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qunitary.cpp
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qunitary.cpp
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#include "qutils.h"
#include "qgate.h"
#include "qunitary.h"
uint8_t compileUnitaryOp(const string& inFilename, QNet_t& Net, ofstream& outFile) {
if (Verbose) cout << "In function " << __FUNCTION__ << endl;
cout << "File: " << inFilename << "\n";
cx_mat U;
U.load(inFilename, raw_ascii);
if ((U.n_rows == U.n_cols) && (U.n_rows == 0)) { cerr << "FORMAT ERROR: matrix could not be read\n"; exit(1); }
if (Verbose) U.print("U:");
const uint64_t N = U.n_rows;
const uint64_t lgN = round(log2(N));
uint64_t QubitSize = lgN;
if (Net.useMap && (Net.physMap.size() < QubitSize)) { cerr << "Provided logical to physical qubit mapping is incompatible with the unitary operator\n"; exit(1); }
if (Net.useMap && (Net.physMap.size() > QubitSize)) QubitSize = Net.physMap.size();
if (Net.useTop && (Net.topology.n_rows < QubitSize)) { cerr << "Provided topology graph is incompatible with the unitary operator\n"; exit(1); }
if (Net.useTop && (Net.topology.n_rows > QubitSize)) QubitSize = Net.topology.n_rows;
if (doStatePrep) {
if (1 != U.n_cols) { cerr << "Initial-state s should be a column-vector\n"; exit(1); }
double E = l2norm(U);
if (abs(E - 1.0) > QC_TOL) { cerr << "Initial-state s should have unit energy. Got energy = " << E << "\n"; exit(1); }
}
else {
if (N != U.n_cols) { cerr << "Matrix U should be square\n"; exit(1); }
if (l2norm(U*U.t() - eye<cx_mat>(arma::size(U))) > QC_TOL) { cerr << "Matrix U should be unitary\n"; exit(1); }
}
vector<uint64_t> gamma(N);
getRowEncoding(gamma);
vector<cx_mat> VG;
vector<vector<uint64_t>> VGcontrols;
GivensDecompose(U, gamma, VG, VGcontrols); //Givens decompose inverse of U
outFile << "\n//Quantum netlist implementing unitary operator '"
<< inFilename << "' using simple gates:\n";
Net.Gates = vector<vector<QG_t>>(QubitSize); //One vector for each qubit timeline
if (Verbose) cout << "\n________________________________\n";
//\Pi_i G_i' == U; so apply the G_i' in reverse order to affect U (post-fix)
for (int64_t i=VG.size()-1; i>=0; i--) lowerCnG(lgN, VG[i].t(), VGcontrols[i], Net, !useNaturalPivot);
if (Verbose) cout << "________________________________\n" << endl;
return lgN;
}
void getRowEncoding(vector<uint64_t>& gamma) {
if (Verbose) cout << "In function " << __FUNCTION__ << endl;
//Form a standard Gray code (not unique) or use Natural encoding
for(uint64_t i=0; i<gamma.size(); i++) gamma[i] = (useNaturalPivot ? i : (i ^ (i/2)));
#ifdef VERY_VERBOSE
if (Verbose) {
cout << "Gamma: [ ";
for (auto i = gamma.begin(); i != gamma.end(); i++) cout << *i << ' ';
cout << "]\n" << endl;
}
#endif
}
inline void adjustGivensRows(cx_mat& U, const cx_mat& G, uint64_t gJ, uint64_t gJ1) {
if (Verbose) cout << "In function " << __FUNCTION__ << endl;
//Adjust the rows gJ, gJ1 of U
//k,c: u'_k,i * u_k,c + u'_j,i * u_j,c / Norm (== 1 when c==i)
//j,c: -u_j,i * u_k,c + u_k,i * u_j,c / Norm (== 0 when c==i)
for (uint64_t c=0; c<U.n_cols; c++) {
complex<double> tmp = G(0, 0)*U(gJ1, c) + G(0, 1)*U(gJ, c);
U(gJ, c) = G(1, 0)*U(gJ1, c) + G(1, 1)*U(gJ, c);
U(gJ1, c) = tmp;
}
}
void GivensDecompose(const cx_mat& UU, const vector<uint64_t>& gamma, vector<cx_mat>& VG, vector<vector<uint64_t>>& VGcontrols) {
if (Verbose) cout << "In function " << __FUNCTION__ << endl;
// 2 use cases:
//
// (A) Unitary Operator:
// [(\Pi_{i=1..m} G_i).U = I] => [(\Pi_{i=m..1} G_i') = U]
//
// (B) State Preparation:
// [(\Pi_{i=1..m} G_i).s = e0] => [(\Pi_{i=m..1} G_i').e0 = s]
//
//So, in either case, we need the quantum-gate implementation for the product: (\Pi_{i=m..1} G_i')
cx_mat U = UU; //Work on a copy. NOTE: Matrix U gets clobbered to I in the end
const uint64_t N = U.n_rows;
for (uint64_t i=0; i<(doStatePrep ? 1 : (N-1)); i++) { //Column loop
uint64_t gI = gamma[i];
for (uint64_t j=(N-1); j>i; j--) { //Row loop
uint64_t gJ = gamma[j], gJ1 = gamma[j-1];
cx_mat G(2, 2);
G << conj(U(gJ1, gI)) << conj(U(gJ, gI)) << endr << -U(gJ, gI) << U(gJ1, gI);
complex<double> dG = det2x2(G);
if (abs(dG) < QC_TOL) continue;
G /= sqrt(dG); //So now G is unitary
if (l2norm(G - I2) > QC_TOL) { //Null (gJ, gI) using U(gJ1, gI)
if (Verbose)
cout << "\n________________________________\n"
<< "Objective: Null U(" << gJ << ", " << gI << ") using U(" << gJ1 << ", " << gI << ")\n";
VG.push_back(G); //Multiply elements in V in reverse to get back U
vector<uint64_t> control(3);
control[0] = gJ; control[1] = gJ1; control[2] = gI;
VGcontrols.push_back(control);
if (Verbose) {
cout << "Givens " << gI << "_G_(" << gJ << "," << gJ1 << ")" << endl;
cout << G << endl;
}
//Adjust the rows gJ, gJ1 of U
adjustGivensRows(U, G, gJ, gJ1);
if (Verbose) {
U.print("U:");
cout << "________________________________\n";
}
}
if (abs(U(gJ, gI)) > QC_TOL) { cerr << "(" << gJ << "," << gI << ") : " << U(gJ, gI) << ": Matrix was not Givens deomposed correctly\n"; U.print("U:"); exit(1); }
}
if (abs(U(gI, gI)-1.0) > QC_TOL) { cerr << "(" << gI << "," << gI << ") : " << U(gI, gI) << ": Matrix was not Givens deomposed correctly\n"; exit(1); }
}
complex<double> dU = (doStatePrep ? U(0, 0) : diagProd(U)); //abs(dU) == 1, guaranteed as either ||s||_2 = 1 or |det(U)| = 1
if (abs(dU-1.0) > QC_TOL) {
//Only the gamma[(N-1)]^th diagonal element can be non-unity for unitary operators
//Similarly, only the gamma[0]^th element can be non-unity for state-preparation
uint64_t gI = gamma[doStatePrep ? 0 : (N-1)], gJ = gamma[doStatePrep ? 1 : 0], gJ1 = gamma[doStatePrep ? 0 : (N-1)];
//We use the (gJ, gI)^th entry (ie., by extension, the entire gJ^th row) to make (gJ1, gI)^th entry 1
cx_mat G(2, 2);
G << 1.0/dU << 0.0 << endr << 0.0 << 1.0;
VG.push_back(G); //Multiply elements in V in reverse to get back U
vector<uint64_t> control(3);
control[0] = gJ; control[1] = gJ1; control[2] = gI;
VGcontrols.push_back(control);
adjustGivensRows(U, G, gJ, gJ1);
bool done = (doStatePrep ? true : isDiagIdentity(U));
if (!done) { //Elaborate check that the Givens decomposition was correct (Skip for state-preparations)
cx_mat P=eye<cx_mat>(arma::size(UU));
for (int64_t i=VG.size()-1; i>=0; i--) {
cx_mat Qi=eye<cx_mat>(arma::size(UU));
uint64_t J1=VGcontrols[i][1], J=VGcontrols[i][0];
Qi(J1, J1) = VG[i](0, 0);
Qi(J1, J) = VG[i](0, 1);
Qi(J, J1) = VG[i](1, 0);
Qi(J, J) = VG[i](1, 1);
P *= Qi;
}
P *= UU;
if (l2norm(P - eye<cx_mat>(arma::size(P))) > QC_TOL) {
cerr << "Givens decomposition was not exact!\n\n";
if (Verbose) cerr << "[(\\Pi_i G_i) * Op]:\n" << P << "\n\n";
exit(1);
}
}
}
}
void lowerCnG(uint64_t S, const cx_mat& G, const vector<uint64_t>& control, QNet_t& Net, bool useGrayCode) {
if (Verbose) cout << "In function " << __FUNCTION__ << endl;
if (Verbose) {
if (control.size() == 3) //This is for Givens lowering
cout << "Givens " << control[2] << "_G_(" << control[0] << "," << control[1] << "):\n";
else //This is for Swap lowering (Natural encoding only)
cout << "Swap S_(" << control[0] << "," << control[1] << "):\n";
cout << G << endl;
}
uint64_t first=control[0], last=control[1], all=((1<<S)-1);
if (useGrayCode) {
if (control.size() != 3) { cerr << "Swaps cannot be lowered with Gray coded qubit sequence\n"; exit(1); }
if (Verbose) cout << "Using Gray encoded qubit lines\n";
//Form single qubit NOT gate network to take the mask to all 1 for the two rows on which G should act
const uint64_t toggle = (first ^ last); //Bits which need to be '0' to act as control
const uint8_t target = round(log2(toggle));
const uint64_t mask = (~first) & all; //Bits which need to be '0' to act as control
const uint64_t cMask = (~toggle) & all;
#ifdef VERY_VERBOSE
if (Verbose) cout << "Mask: " << mask << ", Toggle: " << toggle << endl;
#endif
//Prep mask bits to be all '1'
if (cMask) for (uint8_t b=0; b<S; b++)
if (mask & (1<<b)) addGate(Net, X, {b}); //If this bit needs to be '0' for the control-G to act
//Convert the C^(S-1)G gate to a network of simpler single qubit and CNOT gates in a recursive manner
lowerCnW(S, G, target, cMask, Net); //1-qubit gate, control-qubits, target-qubit
//Reverse-prep mask bits to be what they were originally
if (cMask) for (uint8_t b=0; b<S; b++)
if (mask & (1<<b)) addGate(Net, X, {b}); //If this bit needs to be '0' for the control-G to act
}
else {
if (Verbose) cout << "Using Naturally encoded qubit lines\n";
//NOTE: Does not matter that we always take c1 as first. If c2 were to be 1st, #bit-flips remain same
//Setup so that last is all-1's
const uint64_t gmask = (~last) & all; //Bits to be negated to bring last-index to all-one's
last = all;
first ^= gmask; //After transforming last <= all; this is new first
#ifdef VERY_VERBOSE
if (Verbose) cout << "First: " << first << ", Last: " << last << ", Gmask: " << gmask << "\n";
#endif
for (uint8_t b=0; b<S; b++)
if (gmask & (1<<b)) {
addGate(Net, X, {b}); //If this bit needs to be '0' for the control-G to act
if (Verbose) cout << "X(" << int(b) << ")\n";
}
//Walk from first to last-but-one with a Gray code, flipping 1 bit at a time
uint64_t current=first, tmask;
int8_t target;
for (target=0; target<S; target++) {
tmask = (1<<target);
if (!(first & tmask)) {
uint64_t next = current^tmask;
if (next == last) break; //When this loop breaks, target := last-bit-to-flip-towards-all-1's
current = next;
uint64_t mask = ((~current)&last) ^ tmask;
for (uint8_t b=0; b<S; b++)
if (mask & (1<<b)) addGate(Net, X, {b}); //If this bit needs to be '0' for the control-G to act
//Convert the C^(S-1)X gate to a network of simpler single qubit and CNOT gates in a recursive manner
lowerCnW(S, X, target, last^tmask, Net); //1-qubit gate, control-qubits, target-qubit
for (uint8_t b=0; b<S; b++)
if (mask & (1<<b)) addGate(Net, X, {b}); //If this bit needs to be '0' for the control-G to act
}
}
//Convert the C^(S-1)X gate to a network of simpler single qubit and CNOT gates in a recursive manner
lowerCnW(S, G, target, all^tmask, Net); //1-qubit gate, control-qubits, target-qubit
//Walk back from last-but-one to first with same Gray code, flipping 1 bit at a time
for (target=target-1; target>=0; target--) {
tmask = (1<<target);
if (!(first & tmask)) {
current ^= tmask;
uint64_t mask = ((~current)&last) ^ tmask;
for (uint8_t b=0; b<S; b++)
if (mask & (1<<b)) addGate(Net, X, {b}); //If this bit needs to be '0' for the control-G to act
//Convert the C^(S-1)X gate to a network of simpler single qubit and CNOT gates in a recursive manner
lowerCnW(S, X, target, last^tmask, Net); //1-qubit gate, control-qubits, target-qubit
for (uint8_t b=0; b<S; b++)
if (mask & (1<<b)) addGate(Net, X, {b}); //If this bit needs to be '0' for the control-G to act
if (current == first) break;
}
}
//Unwind the gmask, by reversing the NOTs
for (uint8_t b=0; b<S; b++)
if (gmask & (1<<b)) addGate(Net, X, {b}); //If this bit needs to be '0' for the control-G to act
}
}