39 lines
1.4 KiB
Common Lisp
39 lines
1.4 KiB
Common Lisp
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;;;; An example of Grover's algorithm (quantum search)
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(in-package :cl-quantum/examples)
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(defun count-grover-iterations (bits targets)
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"Count the number of iterations it takes to have a high probability of finding
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TARGETS in a search space of 2^BITS."
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(values (floor (* (/ pi 4) (sqrt (/ (ash 1 bits) targets))))))
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(defun make-grover-circuit (bits target)
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"Generate a quantum circuit that runs Grover's algorithm over a state of BITS
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bits and finds when the state is equal to TARGET."
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(assert (> (ash 1 bits) target)
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(bits target)
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"Target bit of ~s out of range for state with ~s bits." target bits)
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(with-build-circuit
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;; Setup
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(loop for i below bits do (:h i))
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;; Oracle
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(loop
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repeat (count-grover-iterations bits 1)
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do
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(loop for i below bits
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for cur = (logand (ash target (- i)) 1)
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when (zerop cur)
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do (:x i))
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(:ncz 0 (loop for i from 1 below bits collect i))
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(loop for i below bits
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for cur = (logand (ash target (- i)) 1)
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when (zerop cur)
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do (:x i))
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;; Diffuser
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(loop for i below bits do (:h i))
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(loop for i below bits do (:x i))
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(:ncz 0 (loop for i from 1 below bits collect i))
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(loop for i below bits do (:x i))
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(loop for i below bits do (:h i)))))
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