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Feature/hardcode c3x, c4x decompositions (#134)
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* Hardcode C3X and C4X decompositions

* Add base case handling to cnx dexomposition

* Add test cases

* Add changelog entry

* Add a test case for incrementer_borrow_n_qubits

* Add more test cases

* Improve cases handling in one-ancilla incrementer

* Add docstrings and make private functions static

* Correct CX count for C4X decomposition
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@yao-cqc
yao-cqc authored Dec 10, 2021
1 parent 1161906 commit d70f4f6
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Showing 5 changed files with 283 additions and 173 deletions.
1 change: 1 addition & 0 deletions pytket/docs/changelog.rst
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Expand Up @@ -7,6 +7,7 @@ Changelog
Minor new features:

* Add `NodeGraph` as abstract base class for device connectivity graphs.
* Improved CnX gate decomposition.

0.17.0 (November 2021)
----------------------
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123 changes: 123 additions & 0 deletions tket/src/Circuit/CircPool.cpp
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Expand Up @@ -296,6 +296,129 @@ const Circuit &CCX_normal_decomp() {
return *C;
}

const Circuit &C3X_normal_decomp() {
static std::unique_ptr<const Circuit> C = std::make_unique<Circuit>([]() {
Circuit c(4);
c.add_op<unsigned>(OpType::H, {3});
c.add_op<unsigned>(OpType::U1, 0.125, {0});
c.add_op<unsigned>(OpType::U1, 0.125, {1});
c.add_op<unsigned>(OpType::U1, 0.125, {2});
c.add_op<unsigned>(OpType::U1, 0.125, {3});
c.add_op<unsigned>(OpType::CX, {0, 1});
c.add_op<unsigned>(OpType::U1, -0.125, {1});
c.add_op<unsigned>(OpType::CX, {0, 1});
c.add_op<unsigned>(OpType::CX, {1, 2});
c.add_op<unsigned>(OpType::U1, -0.125, {2});
c.add_op<unsigned>(OpType::CX, {0, 2});
c.add_op<unsigned>(OpType::U1, 0.125, {2});
c.add_op<unsigned>(OpType::CX, {1, 2});
c.add_op<unsigned>(OpType::U1, -0.125, {2});
c.add_op<unsigned>(OpType::CX, {0, 2});
c.add_op<unsigned>(OpType::CX, {2, 3});
c.add_op<unsigned>(OpType::U1, -0.125, {3});
c.add_op<unsigned>(OpType::CX, {1, 3});
c.add_op<unsigned>(OpType::U1, 0.125, {3});
c.add_op<unsigned>(OpType::CX, {2, 3});
c.add_op<unsigned>(OpType::U1, -0.125, {3});
c.add_op<unsigned>(OpType::CX, {0, 3});
c.add_op<unsigned>(OpType::U1, 0.125, {3});
c.add_op<unsigned>(OpType::CX, {2, 3});
c.add_op<unsigned>(OpType::U1, -0.125, {3});
c.add_op<unsigned>(OpType::CX, {1, 3});
c.add_op<unsigned>(OpType::U1, 0.125, {3});
c.add_op<unsigned>(OpType::CX, {2, 3});
c.add_op<unsigned>(OpType::U1, -0.125, {3});
c.add_op<unsigned>(OpType::CX, {0, 3});
c.add_op<unsigned>(OpType::H, {3});
return c;
}());
return *C;
}

// Implementing C3X up to a relative phase
// https://arxiv.org/pdf/1508.03273.pdf figure 4
static const Circuit &RC3X_normal_decomp() {
static std::unique_ptr<const Circuit> C = std::make_unique<Circuit>([]() {
Circuit c(4);
c.add_op<unsigned>(OpType::U2, {0, 1}, {3});
c.add_op<unsigned>(OpType::U1, 0.25, {3});
c.add_op<unsigned>(OpType::CX, {2, 3});
c.add_op<unsigned>(OpType::U1, -0.25, {3});
c.add_op<unsigned>(OpType::U2, {0, 1}, {3});
c.add_op<unsigned>(OpType::CX, {0, 3});
c.add_op<unsigned>(OpType::U1, 0.25, {3});
c.add_op<unsigned>(OpType::CX, {1, 3});
c.add_op<unsigned>(OpType::U1, -0.25, {3});
c.add_op<unsigned>(OpType::CX, {0, 3});
c.add_op<unsigned>(OpType::U1, 0.25, {3});
c.add_op<unsigned>(OpType::CX, {1, 3});
c.add_op<unsigned>(OpType::U1, -0.25, {3});
c.add_op<unsigned>(OpType::U2, {0, 1}, {3});
c.add_op<unsigned>(OpType::U1, 0.25, {3});
c.add_op<unsigned>(OpType::CX, {2, 3});
c.add_op<unsigned>(OpType::U1, -0.25, {3});
c.add_op<unsigned>(OpType::U2, {0, 1}, {3});
return c;
}());
return *C;
}

// Implementing 3-controlled SX gate
// https://arxiv.org/pdf/quant-ph/9503016.pdf page 17
static const Circuit &C3SX_normal_decomp() {
static std::unique_ptr<const Circuit> C = std::make_unique<Circuit>([]() {
Circuit c(4);
c.add_op<unsigned>(OpType::H, {3});
c.append_qubits(CU1_using_CX(-0.125), {0, 3});
c.add_op<unsigned>(OpType::H, {3});
c.add_op<unsigned>(OpType::CX, {0, 1});
c.add_op<unsigned>(OpType::H, {3});
c.append_qubits(CU1_using_CX(0.125), {1, 3});
c.add_op<unsigned>(OpType::H, {3});
c.add_op<unsigned>(OpType::CX, {0, 1});
c.add_op<unsigned>(OpType::H, {3});
c.append_qubits(CU1_using_CX(-0.125), {1, 3});
c.add_op<unsigned>(OpType::H, {3});
c.add_op<unsigned>(OpType::CX, {1, 2});
c.add_op<unsigned>(OpType::H, {3});
c.append_qubits(CU1_using_CX(0.125), {2, 3});
c.add_op<unsigned>(OpType::H, {3});
c.add_op<unsigned>(OpType::CX, {0, 2});
c.add_op<unsigned>(OpType::H, {3});
c.append_qubits(CU1_using_CX(-0.125), {2, 3});
c.add_op<unsigned>(OpType::H, {3});
c.add_op<unsigned>(OpType::CX, {1, 2});
c.add_op<unsigned>(OpType::H, {3});
c.append_qubits(CU1_using_CX(0.125), {2, 3});
c.add_op<unsigned>(OpType::H, {3});
c.add_op<unsigned>(OpType::CX, {0, 2});
c.add_op<unsigned>(OpType::H, {3});
c.append_qubits(CU1_using_CX(-0.125), {2, 3});
c.add_op<unsigned>(OpType::H, {3});
return c;
}());
return *C;
}

// https://arxiv.org/pdf/quant-ph/9503016.pdf lemma 7.5
const Circuit &C4X_normal_decomp() {
static std::unique_ptr<const Circuit> C = std::make_unique<Circuit>([]() {
Circuit c(5);
c.add_op<unsigned>(OpType::H, {4});
c.append_qubits(CU1_using_CX(-0.5), {3, 4});
c.add_op<unsigned>(OpType::H, {4});

c.append_qubits(RC3X_normal_decomp(), {0, 1, 2, 3});
c.add_op<unsigned>(OpType::H, {4});
c.append_qubits(CU1_using_CX(0.5), {3, 4});
c.add_op<unsigned>(OpType::H, {4});
c.append_qubits(RC3X_normal_decomp().dagger(), {0, 1, 2, 3});
c.append_qubits(C3SX_normal_decomp(), {0, 1, 2, 4});
return c;
}());
return *C;
}

const Circuit &ladder_down() {
static std::unique_ptr<const Circuit> C = std::make_unique<Circuit>([]() {
Circuit c(3);
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6 changes: 6 additions & 0 deletions tket/src/Circuit/CircPool.hpp
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Expand Up @@ -123,6 +123,12 @@ const Circuit &CCX_modulo_phase_shift();
/** Equivalent to CCX, using five CX */
const Circuit &CCX_normal_decomp();

/** Equivalent to CCCX, using 14 CX */
const Circuit &C3X_normal_decomp();

/** Equivalent to CCCCX, using 36 CX */
const Circuit &C4X_normal_decomp();

/** CX[0,1]; CX[2,0]; CCX[0,1,2] */
const Circuit &ladder_down();

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63 changes: 45 additions & 18 deletions tket/src/Transformations/ControlledGates.cpp
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Expand Up @@ -46,7 +46,10 @@ static void lemma73(
Circuit Transform::incrementer_borrow_1_qubit(unsigned n) {
bool is_odd = n % 2;
Circuit circ(n + 1);
if (n < 4) {
if (n < 6) {
if (n > 4)
circ.append_qubits(CircPool::C4X_normal_decomp(), {0, 1, 2, 3, 4});
if (n > 3) circ.append_qubits(CircPool::C3X_normal_decomp(), {0, 1, 2, 3});
if (n > 2) circ.add_op<unsigned>(OpType::CCX, {0, 1, 2});
if (n > 1) circ.add_op<unsigned>(OpType::CX, {0, 1});
if (n > 0) circ.add_op<unsigned>(OpType::X, {0});
Expand Down Expand Up @@ -74,9 +77,12 @@ Circuit Transform::incrementer_borrow_1_qubit(unsigned n) {

Circuit cnx_top;
std::vector<unsigned> cnx1_qbs;
if (k == 2) { // code is unreachable if k<2
cnx_top = CircPool::CCX_normal_decomp();
cnx1_qbs = {0, 1, n};
if (k == 3) { // code is unreachable if k<3
cnx_top = CircPool::C3X_normal_decomp();
cnx1_qbs = {0, 1, 2, n};
} else if (k == 4) {
cnx_top = CircPool::C4X_normal_decomp();
cnx1_qbs = {0, 1, 2, 3, n};
} else {
cnx_top = lemma72(k); // k controls on cnx
cnx1_qbs.resize(
Expand All @@ -99,12 +105,24 @@ Circuit Transform::incrementer_borrow_1_qubit(unsigned n) {
}
bot_qbs[1] = n; // incremented qubit 0 in incrementer is bottom one
} else {
if (j == 3) { // code is unreachable if j<3
bottom_incrementer.add_blank_wires(3);
if (j == 4) { // code is unreachable if j<4
bottom_incrementer.add_blank_wires(4);
bottom_incrementer.append_qubits(
CircPool::C3X_normal_decomp(), {0, 1, 2, 3});
bottom_incrementer.add_op<unsigned>(OpType::CCX, {0, 1, 2});
bottom_incrementer.add_op<unsigned>(OpType::CX, {0, 1});
bottom_incrementer.add_op<unsigned>(OpType::X, {0});
bot_qbs = {n, n - 2, n - 1};
bot_qbs = {n, n - 3, n - 2, n - 1};
} else if (j == 5) {
bottom_incrementer.add_blank_wires(5);
bottom_incrementer.append_qubits(
CircPool::C4X_normal_decomp(), {0, 1, 2, 3, 4});
bottom_incrementer.append_qubits(
CircPool::C3X_normal_decomp(), {0, 1, 2, 3});
bottom_incrementer.add_op<unsigned>(OpType::CCX, {0, 1, 2});
bottom_incrementer.add_op<unsigned>(OpType::CX, {0, 1});
bottom_incrementer.add_op<unsigned>(OpType::X, {0});
bot_qbs = {n, n - 4, n - 3, n - 2, n - 1};
} else {
// insert peeled-out cnx
Circuit cnx_bot = lemma72(j - 1);
Expand Down Expand Up @@ -140,7 +158,7 @@ Circuit Transform::incrementer_borrow_1_qubit(unsigned n) {
{n}); // to convert controlled-incrementer to larger incrementer
for (unsigned i = k; i != n; ++i) circ.add_op<unsigned>(OpType::CX, {n, i});
circ.append_qubits(cnx_top, cnx1_qbs);
if (!is_odd && j > 3) {
if (!is_odd && j > 5) {
// insert peeled-out cnx
Circuit cnx_bot = lemma72(j - 1);
std::vector<unsigned> cnx2_qbs(2 * j - 3);
Expand Down Expand Up @@ -169,7 +187,10 @@ Circuit Transform::incrementer_borrow_n_qubits(unsigned n) {
const unsigned N = 2 * n;
Circuit circ(N);
/* deal with small cases where borrowing qubits is unnecessary */
if (n < 4) {
if (n < 6) {
if (n > 4)
circ.append_qubits(CircPool::C4X_normal_decomp(), {1, 3, 5, 7, 9});
if (n > 3) circ.append_qubits(CircPool::C3X_normal_decomp(), {1, 3, 5, 7});
if (n > 2) circ.add_op<unsigned>(OpType::CCX, {1, 3, 5});
if (n > 1) circ.add_op<unsigned>(OpType::CX, {1, 3});
if (n > 0) circ.add_op<unsigned>(OpType::X, {1});
Expand Down Expand Up @@ -214,7 +235,7 @@ Circuit Transform::incrementer_borrow_n_qubits(unsigned n) {
// `n` = no. of controls
Circuit Transform::cnx_normal_decomp(unsigned n) {
/* handle low qb edge cases */
bool insert_ccxs; // dictate whether to add Toffolis or n>3 controlled Xs
bool insert_c4xs; // dictate whether to add C4Xs or n>4 controlled Xs
// when bootstrapping
switch (n) {
case 0: {
Expand All @@ -227,11 +248,17 @@ Circuit Transform::cnx_normal_decomp(unsigned n) {
return CircPool::CCX_normal_decomp();
}
case 3: {
insert_ccxs = true;
return CircPool::C3X_normal_decomp();
}
case 4: {
return CircPool::C4X_normal_decomp();
}
case 5: {
insert_c4xs = true;
break;
}
default: {
insert_ccxs = false;
insert_c4xs = false;
break;
}
}
Expand All @@ -243,30 +270,30 @@ Circuit Transform::cnx_normal_decomp(unsigned n) {
// first, bootstrap an ancilla qubit
circ.add_op<unsigned>(OpType::H, {n});
Vertex cnx1;
if (insert_ccxs)
cnx1 = circ.add_op<unsigned>(OpType::CCX, {cnx_qbs});
if (insert_c4xs)
circ.append_qubits(CircPool::C4X_normal_decomp(), {cnx_qbs});
else {
cnx1 = circ.add_op<unsigned>(
OpType::CnX,
{cnx_qbs}); /* the CnXs can be decomposed using lemma 7.3 */
}
circ.add_op<unsigned>(OpType::Tdg, {n});
Vertex cx = circ.add_op<unsigned>(OpType::CX, {n - 1, n});
if (!insert_ccxs) {
if (!insert_c4xs) {
Edge e1 = circ.get_nth_in_edge(cx, 0);
lemma73(circ, {e1, cnx1}); // replace first CnX using lemma 7.3
}
circ.add_op<unsigned>(OpType::T, {n});
Vertex cnx2;
if (insert_ccxs)
cnx2 = circ.add_op<unsigned>(OpType::CCX, {cnx_qbs});
if (insert_c4xs)
circ.append_qubits(CircPool::C4X_normal_decomp(), {cnx_qbs});
else {
cnx2 = circ.add_op<unsigned>(OpType::CnX, {cnx_qbs});
}
circ.add_op<unsigned>(OpType::Tdg, {n});
cx = circ.add_op<unsigned>(OpType::CX, {n - 1, n});
Edge e2 = circ.get_nth_in_edge(cx, 0);
if (!insert_ccxs) lemma73(circ, {e2, cnx2});
if (!insert_c4xs) lemma73(circ, {e2, cnx2});
circ.add_op<unsigned>(OpType::T, {n});
circ.add_op<unsigned>(OpType::H, {n});

Expand Down
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