From e492187c080905fecf9989abfe7918d902d27fd2 Mon Sep 17 00:00:00 2001 From: Davis King Date: Thu, 25 Dec 2008 00:32:29 +0000 Subject: [PATCH] Adding a new example program. --HG-- extra : convert_revision : svn%3Afdd8eb12-d10e-0410-9acb-85c331704f74/trunk%402758 --- examples/CMakeLists.txt | 1 + examples/quantum_computing_ex.cpp | 313 ++++++++++++++++++++++++++++++ 2 files changed, 314 insertions(+) create mode 100644 examples/quantum_computing_ex.cpp diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt index 40449945e..1cf16ae39 100644 --- a/examples/CMakeLists.txt +++ b/examples/CMakeLists.txt @@ -48,6 +48,7 @@ add_example(member_function_pointer_ex) add_example(mlp_ex) add_example(multithreaded_object_ex) add_example(pipe_ex) +add_example(quantum_computing_ex) add_example(queue_ex) add_example(rank_features_ex) add_example(rvm_ex) diff --git a/examples/quantum_computing_ex.cpp b/examples/quantum_computing_ex.cpp new file mode 100644 index 000000000..081706134 --- /dev/null +++ b/examples/quantum_computing_ex.cpp @@ -0,0 +1,313 @@ +/* + 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 +#include +#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::float_1a 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 +class uf_gate : public gate_exp > +{ + /*! + 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(*this) {} + + static const long num_bits = bits; + static const long dims = dlib::qc_helpers::exp_2_n::value; + + 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 + qc_scalar_type compute_state_element ( + const matrix_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 +class w_gate : public gate_exp > +{ + /*! + This is the W gate from the Grover algorithm + !*/ +public: + + w_gate() : gate_exp(*this) {} + + static const long num_bits = bits; + static const long dims = dlib::qc_helpers::exp_2_n::value; + + 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 + qc_scalar_type compute_state_element ( + const matrix_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()).apply_gate_to(reg); + (w_gate(),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 lets test out the Shor 9 bit encoding + cout << "\n\n\n\nNow lets 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; + +} + +