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+// The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt
+/*
+    This is an example illustrating the use of the quantum computing
+    simulation classes from the dlib C++ Library.
+
+    This example assumes you are familiar with quantum computing and 
+    Grover's search algorithm and Shor's 9 bit error correcting code
+    in particular.   The example shows how to simulate both of these
+    algorithms.
+
+
+    The code to simulate Grover's algorithm is primarily here to show
+    you how to make custom quantum gate objects.  The Shor ECC example
+    is simpler and uses just the default gates that come with the 
+    library.
+
+*/
+
+
+#include <iostream>
+#include <complex>
+#include <ctime>
+#include <dlib/quantum_computing.h>
+#include <dlib/string.h>
+
+
+using namespace std;
+using namespace dlib;
+
+// ----------------------------------------------------------------------------------------
+// ----------------------------------------------------------------------------------------
+// ----------------------------------------------------------------------------------------
+
+// This declares a random number generator that we will be using below  
+dlib::rand rnd;
+
+// ----------------------------------------------------------------------------------------
+
+void shor_encode (
+    quantum_register& reg
+)
+/*!
+    requires
+        - reg.num_bits() == 1
+    ensures
+        - #reg.num_bits() == 9
+        - #reg == the Shor error coding of the input register
+!*/
+{
+    DLIB_CASSERT(reg.num_bits() == 1,"");
+
+    quantum_register zeros;
+    zeros.set_num_bits(8);
+    reg.append(zeros);
+
+    using namespace dlib::quantum_gates;
+    const gate<1> h = hadamard();
+    const gate<1> i = noop();
+
+    // Note that the expression (h,i) represents the tensor product of the 1 qubit 
+    // h gate with the 1 qubit i gate and larger versions of this expression 
+    // represent even bigger tensor products.  So as you see below, we make gates 
+    // big enough to apply to our quantum register by listing out all the gates we 
+    // want to go into the tensor product and then we just apply the resulting gate 
+    // to the quantum register.
+
+    // Now apply the gates that constitute Shor's encoding to the input register.  
+    (cnot<3,0>(),i,i,i,i,i).apply_gate_to(reg);
+    (cnot<6,0>(),i,i).apply_gate_to(reg);
+    (h,i,i,h,i,i,h,i,i).apply_gate_to(reg);
+    (cnot<1,0>(),i,cnot<1,0>(),i,cnot<1,0>(),i).apply_gate_to(reg);
+    (cnot<2,0>(),cnot<2,0>(),cnot<2,0>()).apply_gate_to(reg);
+}
+
+// ----------------------------------------------------------------------------------------
+
+void shor_decode (
+    quantum_register& reg
+)
+/*!
+    requires
+        - reg.num_bits() == 9
+    ensures
+        - #reg.num_bits() == 1
+        - #reg == the decoded qubit that was in the given input register 
+!*/
+{
+    DLIB_CASSERT(reg.num_bits() == 9,"");
+
+    using namespace dlib::quantum_gates;
+    const gate<1> h = hadamard();
+    const gate<1> i = noop();
+
+    // Now apply the gates that constitute Shor's decoding to the input register
+
+    (cnot<2,0>(),cnot<2,0>(),cnot<2,0>()).apply_gate_to(reg);
+    (cnot<1,0>(),i,cnot<1,0>(),i,cnot<1,0>(),i).apply_gate_to(reg);
+
+    (toffoli<0,1,2>(),toffoli<0,1,2>(),toffoli<0,1,2>()).apply_gate_to(reg);
+
+    (h,i,i,h,i,i,h,i,i).apply_gate_to(reg);
+
+    (cnot<6,0>(),i,i).apply_gate_to(reg);
+    (cnot<3,0>(),i,i,i,i,i).apply_gate_to(reg);
+    (toffoli<0,3,6>(),i,i).apply_gate_to(reg);
+
+    // Now that we have decoded the value we don't need the extra 8 bits any more so 
+    // remove them from the register.
+    for (int i = 0; i < 8; ++i)
+        reg.measure_and_remove_bit(0,rnd);
+}
+
+// ----------------------------------------------------------------------------------------
+// ----------------------------------------------------------------------------------------
+// ----------------------------------------------------------------------------------------
+
+// This is the function we will use in Grover's search algorithm.  In this
+// case the value we are searching for is 257.
+bool is_key (unsigned long n)
+{
+    return n == 257;
+}
+
+// ----------------------------------------------------------------------------------------
+
+template <int bits>
+class uf_gate;
+
+namespace dlib {
+template <int bits>
+struct gate_traits<uf_gate<bits> >
+{
+    static const long num_bits = bits;
+    static const long dims = dlib::qc_helpers::exp_2_n<num_bits>::value;
+};}
+
+template <int bits>
+class uf_gate : public gate_exp<uf_gate<bits> >
+{
+    /*!
+        This gate represents the black box function in Grover's search algorithm.
+        That is, it is the gate defined as follows:
+            Uf|x>|y> = |x>|y XOR is_key(x)>
+
+        See the documentation for the gate_exp object for the details regarding
+        the compute_state_element() and operator() functions defined below.
+    !*/
+public:
+    uf_gate() : gate_exp<uf_gate>(*this) {}
+
+    static const long num_bits = gate_traits<uf_gate>::num_bits;
+    static const long dims = gate_traits<uf_gate>::dims;
+
+    const qc_scalar_type operator() (long r, long c) const 
+    { 
+        unsigned long output = c;
+        // if the input control bit is set
+        if (is_key(output>>1))
+        {
+            output = output^0x1;
+        }
+
+        if ((unsigned long)r == output)
+            return 1;
+        else
+            return 0;
+    }
+
+    template <typename exp>
+    qc_scalar_type compute_state_element (
+        const matrix_exp<exp>& reg,
+        long row_idx
+    ) const
+    {
+        unsigned long output = row_idx;
+        // if the input control bit is set
+        if (is_key(output>>1))
+        {
+            output = output^0x1;
+        }
+
+        return reg(output);
+    }
+};
+
+// ----------------------------------------------------------------------------------------
+
+template <int bits>
+class w_gate;
+
+namespace dlib {
+template <int bits>
+struct gate_traits<w_gate<bits> >
+{
+    static const long num_bits = bits;
+    static const long dims = dlib::qc_helpers::exp_2_n<num_bits>::value;
+}; }
+
+template <int bits>
+class w_gate : public gate_exp<w_gate<bits> >
+{
+    /*!
+        This is the W gate from the Grover algorithm
+    !*/
+public:
+
+    w_gate() : gate_exp<w_gate>(*this) {}
+
+    static const long num_bits = gate_traits<w_gate>::num_bits;
+    static const long dims = gate_traits<w_gate>::dims;
+
+    const qc_scalar_type operator() (long r, long c) const 
+    { 
+        qc_scalar_type res = 2.0/dims;
+        if (r != c)
+            return res;
+        else
+            return res - 1.0;
+    }
+
+    template <typename exp>
+    qc_scalar_type compute_state_element (
+        const matrix_exp<exp>& reg,
+        long row_idx
+    ) const
+    {
+        qc_scalar_type temp = sum(reg)*2.0/dims;
+        // compute this value: temp = temp - reg(row_idx)*2.0/dims + reg(row_idx)*(2.0/dims - 1.0)
+        temp = temp - reg(row_idx);
+
+        return temp;
+    }
+};
+
+// ----------------------------------------------------------------------------------------
+// ----------------------------------------------------------------------------------------
+// ----------------------------------------------------------------------------------------
+
+int main()
+{
+    // seed the random number generator
+    rnd.set_seed(cast_to_string(time(0)));
+
+    // Pick out some of the gates we will be using below
+    using namespace dlib::quantum_gates;
+    const gate<1> h = quantum_gates::hadamard();
+    const gate<1> z = quantum_gates::z();
+    const gate<1> x = quantum_gates::x();
+    const gate<1> i = quantum_gates::noop();
+
+    quantum_register reg;
+
+    // We will be doing the 12 qubit version of Grover's search algorithm.
+    const int bits=12;
+    reg.set_num_bits(bits);
+
+
+    // set the quantum register to its initial state
+    (i,i, i,i,i,i,i, i,i,i,i,x).apply_gate_to(reg);
+
+    // Print out the starting bits
+    cout << "starting bits: ";
+    for (int i = reg.num_bits()-1; i >= 0; --i)
+        cout << reg.probability_of_bit(i);
+    cout << endl;
+
+
+    // Now apply the Hadamard gate to all the input bits
+    (h,h, h,h,h,h,h, h,h,h,h,h).apply_gate_to(reg);
+
+    // Here we do the grover iteration
+    for (int j = 0; j < 35; ++j)
+    {
+        (uf_gate<bits>()).apply_gate_to(reg);
+        (w_gate<bits-1>(),i).apply_gate_to(reg);
+
+
+        cout << j << " probability: bit 1 = " << reg.probability_of_bit(1) << ", bit 9 = " << reg.probability_of_bit(9) << endl;
+    }
+
+    cout << endl;
+
+    // Print out the final probability of measuring a 1 for each of the bits
+    for (int i = reg.num_bits()-1; i >= 1; --i)
+        cout << "probability for bit " << i << " = " << reg.probability_of_bit(i) << endl;
+    cout << endl;
+
+    cout << "The value we want grover's search to find is 257 which means we should measure a bit pattern of 00100000001" << endl;
+    cout << "Measured bits: ";
+    // finally, measure all the bits and print out what they are.
+    for (int i = reg.num_bits()-1; i >= 1; --i)
+        cout << reg.measure_bit(i,rnd);
+    cout << endl;
+
+    
+
+
+
+    // Now let's test out the Shor 9 bit encoding
+    cout << "\n\n\n\nNow let's try playing around with Shor's 9bit error correcting code" << endl;
+
+    // Reset the quantum register to contain a single bit
+    reg.set_num_bits(1);
+    // Set the state of this single qubit to some random mixture of the two computational bases
+    reg.state_vector()(0) = qc_scalar_type(rnd.get_random_double(),rnd.get_random_double());
+    reg.state_vector()(1) = qc_scalar_type(rnd.get_random_double(),rnd.get_random_double());
+    // Make sure the state of the quantum register is a unit vector
+    reg.state_vector() /= sqrt(sum(norm(reg.state_vector())));
+
+    cout << "state: " << trans(reg.state_vector());
+
+    shor_encode(reg);
+    cout << "x bit corruption on bit 8" << endl;
+    (x,i,i,i,i,i,i,i,i).apply_gate_to(reg); // mess up the high order bit 
+    shor_decode(reg); // try to decode the register
+
+    cout << "state: " << trans(reg.state_vector());
+
+    shor_encode(reg);
+    cout << "x bit corruption on bit 1" << endl;
+    (i,i,i,i,i,i,i,x,i).apply_gate_to(reg);
+    shor_decode(reg);
+
+    cout << "state: " << trans(reg.state_vector());
+
+    shor_encode(reg);
+    cout << "z bit corruption on bit 8" << endl;
+    (z,i,i,i,i,i,i,i,i).apply_gate_to(reg);
+    shor_decode(reg);
+
+    cout << "state: " << trans(reg.state_vector());
+
+    cout << "\nThe state of the input qubit survived all the corruptions in tact so the code works." << endl;
+
+}
+
+