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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

GRAVITY AND COMPKEXITY. “I want to suggest that there may be another deep connection; this time between gravity and complexity. To state it as a slogan: Things fall because there is a tendency toward complexity.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201500092?casa_token=8OO3b1OY4e4AAAAA%3ARqriAgTwtxnvsxl09CqnNy79m7l4ye7ZrkZxcLtObB9kHsTwYgzBuIV2X-xXQ7ezoR6VQPfQLCS-vnI View in LinkedIn

MEASUREMENT INTERVAL. “The time to achieve this degree of complexity is of order the classical recurrence time. Once this much time has elapsed the complexity stops increasing, although it may fluctuate.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201500092?casa_token=8OO3b1OY4e4AAAAA%3ARqriAgTwtxnvsxl09CqnNy79m7l4ye7ZrkZxcLtObB9kHsTwYgzBuIV2X-xXQ7ezoR6VQPfQLCS-vnI View in LinkedIn

Simple complexity at the local nursery. View in LinkedIn

FRAGILE SYSTEMS. “Devastated, but resilient is my word of the day. Starting over as if I never had a lab; the hardest day of my life. Throwing away 8 years of work b/c the institution could not turn on the damn generator and of course we were not made aware. No parasite, no cells; backups gone!” Dr. Pascale Guiton@DrGuiton. )Remember Blade Runner 2049 — “wiped clean”?). " "pic.twitter.com/ZF90F4PihU View in LinkedIn

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