Dave....... I started something again months ago....

Help I'm not sure this is even close to being correct...

I also want to know what the output is if the input is

|ψ₁⟩ ⊗ |ψ₂⟩ ⊗ |ψ₃⟩ ⊗ |ψ₄⟩ = (α₁|00⟩ + β₁|01⟩ + γ₁|10⟩ + δ₁|11⟩) ⊗ (α₂|00⟩ + β₂|01⟩ + γ₂|10⟩ + δ₂|11⟩) ⊗ (α₃|00⟩ + β₃|01⟩ + γ₃|10⟩ + δ₃|11⟩) ⊗ (α₄|00⟩ + β₄|01⟩ + γ₄|10⟩ + δ₄|11⟩)

import org.apache.commons.math3.complex.Complex;

import org.apache.commons.math3.linear.Array2DRowFieldMatrix;

import org.apache.commons.math3.linear.FieldMatrix;

import org.apache.commons.math3.linear.MatrixUtils;

import org.apache.commons.math3.linear.RandomMatrixUtils;

public class QuantumRandomization {

public static void main(String[] args) {

// Assign coefficient values

double alpha1 = 0.5;

double beta1 = 0.3;

double gamma1 = 0.1;

double delta1 = 0.2;

double alpha2 = 0.2;

double beta2 = 0.4;

double gamma2 = 0.6;

double delta2 = 0.8;

double alpha3 = 0.7;

double beta3 = 0.9;

double gamma3 = 0.3;

double delta3 = 0.5;

double alpha4 = 0.4;

double beta4 = 0.2;

double gamma4 = 0.8;

double delta4 = 0.6;

// Create four 2-state quantum systems

FieldMatrix system1 = new Array2DRowFieldMatrix<>(new Complex[][] {

{ new Complex(alpha1, 0), new Complex(beta1, 0) },

{ new Complex(gamma1, 0), new Complex(delta1, 0) }

});

FieldMatrix system2 = new Array2DRowFieldMatrix<>(new Complex[][] {

{ new Complex(alpha2, 0), new Complex(beta2, 0) },

{ new Complex(gamma2, 0), new Complex(delta2, 0) }

});

FieldMatrix system3 = new Array2DRowFieldMatrix<>(new Complex[][] {

{ new Complex(alpha3, 0), new Complex(beta3, 0) },

{ new Complex(gamma3, 0), new Complex(delta3, 0) }

});

FieldMatrix system4 = new Array2DRowFieldMatrix<>(new Complex[][] {

{ new Complex(alpha4, 0), new Complex(beta4, 0) },

{ new Complex(gamma4, 0), new Complex(delta4, 0) }

});

// Take the tensor product of the four systems

FieldMatrix tensorProduct = tensorProduct(tensorProduct(tensorProduct(system1, system2), system3), system4);

// Randomize the tensor product using a unitary matrix

FieldMatrix randomizedTensorProduct = tensorProduct.preMultiply(RandomMatrixUtils.createUnitaryMatrix(tensorProduct.getRowDimension()));

// Measure the randomized tensor product, returning a random state

FieldMatrix measuredTensorProduct = measureAndNormalize(randomizedTensorProduct);

// Print the measured tensor product

System.out.println(measuredTensorProduct);

}

// Compute the tensor product of two matrices

public static FieldMatrix tensorProduct(FieldMatrix matrix1, FieldMatrix matrix2) {

int rows1 = matrix1.getRowDimension();

int cols1 = matrix1.getColumnDimension();

int rows2 = matrix2.getRowDimension();

int cols2 = matrix2.getColumnDimension();

FieldMatrix result = new Array2DRowFieldMatrix<>(rows1 * rows2, cols1 * cols2);

for (int i = 0; i < rows1; i++) {

for (int j = 0; j < cols1; j++) {

for (int k = 0; k < rows2; k++) {

for (int l = 0; l < cols2; l++) {

result.setEntry(i * rows2 + k, j * cols2 + l, matrix1.getEntry(i, j).multiply(matrix2.getEntry(k, l)));

}

}

}

}

return result;

}

// Measure the matrix and normalize

public static FieldMatrix measureAndNormalize(FieldMatrix matrix) {

// Compute the squared absolute

double[] probabilities = new double[matrix.getRowDimension()];

for (int i = 0; i < matrix.getRowDimension(); i++) {

Complex entry = matrix.getEntry(i, 0);

probabilities[i] = entry.real() * entry.real() + entry.imag() * entry.imag();

}

// Sample a random state from matrix

int randomIndex = sampleFromDistribution(probabilities);

// Create a new matrix

FieldMatrix measuredMatrix = new Array2DRowFieldMatrix<>(matrix.getField(), matrix.getRowDimension(), matrix.getColumnDimension());

measuredMatrix.setEntry(randomIndex, 0, Complex.ONE);

// Normalize

double norm = MatrixUtils.createFieldVector(measuredMatrix.getColumn(0)).getNorm();

return measuredMatrix.scalarMultiply(1 / norm);

}

public static int sampleFromDistribution(double[] probabilities) {

double randomValue = Math.random();

double cumulativeProbability = 0;

int index = 0;

while (cumulativeProbability < randomValue && index < probabilities.length) {

cumulativeProbability += probabilities[index];

index++;

}

return index - 1;

}

}