Make stim.Tableau.from_stabilizers faster (#713)

- Store the growing reduction as a circuit instead of as a tableau
- Measured 20x faster (140ms -> 6ms) on a 144 qubit case
- Measured 100x faster (15s -> 0.13s) on a 432 qubit case

Author: Strilanc

src/stim/stabilizers/conversions.h

@@ -83,11 +83,13 @@ Circuit stabilizer_state_vector_to_circuit(
 ///     ignore_noise: If the circuit contains noise channels, ignore them instead of raising an exception.
 ///     ignore_measurement: If the circuit contains measurements, ignore them instead of raising an exception.
 ///     ignore_reset: If the circuit contains resets, ignore them instead of raising an exception.
+///     inverse: The last step of the implementation is to invert the tableau. Setting this argument
+///         to true will skip this inversion, saving time but returning the inverse tableau.
 ///
 /// Returns:
 ///     A tableau encoding the given circuit's Clifford operation.
 template <size_t W>
-Tableau<W> circuit_to_tableau(const Circuit &circuit, bool ignore_noise, bool ignore_measurement, bool ignore_reset);
+Tableau<W> circuit_to_tableau(const Circuit &circuit, bool ignore_noise, bool ignore_measurement, bool ignore_reset, bool inverse = false);
 
 /// Simulates the given circuit and outputs a state vector.
 ///

src/stim/stabilizers/conversions.inl

@@ -149,7 +149,7 @@ std::vector<std::vector<std::complex<float>>> tableau_to_unitary(const Tableau<W
 }
 
 template <size_t W>
-Tableau<W> circuit_to_tableau(const Circuit &circuit, bool ignore_noise, bool ignore_measurement, bool ignore_reset) {
+Tableau<W> circuit_to_tableau(const Circuit &circuit, bool ignore_noise, bool ignore_measurement, bool ignore_reset, bool inverse) {
     Tableau<W> result(circuit.count_qubits());
     TableauSimulator<W> sim(std::mt19937_64(0), circuit.count_qubits());
 
@@ -185,7 +185,10 @@ Tableau<W> circuit_to_tableau(const Circuit &circuit, bool ignore_noise, bool ig
         }
     });
 
-    return sim.inv_state.inverse();
+    if (!inverse) {
+        return sim.inv_state.inverse();
+    }
+    return sim.inv_state;
 }
 
 template <size_t W>
@@ -556,7 +559,7 @@ Tableau<W> stabilizers_to_tableau(
     }
 
     for (size_t k1 = 0; k1 < stabilizers.size(); k1++) {
-        for (size_t k2 = 0; k2 < stabilizers.size(); k2++) {
+        for (size_t k2 = k1 + 1; k2 < stabilizers.size(); k2++) {
             if (!stabilizers[k1].ref().commutes(stabilizers[k2])) {
                 std::stringstream ss;
                 ss << "Some of the given stabilizers anticommute.\n";
@@ -568,44 +571,39 @@ Tableau<W> stabilizers_to_tableau(
             }
         }
     }
-    Tableau<W> inverted(num_qubits);
-
-    PauliString<W> cur(num_qubits);
-    std::vector<size_t> targets;
-    while (targets.size() < num_qubits) {
-        targets.push_back(targets.size());
-    }
-    auto overwrite_cur_apply_recorded = [&](const PauliString<W> &e) {
-        PauliStringRef<W> cur_ref = cur.ref();
-        cur.xs.clear();
-        cur.zs.clear();
-        cur.xs.word_range_ref(0, e.xs.num_simd_words) = e.xs;
-        cur.zs.word_range_ref(0, e.xs.num_simd_words) = e.zs;
-        cur.sign = e.sign;
-        inverted.apply_within(cur_ref, targets);
-    };
+    Circuit elimination_instructions;
+    PauliString<W> buf(num_qubits);
 
     size_t used = 0;
     for (const auto &e : stabilizers) {
-        overwrite_cur_apply_recorded(e);
+        if (e.num_qubits == num_qubits) {
+            buf = e;
+        } else {
+            buf.xs.clear();
+            buf.zs.clear();
+            memcpy(buf.xs.u8, e.xs.u8, e.xs.num_u8_padded());
+            memcpy(buf.zs.u8, e.zs.u8, e.zs.num_u8_padded());
+            buf.sign = e.sign;
+        }
+        buf.ref().do_circuit(elimination_instructions);
 
         // Find a non-identity term in the Pauli string past the region used by other stabilizers.
         size_t pivot;
         for (pivot = used; pivot < num_qubits; pivot++) {
-            if (cur.xs[pivot] || cur.zs[pivot]) {
+            if (buf.xs[pivot] || buf.zs[pivot]) {
                 break;
             }
         }
 
         // Check for incompatible / redundant stabilizers.
         if (pivot == num_qubits) {
-            if (cur.xs.not_zero()) {
+            if (buf.xs.not_zero()) {
                 throw std::invalid_argument("Some of the given stabilizers anticommute.");
             }
-            if (cur.sign) {
+            if (buf.sign) {
                 throw std::invalid_argument("Some of the given stabilizers contradict each other.");
             }
-            if (!allow_redundant && cur.zs.not_zero()) {
+            if (!allow_redundant && buf.zs.not_zero()) {
                 throw std::invalid_argument(
                     "Didn't specify allow_redundant=True but one of the given stabilizers is a product of the others. "
                     "To allow redundant stabilizers, pass the argument allow_redundant=True.");
@@ -614,32 +612,36 @@ Tableau<W> stabilizers_to_tableau(
         }
 
         // Change pivot basis to the Z axis.
-        if (cur.xs[pivot]) {
-            std::string name = cur.zs[pivot] ? "H_YZ" : "H_XZ";
-            inverted.inplace_scatter_append(GATE_DATA.at(name).tableau<W>(), {pivot});
+        if (buf.xs[pivot]) {
+            GateType g = buf.zs[pivot] ? GateType::H_YZ : GateType::H;
+            GateTarget t = GateTarget::qubit(pivot);
+            CircuitInstruction instruction{g, {}, &t};
+            elimination_instructions.safe_append(instruction);
+            buf.ref().do_instruction(instruction);
         }
         // Cancel other terms in Pauli string.
         for (size_t q = 0; q < num_qubits; q++) {
-            int p = cur.xs[q] + cur.zs[q] * 2;
+            int p = buf.xs[q] + buf.zs[q] * 2;
             if (p && q != pivot) {
-                inverted.inplace_scatter_append(
-                    GATE_DATA.at(p == 1   ? "XCX"
-                                 : p == 2 ? "XCZ"
-                                          : "XCY")
-                        .tableau<W>(),
-                    {pivot, q});
+                std::array<GateTarget, 2> targets{GateTarget::qubit(pivot), GateTarget::qubit(q)};
+                CircuitInstruction instruction{p == 1 ? GateType::XCX : p == 2 ? GateType::XCZ : GateType::XCY, {}, targets};
+                elimination_instructions.safe_append(instruction);
+                buf.ref().do_instruction(instruction);
             }
         }
 
         // Move pivot to diagonal.
         if (pivot != used) {
-            inverted.inplace_scatter_append(GATE_DATA.at("SWAP").tableau<W>(), {pivot, used});
+            std::array<GateTarget, 2> targets{GateTarget::qubit(pivot), GateTarget::qubit(used)};
+            CircuitInstruction instruction{GateType::SWAP, {}, targets};
+            elimination_instructions.safe_append(instruction);
         }
 
         // Fix sign.
-        overwrite_cur_apply_recorded(e);
-        if (cur.sign) {
-            inverted.inplace_scatter_append(GATE_DATA.at("X").tableau<W>(), {used});
+        if (buf.sign) {
+            GateTarget t = GateTarget::qubit(used);
+            CircuitInstruction instruction{GateType::X, {}, &t};
+            elimination_instructions.safe_append(instruction);
         }
 
         used++;
@@ -653,10 +655,17 @@ Tableau<W> stabilizers_to_tableau(
         }
     }
 
+    if (num_qubits > 0) {
+        // Force size of resulting tableau to be correct.
+        GateTarget t = GateTarget::qubit(num_qubits - 1);
+        elimination_instructions.safe_append(CircuitInstruction{GateType::X, {}, &t});
+        elimination_instructions.safe_append(CircuitInstruction{GateType::X, {}, &t});
+    }
+
     if (invert) {
-        return inverted;
+        return circuit_to_tableau<W>(elimination_instructions.inverse(), false, false, false, true);
     }
-    return inverted.inverse();
+    return circuit_to_tableau<W>(elimination_instructions, false, false, false, true);
 }
 
 }  // namespace stim

src/stim/stabilizers/conversions.perf.cc

@@ -67,3 +67,51 @@ BENCHMARK(independent_to_disjoint_xyz_errors) {
         std::cout << "data dependence";
     }
 }
+
+BENCHMARK(stabilizers_to_tableau) {
+    std::vector<std::complex<float>> offsets{
+        {1, 0},
+        {-1, 0},
+        {0, 1},
+        {0, -1},
+        {3, 6},
+        {-6, 3},
+    };
+    size_t w = 24;
+    size_t h = 12;
+
+    auto normalize = [&](std::complex<float> c) -> std::complex<float> {
+        return {fmodf(c.real() + w*10, w), fmodf(c.imag() + h*10, h)};
+    };
+    auto q2i = [&](std::complex<float> c) -> size_t {
+        c = normalize(c);
+        return (int)c.real() / 2 + c.imag() * (w / 2);
+    };
+
+    std::vector<stim::PauliString<64>> stabilizers;
+    for (size_t x = 0; x < w; x++) {
+        for (size_t y = x % 2; y < h; y += 2) {
+            std::complex<float> s{x % 2 ? -1.0f : +1.0f, 0.0f};
+            std::complex<float> c{(float)x, (float)y};
+            stim::PauliString<64> ps(w * h / 2);
+            for (const auto &offset : offsets) {
+                size_t i = q2i(c + offset * s);
+                if (x % 2 == 0) {
+                    ps.xs[i] = 1;
+                } else {
+                    ps.zs[i] = 1;
+                }
+            }
+            stabilizers.push_back(ps);
+        }
+    }
+
+    size_t dep = 0;
+    benchmark_go([&]() {
+        Tableau<64> t = stabilizers_to_tableau(stabilizers, true, true, false);
+        dep += t.xs[0].zs[0];
+    }).goal_millis(5);
+    if (dep == 99999999) {
+        std::cout << "data dependence";
+    }
+}