libquantum/measure.c

/* measure.c: Quantum register measurement

   Copyright 2003, 2004 Bjoern Butscher, Hendrik Weimer

   This file is part of libquantum

   libquantum is free software; you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published
   by the Free Software Foundation; either version 3 of the License,
   or (at your option) any later version.

   libquantum is distributed in the hope that it will be useful, but
   WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with libquantum; if not, write to the Free Software
   Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
   MA 02110-1301, USA

*/

#include <fcntl.h>
#include <sys/types.h>
#include <sys/stat.h>
#include <stdlib.h>
#include <math.h>
#include <unistd.h>
#include <stdio.h>

#include "qureg.h"
#include "complex.h"
#include "config.h"
#include "objcode.h"
#include "error.h"

/* Generate a uniformly distributed random number between 0 and 1 */

double 
quantum_frand()
{
  return (double) rand() / RAND_MAX;
}

/* Measure the contents of a quantum register */

MAX_UNSIGNED
quantum_measure(quantum_reg reg)
{
  double r;
  int i;

  if(quantum_objcode_put(MEASURE))
    return 0;

  /* Get a random number between 0 and 1 */
  
  r = quantum_frand();

  for (i=0; i<reg.size; i++)
    {
      /* If the random number is less than the probability of the
	 given base state - r, return the base state as the
	 result. Otherwise, continue with the next base state. */

      r -= quantum_prob_inline(reg.amplitude[i]);
      if(0 >= r)
	return reg.state[i];
    }

  /* The sum of all probabilities is less than 1. Usually, the cause
     for this is the application of a non-normalized matrix, but there
     is a slim chance that rounding errors may lead to this as
     well. */

  return -1;
}

/* Measure a single bit of a quantum register. The bit measured is
   indicated by its position POS, starting with 0 as the least
   significant bit. The new state of the quantum register depends on
   the result of the measurement. */

int
quantum_bmeasure(int pos, quantum_reg *reg)
{
  int i;
  int result=0;
  double pa=0, r;
  MAX_UNSIGNED pos2;
  quantum_reg out;
  
  if(quantum_objcode_put(BMEASURE, pos))
     return 0;

  pos2 = (MAX_UNSIGNED) 1 << pos;

  /* Sum up the probability for 0 being the result */

  for(i=0; i<reg->size; i++)
    {
      if(!(reg->state[i] & pos2))
	pa += quantum_prob_inline(reg->amplitude[i]);
    }

  /* Compare the probability for 0 with a random number and determine
     the result of the measurement */

  r = quantum_frand();
  
  if (r > pa)
    result = 1;

  out = quantum_state_collapse(pos, result, *reg);

  quantum_delete_qureg_hashpreserve(reg);
  *reg = out;

  return result;
}

/* Measure a single bit, but do not remove it from the quantum
   register */

int
quantum_bmeasure_bitpreserve(int pos, quantum_reg *reg)
{
  int i, j;
  int size=0, result=0;
  double d=0, pa=0, r;
  MAX_UNSIGNED pos2;
  quantum_reg out;

  if(quantum_objcode_put(BMEASURE_P, pos))
     return 0;

  pos2 = (MAX_UNSIGNED) 1 << pos;

  /* Sum up the probability for 0 being the result */

  for(i=0; i<reg->size; i++)
    {
      if(!(reg->state[i] & pos2))
	pa += quantum_prob_inline(reg->amplitude[i]);
    }

  /* Compare the probability for 0 with a random number and determine
     the result of the measurement */

  r = quantum_frand();
  
  if (r > pa)
    result = 1;

  /* Eradicate all amplitudes of base states which have been ruled out
     by the measurement and get the absolute of the new register */

  for(i=0;i<reg->size;i++)
    {
      if(reg->state[i] & pos2)
	{
	  if(!result)
	    reg->amplitude[i] = 0;
	  else
	    {
	      d += quantum_prob_inline(reg->amplitude[i]);
	      size++;
	    }
	}
      else
	{
	  if(result)
	    reg->amplitude[i] = 0;
	  else
	    {
	      d += quantum_prob_inline(reg->amplitude[i]);
	      size++;
	    }
	}
    }

  /* Build the new quantum register */

  out.size = size;
  out.state = calloc(size, sizeof(MAX_UNSIGNED));
  out.amplitude = calloc(size, sizeof(COMPLEX_FLOAT));

  if(!(out.state && out.amplitude))
    quantum_error(QUANTUM_ENOMEM);

  quantum_memman(size * (sizeof(MAX_UNSIGNED) + sizeof(COMPLEX_FLOAT)));

  out.hashw = reg->hashw;
  out.hash = reg->hash;
  out.width = reg->width;

  /* Determine the numbers of the new base states and norm the quantum
     register */
  
  for(i=0, j=0; i<reg->size; i++)
    {
      if(reg->amplitude[i])
	{
	  out.state[j] = reg->state[i];
	  out.amplitude[j] = reg->amplitude[i] * 1 / (float) sqrt(d);
	
	  j++;
	}
    }

  quantum_delete_qureg_hashpreserve(reg);
  *reg = out;
  return result;
}