commit 0a8dbada39eebedf498fec10d3e07735e8a496be Author: Alexander Rosenberg Date: Fri Dec 6 07:54:58 2024 -0800 Initial commit diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..f288702 --- /dev/null +++ b/LICENSE @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. By contrast, +the GNU General Public License is intended to guarantee your freedom to +share and change all versions of a program--to make sure it remains free +software for all its users. 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If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + Copyright (C) + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/README.md b/README.md new file mode 100644 index 0000000..92124dd --- /dev/null +++ b/README.md @@ -0,0 +1,4 @@ +# cl-quantum + +This is just some experiments with quantum computing emulation that I am doing +for a school project. diff --git a/math.lisp b/math.lisp new file mode 100644 index 0000000..153f422 --- /dev/null +++ b/math.lisp @@ -0,0 +1,391 @@ +(in-package :cl-quantum) + +(defmacro domatrix ((var matrix &optional retval) &body body) + "Execute BODY for with VAR bound once for each element in MATRIX, then +evaluate and return RETVAL. VAR can be of one of the following three forms: + - A symbol that will be bound on each iteration + - A list of three symbols which are variables to bind to the value, row, + and column on each iteration + - A list of two symbols which are variables to bind to the row and column on + each iteration" + (let* ((matrix-var (gensym)) + internal-form row-var col-var) + (cond + ((symbolp var) + (setq row-var (gensym) + col-var (gensym) + internal-form `(let ((,var (aref ,matrix-var ,row-var ,col-var))) + ,@body))) + ((and (listp var) (= (length var) 2)) + (setf internal-form `(progn ,@body) + row-var (first var) + col-var (second var))) + ((and (listp var) (= (length var) 3)) + (setq row-var (second var) + col-var (third var) + internal-form `(let ((,(first var) + (aref ,matrix-var ,row-var ,col-var))) + ,@body))) + (t (error "Malformed VAR spec: ~s" var))) + `(loop with ,matrix-var = ,matrix + for ,row-var below (array-dimension ,matrix-var 0) do + (loop for ,col-var below (array-dimension ,matrix-var 1) do + ,internal-form) + finally (return ,retval)))) + +(defun mapmatrix (function matrix) + "Execute FUNCTION for each element in MATRIX. Return a new matrix made of the +return values of FUNCTION. FUNCTION should be a function of three arguments: the +VALUE, the ROW, and the COLUMN." + (let ((new-mat (make-array (array-dimensions matrix)))) + (domatrix ((elem row col) matrix new-mat) + (setf (aref new-mat row col) (funcall function elem row col))))) + +;; Matrix subroutines +(defun mat-minor (mat i j) + "Find the minor of MAT for I and J." + (destructuring-bind (height width) + (array-dimensions mat) + (let ((minor (make-array (list (1- height) + (1- width))))) + (dotimes (row height minor) + (dotimes (col width) + (unless (or (= row i) + (= col j)) + (let ((out-row (if (> row i) + (1- row) + row)) + (out-col (if (> col j) + (1- col) + col))) + (setf (aref minor out-row out-col) (aref mat row col))))))))) + +(defun first-column-cofactors (mat) + "Find the cofactors for the first column of MAT." + (let* ((height (array-dimension mat 0)) + (out-arr (make-array height))) + (dotimes (i height out-arr) + (setf (aref out-arr i) (cofactor mat i 0))))) + +(defun cofactor-sgn (i j) + "Return the sign of the cofactor at I and J." + (expt -1 (+ i j))) + +(defun cofactor (mat i j) + "Find the cofactor for I and J in MAT." + (* (cofactor-sgn i j) (det (mat-minor mat i j)))) + +(defun det2x2 (mat) + "Find the determinate of a 2x2 matrix MAT." + (let ((a (aref mat 0 0)) + (b (aref mat 0 1)) + (c (aref mat 1 0)) + (d (aref mat 1 1))) + (- (* a d) (* b c)))) + +(defun det (mat &key first-column-cofactors) + "Find the determinant of MAT. If the cofactors for the first column have +already been calculated, they can be supplied in FIRST-COLUMN-COFACTORS." + (destructuring-bind (height width) + (array-dimensions mat) + (if (and (= height 2) + (= width 2)) + (det2x2 mat) + (loop for i below height + when first-column-cofactors + summing (* (aref mat i 0) (aref first-column-cofactors i)) + else + summing (* (aref mat i 0) (cofactor mat i 0)))))) + +(defun invert2x2 (mat) + "Invert the 2x2 matrix MAT." + (let ((a (aref mat 0 0)) + (b (aref mat 0 1)) + (c (aref mat 1 0)) + (d (aref mat 1 1)) + (ood (/ (det2x2 mat)))) + (make-array '(2 2) + :initial-contents (list (list (* ood d) (* ood (- b))) + (list (* ood (- c)) (* ood a)))))) + +(defun invert (mat) + "Invert MAT. This will signal `division-by-zero' if MAT is singular." + (destructuring-bind (height width) + (array-dimensions mat) + (if (and (= width 2) + (= height 2)) + (invert2x2 mat) + (let* ((first-column-cofactors (first-column-cofactors mat)) + (one-over-det (/ (det mat :first-column-cofactors + first-column-cofactors)))) + (mapmatrix (lambda (val row col) + (declare (ignorable val)) + ;; this calculates 1/det * adjugate[i][j] + (* one-over-det + (if (and first-column-cofactors (zerop row)) + (aref first-column-cofactors col) + (cofactor mat col row)))) + mat))))) + +(defun transpose (mat) + "Transpose MAT." + (let ((out-mat (make-array (reverse (array-dimensions mat))))) + (domatrix ((val row col) mat out-mat) + (setf (aref out-mat col row) val)))) + +(defun norm (vec) + "Return the norm of VEC." + (sqrt (reduce (lambda (sum elt) + (+ sum (* elt elt))) + vec :initial-value 0))) + +(defun dot-row-col (mat1 mat2 row col) + "Take the dot (scalar) product of ROW of MAT1 and COL of MAT2." + (let ((sum 0)) + (dotimes (n (array-dimension mat2 0) sum) + (setq sum (+ sum (* (aref mat1 row n) + (aref mat2 n col))))))) + +(defun *mm (mat1 mat2) + "Multiply MAT1 by MAT2." + (assert (= (array-dimension mat1 1) + (array-dimension mat2 0)) + (mat1 mat2) + "Cannot multiply ~s by ~s." mat1 mat2) + (let* ((width (array-dimension mat1 0)) + (height (array-dimension mat2 1)) + (out-mat (make-array (list height width)))) + (dotimes (i height out-mat) + (dotimes (j width) + (let ((dot (dot-row-col mat1 mat2 i j))) + (setf (aref out-mat i j) dot)))))) + +(defun *mv (mat vec) + "Multiply MAT by VEC." + (assert (= (array-dimension mat 1) + (length vec)) + (mat vec) + "Cannot multiply ~s by ~s." mat vec) + (let* ((width (array-dimension mat 1)) + (height (array-dimension mat 0)) + (out-vec (make-array height))) + (dotimes (row height out-vec) + (setf (aref out-vec row) + (loop for col below width + summing (* (aref vec col) (aref mat row col))))))) + +(defun *vm (vec mat) + "Multiply VEC by MAT." + (assert (= (array-dimension mat 0) + (length vec)) + (vec mat) + "Cannot multiply ~s by ~s." vec mat) + (let* ((width (array-dimension mat 1)) + (height (array-dimension mat 0)) + (out-vec (make-array height))) + (dotimes (row height out-vec) + (setf (aref out-vec row) + (loop for col below width + summing (* (aref vec col) (aref mat col row))))))) + +(defun dot (vec1 vec2) + "Compute the dot product (scalar product) of VEC1 and VEC2." + (assert (= (length vec1) (length vec2)) + (vec1 vec2) + "Cannot multiply ~s by ~s." vec1 vec2) + (loop for i below (length vec1) + summing (* (aref vec1 i) (aref vec2 i)))) + +(defun +mm (mat1 mat2) + "Add MAT1 to MAT2." + (assert (equal (array-dimensions mat1) + (array-dimensions mat2)) + (mat1 mat2) + "Cannot add ~s and ~s." mat1 mat2) + (mapmatrix (lambda (val row col) + (declare (ignorable row col)) + (+ val (aref mat2 row col))) + mat1)) + +(defun +vv (vec1 vec2) + "Add VEC1 to VEC2." + (assert (= (length vec1) + (length vec2)) + (vec1 vec2) + "Cannot add ~s and ~s." vec1 vec2) + (let ((sum (make-array (length vec1)))) + (dotimes (i (length vec1) sum) + (setf (aref sum i) (+ (aref vec1 i) + (aref vec2 i)))))) + +(defun -mm (mat1 mat2) + "Subtract MAT2 from MAT1." + (assert (equal (array-dimensions mat1) + (array-dimensions mat2)) + (mat1 mat2) + "Cannot subtract ~s and ~s." mat2 mat1) + (mapmatrix (lambda (val row col) + (declare (ignorable row col)) + (- val (aref mat2 row col))) + mat1)) + +(defun -vv (vec1 vec2) + "Subtract VEC2 from VEC1." + (assert (= (length vec1) + (length vec2)) + (vec1 vec2) + "Cannot subtract ~s from ~s." vec2 vec1) + (let ((sum (make-array (length vec1)))) + (dotimes (i (length vec1) sum) + (setf (aref sum i) (- (aref vec1 i) + (aref vec2 i)))))) + +(defun *ms (mat scalar) + "Multiply MAT by SCALAR." + (mapmatrix (lambda (val row col) + (declare (ignorable row col)) + (* val scalar)) + mat)) + +(defun *vs (vec scalar) + "Multiply VEC by SCALAR." + (map 'vector (lambda (elt) + (* elt scalar)) + vec)) + +(defun /ms (mat scalar) + "Divide MAT by SCALAR." + (*ms mat (/ scalar))) + +(defun /vs (vec scalar) + "Divide VEC by SCALAR." + (*vs vec (/ scalar))) + +(defun mconj (mat) + "Return the conjugate of MAT." + (mapmatrix (lambda (val row col) + (declare (ignorable row col)) + (conjugate val)) + mat)) + +(defun vconj (vec) + "Return the conjugate of VEC." + (map 'vector 'conjugate vec)) + +(defun squarep (mat) + "Return non-nil if MAT is a square matrix." + (and (= (array-rank mat) 2) + (apply '= (array-dimensions mat)))) + +(defun singularp (mat) + "Return non-nil if MAT is singular." + (zerop (det mat))) + +(defun mtrace (mat) + "Return the trace of MAT." + (assert (squarep mat) + (mat) + "Not a square matrix: ~s" mat) + (loop for i below (array-dimension mat 0) + summing (aref mat i i))) + +(defun make-identity-matrix (n) + "Return an N by N identity matrix." + (let ((mat (make-array (list n n)))) + (dotimes (i n mat) + (setf (aref mat i i) 1)))) + +(defun round-to-place (num places &key (base 10)) + "Round NUM to PLACES places in BASE." + (let ((scale (expt base places))) + (/ (floor (+ (* num scale) 1/2)) scale))) + +(defun count-digits (num &key (base 10)) + "Count the number of digits in NUM. If NUM is zero, return 1. If NUM is +negative, return the number of digits in its absolute value." + (if (zerop num) + 1 + ;; throw out the extra values + (values (floor (1+ (log (abs num) base)))))) + +(defun build-float (int dec) + "Create a float with integer part INT and decimal part DEC." + (* (signum int) (+ (abs int) (/ dec (expt 10 (count-digits dec)))))) + +(defconstant +parse-real-regexp+ + (ppcre:create-scanner + "^(\\s*([-+]?[0-9]+)(?:/([0-9]+)|\\.?([0-9]*)(?:[eE]([-+]?[0-9]+))?)\\s*)" + :extended-mode t) + "The regexp scanner used in `parse-real'.") + +(defun parse-real (string &key (start 0) end junk-allowed) + "Parse STRING into a real. Parsing starts at START and ends at END. If end is +nil, the end of the string is used. If JUNK-ALLOWED is non-nil, don't signal an +error if an unexpected character is encountered. Two values are returned, the +first being the value parsed and the second being the index at which parsing +stopped. That is, the index of the first un-parsed character." + (values-list + (or + (ppcre:register-groups-bind (whole main denom decim exp) + (+parse-real-regexp+ string :start start :end end :sharedp t) + (unless (or junk-allowed + (= (length whole) (- (or end (length string)) start))) + (error "Malformed number: ~s" (subseq string start end))) + (let ((num + (cond + (denom + (/ (parse-integer main) + (parse-integer denom))) + ((/= (length decim) 0) + (build-float (parse-integer main) + (parse-integer decim))) + (t + (parse-integer main))))) + (list (if exp + (* num (expt 10 (parse-integer exp))) + num) + (length whole)))) + (if junk-allowed + (list 0 0) + (error "Malformed number: ~s" (subseq string start end)))))) + +(defconstant +parse-complex-regexp+ + (ppcre:create-scanner + "^\\s*([-+])?\\s*([-+]?)([0-9/.]+(?:[eE][-+]?[0-9]+)?)?(i)?" + :extended-mode t) + "The regexp scanner used in `parse-complex'.") + +(defun parse-complex (string &key (start 0) end junk-allowed) + "Parse STRING into a complex number. Parsing starts at START and ends at +END. If end is nil, the end of the string is used. If JUNK-ALLOWED is non-nil, +don't signal an error if an unexpected character is encountered. Two values are +returned, the first being the value parsed and the second being the index at +which parsing stopped. That is, the index of the first un-parsed character." + (unless end (setq end (length string))) + (loop for pos = start then (+ pos (length whole)) + for (whole matches) = (multiple-value-list + (ppcre:scan-to-strings +parse-complex-regexp+ + string + :start pos + :end end)) + for times below 2 + while whole + for coef = (cond + ((aref matches 2) + (parse-real (concatenate 'string (aref matches 1) + (aref matches 2)))) + ((aref matches 3) + (if (equal (aref matches 1) "-") -1 1)) + (t 0)) + for sign = (if (equal (aref matches 0) "-") -1 1) + when (aref matches 3) + summing (complex 0 (* sign coef)) into num + else + summing (* sign coef) into num + finally + (if (and (not junk-allowed) + (< pos end)) + (error "Junk in string: ~s" (subseq string start end)) + (return (values num pos))))) + + diff --git a/package.lisp b/package.lisp new file mode 100644 index 0000000..ca8f737 --- /dev/null +++ b/package.lisp @@ -0,0 +1,2 @@ +(defpackage :cl-quantum + (:use :cl)) diff --git a/state.lisp b/state.lisp new file mode 100644 index 0000000..5b02891 --- /dev/null +++ b/state.lisp @@ -0,0 +1,113 @@ +(in-package :cl-quantum) + +(defun pprint-complex (n &key parens) + "Pretty-print the complex (or real, rational, etc.) number N. If PARENS is +non-nil, surround the output with parenthesis if it is multiple terms." + (let* ((real (realpart n)) + (imag (imagpart n)) + ;; Also put parenthesis on fractions to make them easier to read + (has-frac (and parens + (or (and (not (integerp real)) + (rationalp real)) + (and (not (integerp imag)) + (rationalp imag)))))) + (cond + ((zerop n) "0") + ((not (or (zerop real) + (zerop imag))) + (format nil "~@[~*(~]~a ~:[-~;+~] ~ai~@[~*)~]" + parens real (>= imag 0) (abs imag) parens)) + (t + (format nil "~@[~*(~]~a~@[~*i~]~@[~*)~]" + has-frac (if (zerop real) imag real) + (zerop real) has-frac))))) + +(defun pprint-format-bits (index size) + "A state formatter that converts the index to binary and pads it with zeros." + (format nil "~v,,,'0<~b~>" (ceiling (log size 2)) index)) + +(defun pprint-format-linear (index size) + "A state formatter that just returns the index +1 as a string." + (declare (ignorable size)) + (format nil "~d" (1+ index))) + +(defun pprint-state (state &key (formatter 'pprint-format-linear)) + "Pretty-print STATE, a quantum state represented as an array. FORMATTER is a +function which takes the index of the quantum state and the total size of the +state. It should convert these to a printable representation. This +representation will be put inside of a ket after each coefficient." + (with-output-to-string (out) + (loop with need-sign = nil + for i below (length state) + for coef = (aref state i) + when (and need-sign (not (zerop coef))) + if (>= (realpart coef) 0) + do (format out " + ") + else + do (format out " - ") + and do (setq coef (* -1 coef)) + end + end + unless (zerop coef) + do (format out "~a|~a>" (pprint-complex coef :parens t) + (funcall formatter i (length state))) + and do (setq need-sign t)))) + +(defconstant +parse-state-regexp+ + (ppcre:create-scanner + "^\\s*([-+])?\\s*(\\()?\\s*([-+0-9ei./]*)\\s*(\\))?\\s*\\|([^>]*)>" + :extended-mode t) + "The regexp scanner used in `parse-state'.") + +(defun parse-bits-state (state) + "A `parse-state' parser that parses its state as a binary string." + (parse-integer state :radix 2)) + +(defun parse-state (str &key (parser 'parse-integer)) + "Try to parse STR into a quantum state. PARSER should be a function of one +argument that will take the string inside each ket and return the index of the +state." + (loop for start = 0 then (+ start (length whole)) + for (whole matches) = (multiple-value-list + (ppcre:scan-to-strings +parse-state-regexp+ + str + :sharedp t + :start start)) + while whole + for coef = (if (zerop (length (aref matches 2))) + 1 + (parse-complex (aref matches 2))) + for index = (funcall parser (aref matches 4)) + unless (eq (not (aref matches 1)) + (not (aref matches 3))) + do (error "Mismatches parenthesis: ~s" whole) + when (and (complexp coef) + (not (aref matches 1))) + do (error "Coefficient without matching state: ~s" whole) + collect (if (equal (aref matches 0) "-") + (* -1 coef) + coef) + into coefs + collect index into indecies + maximizing (1+ index) into state-size + finally + (return + (let ((state (make-array state-size))) + (loop for index in indecies + for coef in coefs + do (incf (aref state index) coef)) + state)))) + +(defun normal-state-p (state &key (places 5)) + "Return non-nil if state is normalized. PLACES is the number of places to +round the norm of STATE before checking." + (= (round-to-place (dot state state) places) 1)) + +(defun normalize-state (state) + "Return a copy of STATE that is normalized." + (/vs state (norm state))) + +(defun make-uniform-normal-state (bits) + "Make a uniform normalized quantum state of BITS qbits." + (let ((size (ash 1 bits))) + (make-array (ash 1 bits) :initial-element (/ (sqrt size)))))