TensorProductExample.sc

//f is the tensor product operator

f = { |a, b|
	a.collect { |x|
		x.collect { |y| b * y }.reduce('+++')
	}.reduce('++')
};

//m is the matrix multiplication operator

m = { |self, other|

	var size = self.size;
	var out = Array.fill(size, { Array.new(size) });
	var transposed = other.flop;

	self.do { | row, i |
		size.do { | j |
			var c = transposed[j];
			c !? { out[i].add(sum(row * c)) }
		}
	};

	out
}


//define variables

var x1, x2, x3, x4, x5, x6, t1, t2, t3, t4, t5, h, h1, h2, h3, v, m1, m2, m3, p1, p2;


//define a random unit vector. we should be careful to define this vector first so that it does not update with random parameters and is instead constant throughout the simulation

v = { 1.0.sum3rand }.dup(64);
v = v/sqrt(abs(v*v).sum);


//create individual rotation gates, essentially applying a rotation gate to each qubit. these rotations will become parameterized for our control

x1 = [[1,0],[0,exp(Complex(0,10000.rand))]];
x2 = [[1,0],[0,exp(Complex(0,10000.rand))]];
x3 = [[1,0],[0,exp(Complex(0,10000.rand))]];
x4 = [[1,0],[0,exp(Complex(0,10000.rand))]];
x5 = [[1,0],[0,exp(Complex(0,10000.rand))]];
x6 = [[1,0],[0,exp(Complex(0,10000.rand))]];


//tensor rotation gates together for the full unitary representation

t1 = f.value(x1,x2);
t2 = f.value(t1,x3);
t3 = f.value(t2,x4);
t4 = f.value(t3,x5);
t5 = f.value(t4,x6);


//create a hadamard tensor matrix, representing applying a hadamard operator to each individual qubit

h = [[1,1],[1,-1]]/sqrt(2);
h1=f.value(h,h);
h2=f.value(h1,h1);
h3=f.value(h2,h1);


//multiply the hadamard tensor with the rotation tensor, then multiply that product by the unit vector

p1 = m.value(h3,t5);
p2 = m.value(p1,v.flop);


//the result is that we have an audio representation of a parameterized quantum circuit; a rotation tensor composed with a hadamard gate to mix states up. the next steps could be to use more complicated entangling operators in place of the hadamard, or to have a more complicated ansatz such that the parameters have even more complex behaviors