m7l4ye7ZrkZxcLtObB9kHsTwYgzBuIV2X-xXQ7ezoR6VQPfQLCS-vnI View in LinkedIn

THE ARGUMENT. “But that's hardly the end of the story; the complexity can increase far beyond the Planckian value. This is closely related to the fact that Hawking radiation for old black holes “wells up” out of exponentially small distances. I will argue that the right idea is not exponentially small‐distances, but rather exponentially large complexity.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201500092?casa_token=8OO3b1OY4e4AAAAA%3ARqriAgTwtxnvsxl09CqnNy79m7l4ye7ZrkZxcLtObB9kHsTwYgzBuIV2X-xXQ7ezoR6VQPfQLCS-vnI View in LinkedIn

CONCLUSION. “In an additional experiment, the sweetness of pure D2O was scored significantly higher than that of D2O + 0.9 mM lactisole solution (p = 0.0003), while the same amount of lactisole had no effect on the perception of sweetness of H2O that served as control (Fig. 4b). These results suggest that D2O elicits sweetness via the TAS1R2/TAS1R3 sweet taste receptor.” https://lnkd.in/dzPDm5w View in LinkedIn

THIS DIFFICULT PAPER is a sampling of the extraordinary thinking that physicists studying complexity and black holes are engaged in, and how purely mathematical and logical operations are being used to dissect the possibilities within such an inscrutable object. An exceptionally interesting and challenging paper. https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201500092?casa_token=8OO3b1OY4e4AAAAA%3ARqriAgTwtxnvsxl09CqnNy79m7l4ye7ZrkZxcLtObB9kHsTwYgzBuIV2X-xXQ7ezoR6VQPfQLCS-vnI View in LinkedIn

TESTING THE HYPOTHESIS. “This was first explored by combining water samples with lactisole as an established TAS1R2/TAS1R3 inhibitor. Using the two-alternative forced-choice (2AFC) method, in which the participant must choose between two samples, 18 out of 25 panelists chose pure D2O as sweeter than D2O + 0.9 mM lactisole solution (p 

“FIREWALLS, like reversals of the second law, can occur in one of two ways; either by the action of an extremely complex operation needed to locally reverse the arrow of time, or by bottling up the system for a classical recurrence time. Temporary firewalls can also form if black holes are formed over long time periods.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201500092?casa_token=8OO3b1OY4e4AAAAA%3ARqriAgTwtxnvsxl09CqnNy79m7l4ye7ZrkZxcLtObB9kHsTwYgzBuIV2X-xXQ7ezoR6VQPfQLCS-vnI View in LinkedIn