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-rw-r--r--ml/dlib/dlib/quantum_computing/quantum_computing.h863
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diff --git a/ml/dlib/dlib/quantum_computing/quantum_computing.h b/ml/dlib/dlib/quantum_computing/quantum_computing.h
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--- a/ml/dlib/dlib/quantum_computing/quantum_computing.h
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@@ -1,863 +0,0 @@
-// Copyright (C) 2008 Davis E. King (davis@dlib.net)
-// License: Boost Software License See LICENSE.txt for the full license.
-#ifndef DLIB_QUANTUM_COMPUTINg_1_
-#define DLIB_QUANTUM_COMPUTINg_1_
-
-#include <complex>
-#include <cmath>
-#include "../matrix.h"
-#include "../rand.h"
-#include "../enable_if.h"
-#include "../algs.h"
-#include "quantum_computing_abstract.h"
-
-namespace dlib
-{
-
- template <typename T>
- struct gate_traits {};
-
- namespace qc_helpers
- {
-
- // ------------------------------------------------------------------------------------
-
- // This is a template to compute the value of 2^n at compile time
- template <long n>
- struct exp_2_n
- {
- COMPILE_TIME_ASSERT(0 <= n && n <= 30);
- static const long value = exp_2_n<n-1>::value*2;
- };
-
- template <>
- struct exp_2_n<0>
- {
- static const long value = 1;
- };
-
- // ------------------------------------------------------------------------------------
-
- }
-
- typedef std::complex<double> qc_scalar_type;
-
-// ----------------------------------------------------------------------------------------
-
- class quantum_register
- {
- public:
-
- quantum_register()
- {
- set_num_bits(1);
- }
-
- int num_bits (
- ) const
- {
- return num_bits_in_register;
- }
-
- void set_num_bits (
- int num_bits
- )
- {
- // make sure requires clause is not broken
- DLIB_CASSERT(1 <= num_bits && num_bits <= 30,
- "\tvoid quantum_register::set_num_bits()"
- << "\n\tinvalid arguments to this function"
- << "\n\tnum_bits: " << num_bits
- << "\n\tthis: " << this
- );
-
- num_bits_in_register = num_bits;
-
- unsigned long size = 1;
- for (int i = 0; i < num_bits; ++i)
- size *= 2;
-
- state.set_size(size);
-
- zero_all_bits();
- }
-
- void zero_all_bits()
- {
- set_all_elements(state,0);
- state(0) = 1;
- }
-
- void append (
- const quantum_register& reg
- )
- {
- num_bits_in_register += reg.num_bits_in_register;
- state = tensor_product(state, reg.state);
- }
-
- template <typename rand_type>
- bool measure_bit (
- int bit,
- rand_type& rnd
- )
- {
- // make sure requires clause is not broken
- DLIB_CASSERT(0 <= bit && bit < num_bits(),
- "\tbool quantum_register::measure_bit()"
- << "\n\tinvalid arguments to this function"
- << "\n\tbit: " << bit
- << "\n\tnum_bits(): " << num_bits()
- << "\n\tthis: " << this
- );
-
- const bool value = (rnd.get_random_double() < probability_of_bit(bit));
-
- // Next we set all the states where this bit doesn't have the given value to 0
-
- // But first make a mask that selects our bit
- unsigned long mask = 1;
- for (int i = 0; i < bit; ++i)
- mask <<= 1;
-
- // loop over all the elements in the state vector and zero out those that
- // conflict with the measurement we just made.
- for (long r = 0; r < state.nr(); ++r)
- {
- const unsigned long field = r;
- // if this state indicates that the bit should be set and it isn't
- if ((field & mask) && !value)
- {
- state(r) = 0;
- }
- // else if this state indicates that the bit should not be set and it is
- else if (!(field & mask) && value)
- {
- state(r) = 0;
- }
- }
-
- // normalize the state
- state = state/(std::sqrt(sum(norm(state))));
-
- return value;
- }
-
- template <typename rand_type>
- bool measure_and_remove_bit (
- int bit,
- rand_type& rnd
- )
- {
- // make sure requires clause is not broken
- DLIB_CASSERT(0 <= bit && bit < num_bits() && num_bits() > 0,
- "\tbool quantum_register::measure_and_remove_bit()"
- << "\n\tinvalid arguments to this function"
- << "\n\tbit: " << bit
- << "\n\tnum_bits(): " << num_bits()
- << "\n\tthis: " << this
- );
-
-
- const bool value = (rnd.get_random_double() < probability_of_bit(bit));
- quantum_register temp;
- temp.set_num_bits(num_bits()-1);
-
-
- // Next we set all the states where this bit doesn't have the given value to 0
-
- // But first make a mask that selects our bit
- unsigned long mask = 1;
- for (int i = 0; i < bit; ++i)
- mask <<= 1;
-
- long count = 0;
- for (long r = 0; r < state.nr(); ++r)
- {
- const unsigned long field = r;
- // if this basis vector is one that matches the measured state then keep it
- if (((field & mask) != 0) == value)
- {
- temp.state(count) = state(r);
- ++count;
- }
- }
-
- // normalize the state
- temp.state = temp.state/std::sqrt(sum(norm(temp.state)));
-
- temp.swap(*this);
-
- return value;
- }
-
- double probability_of_bit (
- int bit
- ) const
- {
- // make sure requires clause is not broken
- DLIB_CASSERT(0 <= bit && bit < num_bits(),
- "\tdouble quantum_register::probability_of_bit()"
- << "\n\tinvalid arguments to this function"
- << "\n\tbit: " << bit
- << "\n\tnum_bits(): " << num_bits()
- << "\n\tthis: " << this
- );
-
-
- // make a mask that selects our bit
- unsigned long mask = 1;
- for (int i = 0; i < bit; ++i)
- mask <<= 1;
-
- // now find the total probability of all the states that have the given bit set
- double prob = 0;
- for (long r = 0; r < state.nr(); ++r)
- {
- const unsigned long field = r;
- if (field & mask)
- {
- prob += std::norm(state(r));
- }
- }
-
-
- return prob;
- }
-
- const matrix<qc_scalar_type,0,1>& state_vector() const { return state; }
- matrix<qc_scalar_type,0,1>& state_vector() { return state; }
-
- void swap (
- quantum_register& item
- )
- {
- exchange(num_bits_in_register, item.num_bits_in_register);
- state.swap(item.state);
- }
-
- private:
-
- int num_bits_in_register;
- matrix<qc_scalar_type,0,1> state;
- };
-
- inline void swap (
- quantum_register& a,
- quantum_register& b
- ) { a.swap(b); }
-
-// ----------------------------------------------------------------------------------------
-
- template <typename T>
- class gate_exp
- {
- public:
- static const long num_bits = gate_traits<T>::num_bits;
- static const long dims = gate_traits<T>::dims;
-
- gate_exp(T& exp_) : exp(exp_) {}
-
- const qc_scalar_type operator() (long r, long c) const { return exp(r,c); }
-
- const matrix<qc_scalar_type> mat (
- ) const
- {
- matrix<qc_scalar_type,dims,dims> m;
- for (long r = 0; r < m.nr(); ++r)
- {
- for (long c = 0; c < m.nc(); ++c)
- {
- m(r,c) = exp(r,c);
- }
- }
- return m;
- }
-
- void apply_gate_to (quantum_register& reg) const
- {
- // make sure requires clause is not broken
- DLIB_CASSERT(reg.num_bits() == num_bits,
- "\tvoid gate_exp::apply_gate_to()"
- << "\n\tinvalid arguments to this function"
- << "\n\treg.num_bits(): " << reg.num_bits()
- << "\n\tnum_bits: " << num_bits
- << "\n\tthis: " << this
- );
-
-
- quantum_register temp(reg);
-
-
- // check if any of the elements of the register are 1 and if so then
- // we don't have to do the full matrix multiply. Or check if only a small number are non-zero.
- long non_zero_elements = 0;
- for (long r = 0; r < dims; ++r)
- {
- if (reg.state_vector()(r) != qc_scalar_type(0))
- ++non_zero_elements;
-
- reg.state_vector()(r) = 0;
- }
-
-
- if (non_zero_elements > 3)
- {
- // do a full matrix multiply to compute the output state
- for (long r = 0; r < dims; ++r)
- {
- reg.state_vector()(r) = compute_state_element(temp.state_vector(),r);
- }
- }
- else
- {
- // do a matrix multiply but only use the columns in the gate matrix
- // that correspond to the non-zero register elements
- for (long r = 0; r < dims; ++r)
- {
- if (temp.state_vector()(r) != qc_scalar_type(0))
- {
- for (long i = 0; i < dims; ++i)
- {
- reg.state_vector()(i) += temp.state_vector()(r)*exp(i,r);
- }
- }
- }
- }
- }
-
- template <typename exp>
- qc_scalar_type compute_state_element (
- const matrix_exp<exp>& reg,
- long row_idx
- ) const
- {
- // make sure requires clause is not broken
- DLIB_ASSERT(reg.nr() == dims && reg.nc() == 1 &&
- 0 <= row_idx && row_idx < dims,
- "\tqc_scalar_type gate_exp::compute_state_element(reg,row_idx)"
- << "\n\tinvalid arguments to this function"
- << "\n\treg.nr(): " << reg.nr()
- << "\n\treg.nc(): " << reg.nc()
- << "\n\tdims: " << dims
- << "\n\trow_idx: " << row_idx
- << "\n\tthis: " << this
- );
-
-
- return this->exp.compute_state_element(reg,row_idx);
- }
-
- const T& ref() const { return exp; }
-
- private:
- T& exp;
- };
-
-// ----------------------------------------------------------------------------------------
-
-
- template <typename T, typename U>
- class composite_gate;
-
- template <typename T, typename U>
- struct gate_traits<composite_gate<T,U> >
- {
- static const long num_bits = T::num_bits + U::num_bits;
- static const long dims = qc_helpers::exp_2_n<num_bits>::value;
- };
-
- template <typename T, typename U>
- class composite_gate : public gate_exp<composite_gate<T,U> >
- {
- public:
-
- typedef T lhs_type;
- typedef U rhs_type;
-
- composite_gate(const composite_gate& g) : gate_exp<composite_gate>(*this), lhs(g.lhs), rhs(g.rhs) {}
-
- composite_gate(
- const gate_exp<T>& lhs_,
- const gate_exp<U>& rhs_
- ) : gate_exp<composite_gate>(*this), lhs(lhs_.ref()), rhs(rhs_.ref()) {}
-
-
-
- static const long num_bits = gate_traits<composite_gate>::num_bits;
- static const long dims = gate_traits<composite_gate>::dims;
-
- const qc_scalar_type operator() (long r, long c) const { return lhs(r/U::dims,c/U::dims)*rhs(r%U::dims, c%U::dims); }
-
- template <typename exp>
- qc_scalar_type compute_state_element (
- const matrix_exp<exp>& reg,
- long row_idx
- ) const
- {
- // make sure requires clause is not broken
- DLIB_ASSERT(reg.nr() == dims && reg.nc() == 1 &&
- 0 <= row_idx && row_idx < dims,
- "\tqc_scalar_type composite_gate::compute_state_element(reg,row_idx)"
- << "\n\tinvalid arguments to this function"
- << "\n\treg.nr(): " << reg.nr()
- << "\n\treg.nc(): " << reg.nc()
- << "\n\tdims: " << dims
- << "\n\trow_idx: " << row_idx
- << "\n\tthis: " << this
- );
-
-
- qc_scalar_type result = 0;
- for (long c = 0; c < T::dims; ++c)
- {
- if (lhs(row_idx/U::dims,c) != qc_scalar_type(0))
- {
- result += lhs(row_idx/U::dims,c) * rhs.compute_state_element(subm(reg,c*U::dims,0,U::dims,1), row_idx%U::dims);
- }
- }
-
- return result;
- }
-
-
- const T lhs;
- const U rhs;
- };
-
-// ----------------------------------------------------------------------------------------
-
- template <long bits>
- class gate;
- template <long bits>
- struct gate_traits<gate<bits> >
- {
- static const long num_bits = bits;
- static const long dims = qc_helpers::exp_2_n<num_bits>::value;
- };
-
-// ----------------------------------------------------------------------------------------
-
- template <long bits>
- class gate : public gate_exp<gate<bits> >
- {
- public:
- gate() : gate_exp<gate>(*this) { set_all_elements(data,0); }
- gate(const gate& g) :gate_exp<gate>(*this), data(g.data) {}
-
- template <typename T>
- explicit gate(const gate_exp<T>& g) : gate_exp<gate>(*this)
- {
- COMPILE_TIME_ASSERT(T::num_bits == num_bits);
- for (long r = 0; r < dims; ++r)
- {
- for (long c = 0; c < dims; ++c)
- {
- data(r,c) = g(r,c);
- }
- }
- }
-
- static const long num_bits = gate_traits<gate>::num_bits;
- static const long dims = gate_traits<gate>::dims;
-
- const qc_scalar_type& operator() (long r, long c) const { return data(r,c); }
- qc_scalar_type& operator() (long r, long c) { return data(r,c); }
-
- template <typename exp>
- qc_scalar_type compute_state_element (
- const matrix_exp<exp>& reg,
- long row_idx
- ) const
- {
- // make sure requires clause is not broken
- DLIB_ASSERT(reg.nr() == dims && reg.nc() == 1 &&
- 0 <= row_idx && row_idx < dims,
- "\tqc_scalar_type gate::compute_state_element(reg,row_idx)"
- << "\n\tinvalid arguments to this function"
- << "\n\treg.nr(): " << reg.nr()
- << "\n\treg.nc(): " << reg.nc()
- << "\n\tdims: " << dims
- << "\n\trow_idx: " << row_idx
- << "\n\tthis: " << this
- );
-
-
- return (data*reg)(row_idx);
- }
-
- private:
-
- matrix<qc_scalar_type,dims,dims> data;
- };
-
-// ----------------------------------------------------------------------------------------
-
- namespace qc_helpers
- {
- // This is the maximum number of bits used for cached sub-matrices in composite_gate expressions
- const int qc_block_chunking_size = 8;
-
- template <typename T>
- struct is_composite_gate { const static bool value = false; };
- template <typename T, typename U>
- struct is_composite_gate<composite_gate<T,U> > { const static bool value = true; };
-
-
- // These overloads all deal with intelligently composing chains of composite_gate expressions
- // such that the resulting expression has the form:
- // (gate_exp,(gate_exp,(gate_exp,(gate_exp()))))
- // and each gate_exp contains a cached gate matrix for a gate of at most qc_block_chunking_size bits.
- // This facilitates the optimizations in the compute_state_element() function.
- template <typename T, typename U, typename V, typename enabled = void>
- struct combine_gates;
-
- // This is a base case of this recursive template. It takes care of converting small composite_gates into
- // cached gate objects.
- template <typename T, typename U, typename V>
- struct combine_gates<T,U,V,typename enable_if_c<(T::num_bits + U::num_bits <= qc_block_chunking_size)>::type >
- {
- typedef composite_gate<gate<T::num_bits + U::num_bits>,V> result_type;
-
- static const result_type eval (
- const composite_gate<T,U>& lhs,
- const gate_exp<V>& rhs
- )
- {
- typedef gate<T::num_bits + U::num_bits> gate_type;
- return composite_gate<gate_type,V>(gate_type(lhs), rhs);
- }
- };
-
- // this is the recursive step of this template
- template <typename T, typename U, typename V>
- struct combine_gates<T,U,V,typename enable_if_c<(is_composite_gate<U>::value == true)>::type >
- {
- typedef typename combine_gates<typename U::lhs_type, typename U::rhs_type, V>::result_type inner_type;
- typedef composite_gate<T,inner_type> result_type;
-
- static const result_type eval (
- const composite_gate<T,U>& lhs,
- const gate_exp<V>& rhs
- )
- {
- return composite_gate<T,inner_type>(lhs.lhs, combine_gates<typename U::lhs_type, typename U::rhs_type, V>::eval(lhs.rhs,rhs));
- }
-
- };
-
- // This is a base case of this recursive template. It takes care of adding new gates when the left
- // hand side is too big to just turn it into a cached gate object.
- template <typename T, typename U, typename V>
- struct combine_gates<T,U,V,typename enable_if_c<(T::num_bits + U::num_bits > qc_block_chunking_size &&
- is_composite_gate<U>::value == false)>::type >
- {
- typedef composite_gate<T,composite_gate<U, V> > result_type;
-
- static const result_type eval (
- const composite_gate<T,U>& lhs,
- const gate_exp<V>& rhs
- )
- {
- return result_type(lhs.lhs, composite_gate<U,V>(lhs.rhs, rhs));
- }
-
- };
-
- }
-
- template <typename T, typename U>
- const composite_gate<T,U> operator, (
- const gate_exp<T>& lhs,
- const gate_exp<U>& rhs
- )
- {
- return composite_gate<T,U>(lhs,rhs);
- }
-
- template <typename T, typename U, typename V>
- const typename qc_helpers::combine_gates<T,U,V>::result_type operator, (
- const composite_gate<T,U>& lhs,
- const gate_exp<V>& rhs
- )
- {
- return qc_helpers::combine_gates<T,U,V>::eval(lhs,rhs);
- }
-
- // If you are getting an error here then it means that you are trying to combine a gate expression
- // with an integer somewhere (and that is an error).
- template <typename T> void operator, ( const gate_exp<T>&, int) { COMPILE_TIME_ASSERT(sizeof(T) > 100000000); }
- template <typename T> void operator, ( int, const gate_exp<T>&) { COMPILE_TIME_ASSERT(sizeof(T) > 100000000); }
-
-// ----------------------------------------------------------------------------------------
-
- namespace quantum_gates
- {
- template <int control_bit, int target_bit>
- class cnot;
-
- template <int control_bit1, int control_bit2, int target_bit>
- class toffoli;
- }
-
- template <int control_bit, int target_bit>
- struct gate_traits<quantum_gates::cnot<control_bit, target_bit> >
- {
- static const long num_bits = tabs<control_bit-target_bit>::value+1;
- static const long dims = qc_helpers::exp_2_n<num_bits>::value;
- };
-
- template <int control_bit1, int control_bit2, int target_bit>
- struct gate_traits<quantum_gates::toffoli<control_bit1, control_bit2, target_bit> >
- {
- static const long num_bits = tmax<tabs<control_bit1-target_bit>::value,
- tabs<control_bit2-target_bit>::value>::value+1;
- static const long dims = qc_helpers::exp_2_n<num_bits>::value;
- };
-
-
-// ----------------------------------------------------------------------------------------
-
- namespace quantum_gates
- {
-
- inline const gate<1> hadamard(
- )
- {
- gate<1> h;
- h(0,0) = std::sqrt(1/2.0);
- h(0,1) = std::sqrt(1/2.0);
- h(1,0) = std::sqrt(1/2.0);
- h(1,1) = -std::sqrt(1/2.0);
- return h;
- }
-
- // ------------------------------------------------------------------------------------
-
- inline const gate<1> x(
- )
- {
- gate<1> x;
- x(0,1) = 1;
- x(1,0) = 1;
- return x;
- }
-
- // ------------------------------------------------------------------------------------
-
- inline const gate<1> y(
- )
- {
- gate<1> x;
- qc_scalar_type i(0,1);
- x(0,1) = -i;
- x(1,0) = i;
- return x;
- }
-
- // ------------------------------------------------------------------------------------
-
- inline const gate<1> z(
- )
- {
- gate<1> z;
- z(0,0) = 1;
- z(1,1) = -1;
- return z;
- }
-
- // ------------------------------------------------------------------------------------
-
- inline const gate<1> noop(
- )
- {
- gate<1> i;
- i(0,0) = 1;
- i(1,1) = 1;
- return i;
- }
-
- // ------------------------------------------------------------------------------------
-
- template <int control_bit, int target_bit>
- class cnot : public gate_exp<cnot<control_bit, target_bit> >
- {
- public:
- COMPILE_TIME_ASSERT(control_bit != target_bit);
-
- cnot() : gate_exp<cnot>(*this)
- {
- const int min_bit = std::min(control_bit, target_bit);
-
- control_mask = 1;
- target_mask = 1;
-
- // make the masks so that their only on bit corresponds to the given control_bit and target_bit bits
- for (int i = 0; i < control_bit-min_bit; ++i)
- control_mask <<= 1;
- for (int i = 0; i < target_bit-min_bit; ++i)
- target_mask <<= 1;
- }
-
- static const long num_bits = gate_traits<cnot>::num_bits;
- static const long dims = gate_traits<cnot>::dims;
-
- const qc_scalar_type operator() (long r, long c) const
- {
- unsigned long output;
- // if the input control bit is set
- if (control_mask&c)
- {
- output = c^target_mask;
- }
- else
- {
- output = c;
- }
-
- 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
- {
- // make sure requires clause is not broken
- DLIB_ASSERT(reg.nr() == dims && reg.nc() == 1 &&
- 0 <= row_idx && row_idx < dims,
- "\tqc_scalar_type cnot::compute_state_element(reg,row_idx)"
- << "\n\tinvalid arguments to this function"
- << "\n\treg.nr(): " << reg.nr()
- << "\n\treg.nc(): " << reg.nc()
- << "\n\tdims: " << dims
- << "\n\trow_idx: " << row_idx
- << "\n\tthis: " << this
- );
-
-
- unsigned long output = row_idx;
- // if the input control bit is set
- if (control_mask&output)
- {
- output = output^target_mask;
- }
-
- return reg(output);
- }
-
- private:
-
- unsigned long control_mask;
- unsigned long target_mask;
-
-
- };
-
- // ------------------------------------------------------------------------------------
-
- template <int control_bit1, int control_bit2, int target_bit>
- class toffoli : public gate_exp<toffoli<control_bit1, control_bit2, target_bit> >
- {
- public:
- COMPILE_TIME_ASSERT(control_bit1 != target_bit && control_bit2 != target_bit && control_bit1 != control_bit2);
- COMPILE_TIME_ASSERT((control_bit1 < target_bit && control_bit2 < target_bit) ||(control_bit1 > target_bit && control_bit2 > target_bit) );
-
- toffoli() : gate_exp<toffoli>(*this)
- {
- const int min_bit = std::min(std::min(control_bit1, control_bit2), target_bit);
-
- control1_mask = 1;
- control2_mask = 1;
- target_mask = 1;
-
- // make the masks so that their only on bit corresponds to the given control_bit1 and target_bit bits
- for (int i = 0; i < control_bit1-min_bit; ++i)
- control1_mask <<= 1;
- for (int i = 0; i < control_bit2-min_bit; ++i)
- control2_mask <<= 1;
- for (int i = 0; i < target_bit-min_bit; ++i)
- target_mask <<= 1;
- }
-
- static const long num_bits = gate_traits<toffoli>::num_bits;
- static const long dims = gate_traits<toffoli>::dims;
-
- const qc_scalar_type operator() (long r, long c) const
- {
- unsigned long output;
- // if the input control bits are set
- if ((control1_mask&c) && (control2_mask&c))
- {
- output = c^target_mask;
- }
- else
- {
- output = c;
- }
-
- 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
- {
- // make sure requires clause is not broken
- DLIB_ASSERT(reg.nr() == dims && reg.nc() == 1 &&
- 0 <= row_idx && row_idx < dims,
- "\tqc_scalar_type toffoli::compute_state_element(reg,row_idx)"
- << "\n\tinvalid arguments to this function"
- << "\n\treg.nr(): " << reg.nr()
- << "\n\treg.nc(): " << reg.nc()
- << "\n\tdims: " << dims
- << "\n\trow_idx: " << row_idx
- << "\n\tthis: " << this
- );
-
-
- unsigned long output;
- // if the input control bits are set
- if ((control1_mask&row_idx) && (control2_mask&row_idx))
- {
- output = row_idx^target_mask;
- }
- else
- {
- output = row_idx;
- }
-
- return reg(output);
-
- }
-
- private:
-
- unsigned long control1_mask;
- unsigned long control2_mask;
- unsigned long target_mask;
-
-
- };
-
-
- // ------------------------------------------------------------------------------------
-
- }
-
-// ----------------------------------------------------------------------------------------
-
-}
-
-#endif // DLIB_QUANTUM_COMPUTINg_1_
-
-
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