GCC Code Coverage Report

Directory: ./
File: Clifford/CliffTableau.cpp
Date: 2022-10-15 05:10:18
Warnings: 4 unchecked decisions!
Exec Total Coverage
Lines: 332 441 75.3%
Functions: 22 24 91.7%
Branches: 365 681 53.6%
Decisions: 80 120 66.7%
Line Branch Decision Exec Source
1 // Copyright 2019-2022 Cambridge Quantum Computing
2 //
3 // Licensed under the Apache License, Version 2.0 (the "License");
4 // you may not use this file except in compliance with the License.
5 // You may obtain a copy of the License at
6 //
7 // http://www.apache.org/licenses/LICENSE-2.0
8 //
9 // Unless required by applicable law or agreed to in writing, software
10 // distributed under the License is distributed on an "AS IS" BASIS,
11 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12 // See the License for the specific language governing permissions and
13 // limitations under the License.
14
15 #include "CliffTableau.hpp"
16
17 #include <stdexcept>
18
19 #include "OpType/OpType.hpp"
20 #include "OpType/OpTypeInfo.hpp"
21 #include "Utils/MatrixAnalysis.hpp"
22 #include "tkassert/Assert.hpp"
23
24 namespace tket {
25
26 const std::map<
27 std::pair<CliffTableau::BoolPauli, CliffTableau::BoolPauli>,
28 std::pair<CliffTableau::BoolPauli, Complex>>
29 CliffTableau::mult_lut = {
30 // {{{x1,z1},{x2,z2}}, {{x,z},ph}}
31 {{{false, false}, {false, false}}, {{false, false}, 1.}},
32 {{{false, false}, {false, true}}, {{false, true}, 1.}},
33 {{{false, false}, {true, false}}, {{true, false}, 1.}},
34 {{{false, false}, {true, true}}, {{true, true}, 1.}},
35 {{{false, true}, {false, false}}, {{false, true}, 1.}},
36 {{{false, true}, {false, true}}, {{false, false}, 1.}},
37 {{{false, true}, {true, false}}, {{true, true}, i_}},
38 {{{false, true}, {true, true}}, {{true, false}, -i_}},
39 {{{true, false}, {false, false}}, {{true, false}, 1.}},
40 {{{true, false}, {false, true}}, {{true, true}, -i_}},
41 {{{true, false}, {true, false}}, {{false, false}, 1.}},
42 {{{true, false}, {true, true}}, {{false, true}, i_}},
43 {{{true, true}, {false, false}}, {{true, true}, 1.}},
44 {{{true, true}, {false, true}}, {{true, false}, i_}},
45 {{{true, true}, {true, false}}, {{false, true}, -i_}},
46 {{{true, true}, {true, true}}, {{false, false}, 1.}}};
47
48
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 53 CliffTableau::CliffTableau(unsigned n) : size_(n) {
49
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 53 xpauli_x = MatrixXb::Identity(n, n);
50
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 53 xpauli_z = MatrixXb::Zero(n, n);
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 53 xpauli_phase = VectorXb::Zero(n);
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 53 zpauli_x = MatrixXb::Zero(n, n);
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 53 zpauli_z = MatrixXb::Identity(n, n);
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 53 zpauli_phase = VectorXb::Zero(n);
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 294 for (unsigned i = 0; i < n; i++) {
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 241 qubits_.insert({Qubit(q_default_reg(), i), i});
57 }
58 53 }
59
60
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 110 CliffTableau::CliffTableau(const qubit_vector_t &qbs) : size_(qbs.size()) {
61 110 const unsigned n = size_;
62
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 110 xpauli_x = MatrixXb::Identity(n, n);
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 110 xpauli_z = MatrixXb::Zero(n, n);
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 110 xpauli_phase = VectorXb::Zero(n);
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 110 zpauli_x = MatrixXb::Zero(n, n);
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 110 zpauli_z = MatrixXb::Identity(n, n);
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 110 zpauli_phase = VectorXb::Zero(n);
68
69 110 unsigned i = 0;
70
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 466 for (const Qubit &q : qbs) {
71
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 356 qubits_.insert({q, i});
72 356 i++;
73 }
74 110 }
75
76 943 static QubitPauliTensor get_pauli(
77 const Qubit &qb, const boost::bimap<Qubit, unsigned> &qubits_,
78 const MatrixXb &pauli_x, const MatrixXb &pauli_z,
79 const VectorXb &pauli_phase) {
80
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 943 unsigned uqb = qubits_.left.at(qb);
81 943 Complex phase = 1.;
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 943 if (pauli_phase(uqb)) phase = -1.;
83 943 QubitPauliTensor res(phase);
84
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 1886 for (boost::bimap<Qubit, unsigned>::const_iterator iter = qubits_.begin(),
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 943 iend = qubits_.end();
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 4406 iter != iend; ++iter) {
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 3463 unsigned origin = iter->right;
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 3463 if (pauli_x(uqb, origin)) {
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 716 if (pauli_z(uqb, origin)) {
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 126 res = res * QubitPauliTensor(iter->left, Pauli::Y);
91 } else {
92
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 590 res = res * QubitPauliTensor(iter->left, Pauli::X);
93 }
94
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 2747 } else if (pauli_z(uqb, origin)) {
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 480 res = res * QubitPauliTensor(iter->left, Pauli::Z);
96 }
97 }
98 1886 return res;
99 }
100
101 550 QubitPauliTensor CliffTableau::get_zpauli(const Qubit &qb) const {
102 550 return get_pauli(qb, qubits_, zpauli_x, zpauli_z, zpauli_phase);
103 }
104
105 393 QubitPauliTensor CliffTableau::get_xpauli(const Qubit &qb) const {
106 393 return get_pauli(qb, qubits_, xpauli_x, xpauli_z, xpauli_phase);
107 }
108
109 80 std::set<Qubit> CliffTableau::get_qubits() const {
110 80 std::set<Qubit> result;
111
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 160 for (boost::bimap<Qubit, unsigned>::const_iterator iter = qubits_.begin(),
112
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 80 iend = qubits_.end();
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 357 iter != iend; ++iter) {
114
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 277 result.insert(iter->left);
115 }
116 80 return result;
117 }
118
119 1486 void CliffTableau::row_mult(
120 const MatrixXb::RowXpr &xa, const MatrixXb::RowXpr &za, const bool &pa,
121 const MatrixXb::RowXpr &xb, const MatrixXb::RowXpr &zb, const bool &pb,
122 Complex phase, MatrixXb::RowXpr &xw, MatrixXb::RowXpr &zw, bool &pw) {
123
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 1486 if (pa) phase *= -1;
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 1486 if (pb) phase *= -1;
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 7784 for (unsigned i = 0; i < size_; i++) {
126 std::pair<BoolPauli, Complex> res =
127
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 6298 mult_lut.at({{xa(i), za(i)}, {xb(i), zb(i)}});
128
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 6298 xw(i) = res.first.x;
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 6298 zw(i) = res.first.z;
130 6298 phase *= res.second;
131 }
132 1486 pw = (phase == -1.);
133 1486 }
134
135 3164 void CliffTableau::col_mult(
136 const MatrixXb::ColXpr &a, const MatrixXb::ColXpr &b, bool flip,
137 MatrixXb::ColXpr &w, VectorXb &pw) {
138
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 14188 for (unsigned i = 0; i < size_; i++) {
139
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 11024 pw(i) = pw(i) ^ (a(i) && (b(i) ^ flip));
140 11024 w(i) = a(i) ^ b(i);
141 }
142 3164 }
143
144 1063 void CliffTableau::apply_S_at_front(unsigned qb) {
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 1063 MatrixXb::ColXpr xx = xpauli_x.col(qb);
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 1063 MatrixXb::ColXpr xz = xpauli_z.col(qb);
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 1063 MatrixXb::ColXpr zx = zpauli_x.col(qb);
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 1063 MatrixXb::ColXpr zz = zpauli_z.col(qb);
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 1063 col_mult(xx, xz, true, xz, xpauli_phase);
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 1063 col_mult(zx, zz, true, zz, zpauli_phase);
151 1063 }
152
153 349 void CliffTableau::apply_S_at_end(unsigned qb) {
154
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 349 MatrixXb::RowXpr xx = xpauli_x.row(qb);
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 349 MatrixXb::RowXpr xz = xpauli_z.row(qb);
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 349 MatrixXb::RowXpr zx = zpauli_x.row(qb);
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 349 MatrixXb::RowXpr zz = zpauli_z.row(qb);
158 349 row_mult(
159
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 349 zx, zz, zpauli_phase(qb), xx, xz, xpauli_phase(qb), i_, xx, xz,
160
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 349 xpauli_phase(qb));
161 349 }
162
163 519 void CliffTableau::apply_V_at_front(unsigned qb) {
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 519 MatrixXb::ColXpr xx = xpauli_x.col(qb);
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 519 MatrixXb::ColXpr xz = xpauli_z.col(qb);
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 519 MatrixXb::ColXpr zx = zpauli_x.col(qb);
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 519 MatrixXb::ColXpr zz = zpauli_z.col(qb);
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 519 col_mult(xx, xz, false, xx, xpauli_phase);
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 519 col_mult(zx, zz, false, zx, zpauli_phase);
170 519 }
171
172 487 void CliffTableau::apply_V_at_end(unsigned qb) {
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 487 MatrixXb::RowXpr xx = xpauli_x.row(qb);
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 487 MatrixXb::RowXpr xz = xpauli_z.row(qb);
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 487 MatrixXb::RowXpr zx = zpauli_x.row(qb);
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 487 MatrixXb::RowXpr zz = zpauli_z.row(qb);
177 487 row_mult(
178
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 487 xx, xz, xpauli_phase(qb), zx, zz, zpauli_phase(qb), i_, zx, zz,
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 487 zpauli_phase(qb));
180 487 }
181
182 67 void CliffTableau::apply_CX_at_front(unsigned control, unsigned target) {
183
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 328 for (unsigned i = 0; i < size_; i++) {
184 522 xpauli_phase(i) =
185
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 275 xpauli_phase(i) ^ (xpauli_x(i, control) && xpauli_z(i, target) &&
186
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 14 !(xpauli_x(i, target) ^ xpauli_z(i, control)));
187 261 xpauli_x(i, target) = xpauli_x(i, control) ^ xpauli_x(i, target);
188 261 xpauli_z(i, control) = xpauli_z(i, control) ^ xpauli_z(i, target);
189 522 zpauli_phase(i) =
190
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 290 zpauli_phase(i) ^ (zpauli_x(i, control) && zpauli_z(i, target) &&
191
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 29 !(zpauli_x(i, target) ^ zpauli_z(i, control)));
192 261 zpauli_x(i, target) = zpauli_x(i, control) ^ zpauli_x(i, target);
193 261 zpauli_z(i, control) = zpauli_z(i, control) ^ zpauli_z(i, target);
194 }
195 67 }
196
197 282 void CliffTableau::apply_CX_at_end(unsigned control, unsigned target) {
198
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 282 MatrixXb::RowXpr xxc = xpauli_x.row(control);
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 282 MatrixXb::RowXpr xzc = xpauli_z.row(control);
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 282 MatrixXb::RowXpr zxt = zpauli_x.row(target);
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 282 MatrixXb::RowXpr zzt = zpauli_z.row(target);
202 ✗ row_mult(
203
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 282 xxc, xzc, xpauli_phase(control), xpauli_x.row(target),
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 282 xpauli_z.row(target), xpauli_phase(target), 1., xxc, xzc,
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 282 xpauli_phase(control));
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 282 row_mult(
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 282 zpauli_x.row(control), zpauli_z.row(control), zpauli_phase(control), zxt,
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 282 zzt, zpauli_phase(target), 1., zxt, zzt, zpauli_phase(target));
209 282 }
210
211 14 void CliffTableau::apply_gate_at_front(
212 OpType type, const std::vector<unsigned> &qbs) {
213
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 14 switch (type) {
214
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 ✗ case OpType::Z: {
215 ✗ apply_S_at_front(qbs.at(0));
216 ✗ apply_S_at_front(qbs.at(0));
217 ✗ break;
218 }
219
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 ✗ case OpType::X: {
220 ✗ apply_V_at_front(qbs.at(0));
221 ✗ apply_V_at_front(qbs.at(0));
222 ✗ break;
223 }
224
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 ✗ case OpType::Y: {
225 ✗ apply_S_at_front(qbs.at(0));
226 ✗ apply_S_at_front(qbs.at(0));
227 ✗ apply_V_at_front(qbs.at(0));
228 ✗ apply_V_at_front(qbs.at(0));
229 ✗ break;
230 }
231
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 2 case OpType::S: {
232 2 apply_S_at_front(qbs.at(0));
233 2 break;
234 }
235
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 ✗ case OpType::Sdg: {
236 ✗ apply_S_at_front(qbs.at(0));
237 ✗ apply_S_at_front(qbs.at(0));
238 ✗ apply_S_at_front(qbs.at(0));
239 ✗ break;
240 }
241
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 ✗ case OpType::V: {
242 ✗ apply_V_at_front(qbs.at(0));
243 ✗ break;
244 }
245
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 2 case OpType::Vdg: {
246 2 apply_V_at_front(qbs.at(0));
247 2 apply_V_at_front(qbs.at(0));
248 2 apply_V_at_front(qbs.at(0));
249 2 break;
250 }
251
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 1 case OpType::H: {
252 1 apply_S_at_front(qbs.at(0));
253 1 apply_V_at_front(qbs.at(0));
254 1 apply_S_at_front(qbs.at(0));
255 1 break;
256 }
257
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 8 case OpType::CX: {
258 8 apply_CX_at_front(qbs.at(0), qbs.at(1));
259 8 break;
260 }
261
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 ✗ case OpType::CY: {
262 ✗ apply_V_at_front(qbs.at(1));
263 ✗ apply_V_at_front(qbs.at(1));
264 ✗ apply_V_at_front(qbs.at(1));
265 ✗ apply_CX_at_front(qbs.at(0), qbs.at(1));
266 ✗ apply_V_at_front(qbs.at(1));
267 ✗ break;
268 }
269
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 ✗ case OpType::CZ: {
270 ✗ apply_S_at_front(qbs.at(1));
271 ✗ apply_V_at_front(qbs.at(1));
272 ✗ apply_S_at_front(qbs.at(1));
273 ✗ apply_CX_at_front(qbs.at(0), qbs.at(1));
274 ✗ apply_S_at_front(qbs.at(1));
275 ✗ apply_V_at_front(qbs.at(1));
276 ✗ apply_S_at_front(qbs.at(1));
277 ✗ break;
278 }
279
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 ✗ case OpType::SWAP: {
280 ✗ apply_CX_at_front(qbs.at(0), qbs.at(1));
281 ✗ apply_CX_at_front(qbs.at(1), qbs.at(0));
282 ✗ apply_CX_at_front(qbs.at(0), qbs.at(1));
283 ✗ break;
284 }
285
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 ✗ case OpType::BRIDGE: {
286 ✗ apply_CX_at_front(qbs.at(0), qbs.at(2));
287 ✗ break;
288 }
289 ✗ case OpType::noop:
290 case OpType::Phase: {
291 ✗ break;
292 }
293
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 1 default: {
294
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 1 throw BadOpType("Not a Clifford gate", type);
295 }
296 }
297 13 }
298
299 ✗ void CliffTableau::apply_gate_at_front(OpType type, const qubit_vector_t &qbs) {
300 ✗ std::vector<unsigned> uqbs;
301
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 ✗ for (const Qubit &qb : qbs) {
302 ✗ uqbs.push_back(qubits_.left.at(qb));
303 }
304 ✗ apply_gate_at_front(type, uqbs);
305 }
306
307 747 void CliffTableau::apply_gate_at_end(
308 OpType type, const std::vector<unsigned> &qbs) {
309
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 747 switch (type) {
310
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 ✗ case OpType::Z: {
311 ✗ apply_S_at_end(qbs.at(0));
312 ✗ apply_S_at_end(qbs.at(0));
313 ✗ break;
314 }
315
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 17 case OpType::X: {
316 17 apply_V_at_end(qbs.at(0));
317 17 apply_V_at_end(qbs.at(0));
318 17 break;
319 }
320
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 ✗ case OpType::Y: {
321 ✗ apply_S_at_end(qbs.at(0));
322 ✗ apply_S_at_end(qbs.at(0));
323 ✗ apply_V_at_end(qbs.at(0));
324 ✗ apply_V_at_end(qbs.at(0));
325 ✗ break;
326 }
327
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 26 case OpType::S: {
328 26 apply_S_at_end(qbs.at(0));
329 26 break;
330 }
331
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 1 case OpType::Sdg: {
332 1 apply_S_at_end(qbs.at(0));
333 1 apply_S_at_end(qbs.at(0));
334 1 apply_S_at_end(qbs.at(0));
335 1 break;
336 }
337
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 251 case OpType::V: {
338 251 apply_V_at_end(qbs.at(0));
339 251 break;
340 }
341
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 14 case OpType::Vdg: {
342 14 apply_V_at_end(qbs.at(0));
343 14 apply_V_at_end(qbs.at(0));
344 14 apply_V_at_end(qbs.at(0));
345 14 break;
346 }
347
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 154 case OpType::H: {
348 154 apply_S_at_end(qbs.at(0));
349 154 apply_V_at_end(qbs.at(0));
350 154 apply_S_at_end(qbs.at(0));
351 154 break;
352 }
353
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 279 case OpType::CX: {
354 279 apply_CX_at_end(qbs.at(0), qbs.at(1));
355 279 break;
356 }
357
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 ✗ case OpType::CY: {
358 ✗ apply_V_at_end(qbs.at(1));
359 ✗ apply_V_at_end(qbs.at(1));
360 ✗ apply_V_at_end(qbs.at(1));
361 ✗ apply_CX_at_end(qbs.at(0), qbs.at(1));
362 ✗ apply_V_at_end(qbs.at(1));
363 ✗ break;
364 }
365
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 3 case OpType::CZ: {
366 3 apply_S_at_end(qbs.at(1));
367 3 apply_V_at_end(qbs.at(1));
368 3 apply_S_at_end(qbs.at(1));
369 3 apply_CX_at_end(qbs.at(0), qbs.at(1));
370 3 apply_S_at_end(qbs.at(1));
371 3 apply_V_at_end(qbs.at(1));
372 3 apply_S_at_end(qbs.at(1));
373 3 break;
374 }
375
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 ✗ case OpType::SWAP: {
376 ✗ apply_CX_at_end(qbs.at(0), qbs.at(1));
377 ✗ apply_CX_at_end(qbs.at(1), qbs.at(0));
378 ✗ apply_CX_at_end(qbs.at(0), qbs.at(1));
379 ✗ break;
380 }
381
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 ✗ case OpType::BRIDGE: {
382 ✗ apply_CX_at_end(qbs.at(0), qbs.at(2));
383 ✗ break;
384 }
385 ✗ case OpType::noop:
386 case OpType::Phase: {
387 ✗ break;
388 }
389
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 2 default: {
390
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 2 throw BadOpType("Not a Clifford gate", type);
391 }
392 }
393 745 }
394
395 489 void CliffTableau::apply_gate_at_end(OpType type, const qubit_vector_t &qbs) {
396 489 std::vector<unsigned> uqbs;
397
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 1165 for (const Qubit &qb : qbs) {
398
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 676 uqbs.push_back(qubits_.left.at(qb));
399 }
400
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 489 apply_gate_at_end(type, uqbs);
401 489 }
402
403 22 void CliffTableau::apply_pauli_at_front(
404 const QubitPauliTensor &pauli, unsigned half_pis) {
405
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 22 CliffTableau pauli_tab(size_);
406
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 22 pauli_tab.qubits_ = this->qubits_;
407
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 22 pauli_tab.apply_pauli_at_end(pauli, half_pis);
408
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 22 CliffTableau product = CliffTableau::compose(pauli_tab, *this);
409
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 22 this->xpauli_x = product.xpauli_x;
410
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 22 this->xpauli_z = product.xpauli_z;
411
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 22 this->xpauli_phase = product.xpauli_phase;
412
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 22 this->zpauli_x = product.zpauli_x;
413
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 22 this->zpauli_z = product.zpauli_z;
414
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 22 this->zpauli_phase = product.zpauli_phase;
415 22 }
416
417 23 void CliffTableau::apply_pauli_at_end(
418 const QubitPauliTensor &pauli, unsigned half_pis) {
419 23 half_pis = half_pis % 4;
420
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 23 if (half_pis == 0) return; // Identity
421
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 23 if (half_pis == 2) { // Degenerates to product of PI rotations
422
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 ✗ for (const std::pair<const Qubit, Pauli> &term : pauli.string.map) {
423 ✗ switch (term.second) {
424
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 ✗ case Pauli::I: {
425 ✗ break;
426 }
427
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 ✗ case Pauli::X: {
428 ✗ apply_gate_at_end(OpType::X, {term.first});
429 ✗ break;
430 }
431
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 ✗ case Pauli::Y: {
432 ✗ apply_gate_at_end(OpType::Y, {term.first});
433 ✗ break;
434 }
435
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 ✗ case Pauli::Z: {
436 ✗ apply_gate_at_end(OpType::Z, {term.first});
437 ✗ break;
438 }
439 }
440 }
441 ✗ return;
442 }
443
444 // From here, half_pis == 1 or 3
445 // They act the same except for a phase flip on the product term
446
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 46 MatrixXb product_x = MatrixXb::Zero(1, size_);
447
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 46 MatrixXb product_z = MatrixXb::Zero(1, size_);
448
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 23 MatrixXb::RowXpr px = product_x.row(0);
449
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 23 MatrixXb::RowXpr pz = product_z.row(0);
450
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 23 if (pauli.coeff != 1. && pauli.coeff != -1.)
451 ✗ throw std::invalid_argument(
452 "Can only apply Paulis with real unit coefficients to "
453 ✗ "CliffTableaus");
454 23 bool phase = (pauli.coeff == -1.) ^ (half_pis == 3);
455
456 // Collect the product term
457
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 61 for (const std::pair<const Qubit, Pauli> &term : pauli.string.map) {
458
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 38 unsigned uqb = qubits_.left.at(term.first);
459
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 38 switch (term.second) {
460
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 ✗ case Pauli::I: {
461 ✗ break;
462 }
463
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 20 case Pauli::X: {
464
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 40 row_mult(
465
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 20 xpauli_x.row(uqb), xpauli_z.row(uqb), xpauli_phase(uqb), px, pz,
466 phase, 1., px, pz, phase);
467 20 break;
468 }
469
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 5 case Pauli::Y: {
470
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 10 row_mult(
471
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 5 zpauli_x.row(uqb), zpauli_z.row(uqb), zpauli_phase(uqb), px, pz,
472 phase, 1., px, pz, phase);
473
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 5 row_mult(
474
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 5 xpauli_x.row(uqb), xpauli_z.row(uqb), xpauli_phase(uqb), px, pz,
475 phase, i_, px, pz, phase);
476 5 break;
477 }
478
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 13 case Pauli::Z: {
479
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 26 row_mult(
480
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 13 zpauli_x.row(uqb), zpauli_z.row(uqb), zpauli_phase(uqb), px, pz,
481 phase, 1., px, pz, phase);
482 13 break;
483 }
484 }
485 }
486
487 // Apply the product term on the anti-commuting rows
488
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 61 for (const std::pair<const Qubit, Pauli> &term : pauli.string.map) {
489
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 38 unsigned uqb = qubits_.left.at(term.first);
490
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 38 MatrixXb::RowXpr xx = xpauli_x.row(uqb);
491
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 38 MatrixXb::RowXpr xz = xpauli_z.row(uqb);
492
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 38 MatrixXb::RowXpr zx = zpauli_x.row(uqb);
493
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 38 MatrixXb::RowXpr zz = zpauli_z.row(uqb);
494
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 38 switch (term.second) {
495
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 ✗ case Pauli::I: {
496 ✗ break;
497 }
498
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 20 case Pauli::X: {
499 20 row_mult(
500
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 20 px, pz, phase, zx, zz, zpauli_phase(uqb), i_, zx, zz,
501
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 20 zpauli_phase(uqb));
502 20 break;
503 }
504
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 5 case Pauli::Y: {
505 5 row_mult(
506
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 5 px, pz, phase, zx, zz, zpauli_phase(uqb), i_, zx, zz,
507
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 5 zpauli_phase(uqb));
508 5 row_mult(
509
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 5 px, pz, phase, xx, xz, xpauli_phase(uqb), i_, xx, xz,
510
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 5 xpauli_phase(uqb));
511 5 break;
512 }
513
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 13 case Pauli::Z: {
514 13 row_mult(
515
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 13 px, pz, phase, xx, xz, xpauli_phase(uqb), i_, xx, xz,
516
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 13 xpauli_phase(uqb));
517 13 break;
518 }
519 }
520 }
521 }
522
523 ✗ std::ostream &operator<<(std::ostream &os, CliffTableau const &tab) {
524 ✗ MatrixXb full(2 * tab.size_, 2 * tab.size_ + 1);
525 ✗ full << tab.xpauli_x, tab.xpauli_z, tab.xpauli_phase, tab.zpauli_x,
526 ✗ tab.zpauli_z, tab.zpauli_phase;
527 ✗ os << full;
528 ✗ return os;
529 }
530
531 10 bool CliffTableau::operator==(const CliffTableau &other) const {
532 10 bool same = this->size_ == other.size_;
533 10 same &= this->qubits_ == other.qubits_;
534 10 same &= this->xpauli_x == other.xpauli_x;
535 10 same &= this->xpauli_z == other.xpauli_z;
536 10 same &= this->xpauli_phase == other.xpauli_phase;
537 10 same &= this->zpauli_x == other.zpauli_x;
538 10 same &= this->zpauli_z == other.zpauli_z;
539 10 same &= this->zpauli_phase == other.zpauli_phase;
540 10 return same;
541 }
542
543 138 static std::vector<Complex> cphase_from_tableau(
544 const MatrixXb &pauli_x, const MatrixXb &pauli_z,
545 const VectorXb &pauli_phase) {
546 138 std::vector<Complex> cphase;
547 138 const unsigned n = pauli_phase.size();
548
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 804 for (unsigned i = 0; i < n; i++) {
549
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 666 Complex cp = pauli_phase(i) ? -1. : 1.;
550
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 3924 for (unsigned j = 0; j < n; j++) {
551
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 3258 if (pauli_x(i, j) && pauli_z(i, j)) cp *= i_;
552 }
553
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 666 cphase.push_back(cp);
554 }
555 138 return cphase;
556 }
557
558 23 CliffTableau CliffTableau::compose(
559 const CliffTableau &first, const CliffTableau &second) {
560
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 23 if (first.qubits_ != second.qubits_)
561 ✗ throw std::logic_error(
562 ✗ "Cannot compose Clifford Tableaus with different qubit maps");
563 23 const unsigned n = first.size_;
564 std::vector<Complex> first_x_cphase =
565
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 23 cphase_from_tableau(first.xpauli_x, first.xpauli_z, first.xpauli_phase);
566 std::vector<Complex> first_z_cphase =
567
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 23 cphase_from_tableau(first.zpauli_x, first.zpauli_z, first.zpauli_phase);
568 std::vector<Complex> second_x_cphase = cphase_from_tableau(
569
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 23 second.xpauli_x, second.xpauli_z, second.xpauli_phase);
570 std::vector<Complex> second_z_cphase = cphase_from_tableau(
571
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 23 second.zpauli_x, second.zpauli_z, second.zpauli_phase);
572
573
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 23 CliffTableau result(n);
574
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 23 result.xpauli_x.setZero();
575
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 23 result.xpauli_z.setZero();
576
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 23 result.zpauli_x.setZero();
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 23 result.zpauli_z.setZero();
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 23 result.qubits_ = first.qubits_;
579
580 // Target cphases
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 23 std::vector<Complex> xpauli_cphase(n);
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 23 std::vector<Complex> zpauli_cphase(n);
583
584 // Calculate xpauli rows
585
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 134 for (unsigned i = 0; i < n; i++) { // row in second
586 // Sum rows from first according to second.xpauli
587 111 xpauli_cphase[i] = second_x_cphase[i];
588 111 bool phase_flip = false;
589
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 654 for (unsigned j = 0; j < n; j++) { // col in second
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 543 if (second.xpauli_x(i, j)) {
591 // add first.xpauli to xpauli
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 460 for (unsigned k = 0; k < n; k++) {
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 380 phase_flip ^= result.xpauli_z(i, k) && first.xpauli_x(j, k);
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 380 result.xpauli_x(i, k) = result.xpauli_x(i, k) != first.xpauli_x(j, k);
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 380 result.xpauli_z(i, k) = result.xpauli_z(i, k) != first.xpauli_z(j, k);
596 }
597 80 xpauli_cphase[i] *= first_x_cphase[j];
598 }
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 543 if (second.xpauli_z(i, j)) {
600 // add first.zpauli to xpauli
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 654 for (unsigned k = 0; k < n; k++) {
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 543 phase_flip ^= result.xpauli_z(i, k) && first.zpauli_x(j, k);
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 543 result.xpauli_x(i, k) = result.xpauli_x(i, k) != first.zpauli_x(j, k);
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 543 result.xpauli_z(i, k) = result.xpauli_z(i, k) != first.zpauli_z(j, k);
605 }
606 111 xpauli_cphase[i] *= first_z_cphase[j];
607 }
608 }
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 111 if (phase_flip) xpauli_cphase[i] *= -1.;
610 }
611
612 // Calculate zpauli rows
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 134 for (unsigned i = 0; i < n; i++) { // row in second
614 // Sum rows from first according to second.zpauli
615 111 zpauli_cphase[i] = second_z_cphase[i];
616 111 bool phase_flip = false;
617
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 654 for (unsigned j = 0; j < n; j++) { // col in second
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 543 if (second.zpauli_x(i, j)) {
619 // add first.xpauli to zpauli
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 554 for (unsigned k = 0; k < n; k++) {
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 459 phase_flip ^= result.zpauli_z(i, k) && first.xpauli_x(j, k);
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 459 result.zpauli_x(i, k) = result.zpauli_x(i, k) != first.xpauli_x(j, k);
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 459 result.zpauli_z(i, k) = result.zpauli_z(i, k) != first.xpauli_z(j, k);
624 }
625 95 zpauli_cphase[i] *= first_x_cphase[j];
626 }
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 543 if (second.zpauli_z(i, j)) {
628 // add first.zpauli to zpauli
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 518 for (unsigned k = 0; k < n; k++) {
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 429 phase_flip ^= result.zpauli_z(i, k) && first.zpauli_x(j, k);
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 429 result.zpauli_x(i, k) = result.zpauli_x(i, k) != first.zpauli_x(j, k);
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 429 result.zpauli_z(i, k) = result.zpauli_z(i, k) != first.zpauli_z(j, k);
633 }
634 89 zpauli_cphase[i] *= first_z_cphase[j];
635 }
636 }
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 111 if (phase_flip) zpauli_cphase[i] *= -1.;
638 }
639
640 std::vector<Complex> current_x_cphase = cphase_from_tableau(
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 23 result.xpauli_x, result.xpauli_z, result.xpauli_phase);
642 std::vector<Complex> current_z_cphase = cphase_from_tableau(
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 23 result.zpauli_x, result.zpauli_z, result.zpauli_phase);
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 134 for (unsigned i = 0; i < n; i++) {
646 TKET_ASSERT((current_x_cphase[i] * xpauli_cphase[i]).imag() == 0);
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 111 result.xpauli_phase(i) = (current_x_cphase[i] == -xpauli_cphase[i]);
648 TKET_ASSERT((current_z_cphase[i] * zpauli_cphase[i]).imag() == 0);
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 111 result.zpauli_phase(i) = (current_z_cphase[i] == -zpauli_cphase[i]);
650 }
651
652 46 return result;
653 23 }
654
655 } // namespace tket
656