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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

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GRIST FOR THE MILL. “The subconscious mind is not merely a kind of deep seat repository of sunken memories and atavistic desires, but of forces which can, under special circumstances, manifest themselves in the physical world with a force which goes beyond anything which the conscious mind could command.” (Wilson, 1971:445). https://lnkd.in/d4sDpAu View in LinkedIn

COMPLEXITY GRADIENT. “Operators supported on the outer edge of the near‐horizon region—the onion skin—have the minimal complexity. As we peel the onion, the complexity increases. Eventually we get to the Planckian layer where the complexity has increased to a particular value .” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201500092?casa_token=8OO3b1OY4e4AAAAA%3ARqriAgTwtxnvsxl09CqnNy79m7l4ye7ZrkZxcLtObB9kHsTwYgzBuIV2X-xXQ7ezoR6VQPfQLCS-vnI View in LinkedIn

ZERO DERIVATIVE. “The complexity can be large, but have zero time‐derivative. If evolved forward or backward the complexity will increase.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201500092?casa_token=8OO3b1OY4e4AAAAA%3ARqriAgTwtxnvsxl09CqnNy79m7l4ye7ZrkZxcLtObB9kHsTwYgzBuIV2X-xXQ7ezoR6VQPfQLCS-vnI View in LinkedIn

LAYERS OF THE ONION. “To understand the connection between complexity and black holes it is important to think of a black hole as an onion. The near‐horizon region of the black hole is a layered structure. Each layer has its own degrees of freedom. The CFT representation of the various layers differ in their degree of complexity.“ (CFT = Conformal field theory). https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201500092?casa_token=8OO3b1OY4e4AAAAA%3ARqriAgTwtxnvsxl09CqnNy79m7l4ye7ZrkZxcLtObB9kHsTwYgzBuIV2X-xXQ7ezoR6VQPfQLCS-vnI View in LinkedIn

ORDER DERIVATIVES. “Aristotle's theory of gravity was first‐order in derivatives; force is equal to mass times velocity. The complexity‐based theory looks more like a second order theory because complexity and it's rate of change are independent variables.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201500092?casa_token=8OO3b1OY4e4AAAAA%3ARqriAgTwtxnvsxl09CqnNy79m7l4ye7ZrkZxcLtObB9kHsTwYgzBuIV2X-xXQ7ezoR6VQPfQLCS-vnI View in LinkedIn

COMPLEXITY AND ENTROPY. “Let's begin with the fact that complexity satisfies a law similar to the second law of thermodynamics. It tends to increase, but with caveats that are similar to those that apply to the increase in entropy.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201500092?casa_token=8OO3b1OY4e4AAAAA%3ARqriAgTwtxnvsxl09CqnNy79m7l4ye7ZrkZxcLtObB9kHsTwYgzBuIV2X-xXQ7ezoR6VQPfQLCS-vnI View in LinkedIn