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add hamiltonian simulation with block-encoding #189

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add hamiltonian simulation with block-encoding #189

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120 changes: 120 additions & 0 deletions ...an_simulation/hamiltonian_simulation_with_block_encoding/hamiltonian_simulation_qsvt.qmod
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qfunc identify_block<num_data_qubits: int>(qvar: qbit[], qbit: qbit) {
block_qubits: qnum<qvar.len - num_data_qubits, False, 0>;
data: qbit[num_data_qubits];
qvar -> {block_qubits, data};
qbit ^= block_qubits == 0;
{block_qubits, data} -> qvar;
}

qfunc apply_pauli_term<pauli_string: PauliTerm>(x: qbit[]) {
repeat (index: x.len) {
switch<pauli_string.pauli[index], [lambda() {
IDENTITY(x[(pauli_string.pauli.len - index) - 1]);
}, lambda() {
X(x[(pauli_string.pauli.len - index) - 1]);
}, lambda() {
Y(x[(pauli_string.pauli.len - index) - 1]);
}, lambda() {
Z(x[(pauli_string.pauli.len - index) - 1]);
}]>();
}
}

qfunc lcu_paulis<pauli_terms_list: PauliTerm[], probs: real[]>(block: qnum, data: qbit[]) {
within {
inplace_prepare_state<probs, 0.0>(block);
} apply {
repeat (i: pauli_terms_list.len) {
control (block == i) {
apply_pauli_term<pauli_terms_list[i]>(data);
}
}
}
}

qfunc my_qsvt<phases: real[]>(qsvt_aux: qbit, block_ham: qbit[], data: qbit[]) {
combined_vars: qbit[];
{block_ham, data} -> combined_vars;
qsvt<phases, lambda(qvar, qbit) {
identify_block<data.len>(qvar, qbit);
}, lambda(qvar, qbit) {
identify_block<data.len>(qvar, qbit);
}, lambda(x) {
lcu_paulis<[
PauliTerm {
pauli=[Pauli::I, Pauli::I],
coefficient=0.4
},
PauliTerm {
pauli=[Pauli::I, Pauli::Z],
coefficient=0.1
},
PauliTerm {
pauli=[Pauli::X, Pauli::X],
coefficient=0.05
},
PauliTerm {
pauli=[Pauli::Z, Pauli::Z],
coefficient=0.2
}
], [
0.533333333333,
0.133333333333,
0.066666666667,
0.266666666667
]>(x[0:block_ham.len], x[block_ham.len:x.len]);
}>(combined_vars, qsvt_aux);
combined_vars -> {block_ham, data};
}

qfunc main(output qsvt_aux: qbit, output block_ham: qnum, output data: qnum, output block_exp: qbit) {
allocate<1>(qsvt_aux);
allocate<1>(block_exp);
allocate<2>(block_ham);
prepare_amplitudes<[
0.48587965335,
0.797920098145,
0.047888630623,
0.353484311524
], 0.0>(data);
within {
H(block_exp);
} apply {
control (block_exp == 0) {
my_qsvt<[
2.165090221257,
2.804630670098,
5.917462428618,
4.345252560942,
3.600632871756,
2.4490316684,
1.068732911576,
2.449031668413,
3.600632871777,
4.345252560989,
(-0.365722878571),
9.087815977228,
(-38.675614275419)
]>(qsvt_aux, block_ham, data);
}
control (block_exp == 1) {
U<0, 0, 0, pi / 2>(qsvt_aux);
my_qsvt<[
4.470362447654,
4.607012939067,
1.442128313968,
2.548694823934,
2.950937973684,
1.347475644731,
5.707035852645,
(-0.576149454516),
7.630660951833,
2.950937973609,
2.548694824062,
1.442128313861,
4.607012938959,
(-39.511934702504)
]>(qsvt_aux, block_ham, data);
}
}
}
1 change: 1 addition & 0 deletions ...ltonian_simulation_with_block_encoding/hamiltonian_simulation_qsvt.synthesis_options.json
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{}
111 changes: 111 additions & 0 deletions ...ation/hamiltonian_simulation_with_block_encoding/hamiltonian_simulation_qubitization.qmod
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qfunc apply_pauli_term<pauli_string: PauliTerm>(x: qbit[]) {
repeat (index: x.len) {
switch<pauli_string.pauli[index], [lambda() {
IDENTITY(x[(pauli_string.pauli.len - index) - 1]);
}, lambda() {
X(x[(pauli_string.pauli.len - index) - 1]);
}, lambda() {
Y(x[(pauli_string.pauli.len - index) - 1]);
}, lambda() {
Z(x[(pauli_string.pauli.len - index) - 1]);
}]>();
}
}

qfunc lcu_paulis<pauli_terms_list: PauliTerm[], probs: real[]>(block: qnum, data: qbit[]) {
within {
inplace_prepare_state<probs, 0.0>(block);
} apply {
repeat (i: pauli_terms_list.len) {
control (block == i) {
apply_pauli_term<pauli_terms_list[i]>(data);
}
}
}
}

qfunc my_walk_operator(block: qbit[], data: qbit[]) {
lcu_paulis<[
PauliTerm {
pauli=[Pauli::I, Pauli::I],
coefficient=0.4
},
PauliTerm {
pauli=[Pauli::I, Pauli::Z],
coefficient=0.1
},
PauliTerm {
pauli=[Pauli::X, Pauli::X],
coefficient=0.05
},
PauliTerm {
pauli=[Pauli::Z, Pauli::Z],
coefficient=0.2
}
], [
0.533333333333,
0.133333333333,
0.066666666667,
0.266666666667
]>(block, data);
reflect_about_zero(block);
RY<2 * pi>(block[0]);
}

qfunc lcu_cheb<coef: real[], generalized_signs: int[], walk_operator: qfunc (arg0: qnum, arg1: qbit[])>(walk_block: qnum, walk_data: qbit[], cheb_block: qnum) {
within {
inplace_prepare_state<coef, 0.0>(cheb_block);
} apply {
repeat (k: generalized_signs.len) {
control (cheb_block == k) {
U<0, 0, 0, (pi / 2) * generalized_signs[k]>(walk_data[0]);
power (k) {
walk_operator(walk_block, walk_data);
}
}
}
}
}

qfunc main(output ham_block: qnum, output data: qnum, output exp_block: qnum) {
allocate<4>(exp_block);
allocate<2>(ham_block);
prepare_amplitudes<[
0.48587965335,
0.797920098145,
0.047888630623,
0.353484311524
], 0.0>(data);
lcu_cheb<[
0.066463021055,
0.067500417785,
0.1149259307,
0.128794247492,
0.011890532707,
0.141477482379,
0.176746110466,
0.141316294366,
0.087044305684,
0.044378224427,
0.01946343294,
0,
0,
0,
0,
0
], [
0.0,
1.0,
0.0,
1.0,
0.0,
1.0,
2.0,
3.0,
0.0,
1.0,
2.0
], lambda(x, y) {
my_walk_operator(x, y);
}>(ham_block, data, exp_block);
}
1 change: 1 addition & 0 deletions ...simulation_with_block_encoding/hamiltonian_simulation_qubitization.synthesis_options.json
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{}
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