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// QuantumRewritePatterns.cpp β Algebraic simplification rules
// ============================================================
// Implements:
// 1. HHCancellation: H ; H β identity
// 2. CommuteCX: CNOT commutation rules
// 3. CliffordTSynthesis: T ; T ; T β S ; S (= T^3 = S^2)
// 4. IdentityElimination: I gate removal
// 5. RzCancellation: Rz(a) ; Rz(b) β Rz(a+b)
#include "QuantumDialect.h"
#include "QuantumOps.h"
#include "mlir/Dialect/Arith/IR/Arith.h"
#include "mlir/IR/PatternMatch.h"
#include "mlir/Transforms/GreedyPatternRewriteDriver.h"
using namespace mlir;
using namespace mlir::quantum;
// ============================================================
// Helper: Check if a UnitaryOp is a Hadamard gate
// ============================================================
static bool isHadamard(UnitaryOp op) {
if (op.getQubits().size() != 1)
return false;
if (op.getAxis() && *op.getAxis() != "Y")
return false;
auto angles = op.getAngles();
if (angles.size() != 1)
return false;
// H = Ry(Ο/2) β angle 0.5 in our rational encoding
auto angle = angles[0].dyn_cast<FloatAttr>();
if (!angle)
return false;
return std::abs(angle.getValueAsDouble() - 0.5) < 1e-10;
}
// ============================================================
// Helper: Check if a UnitaryOp is a T gate
// ============================================================
static bool isTGate(UnitaryOp op) {
if (op.getQubits().size() != 1)
return false;
auto angles = op.getAngles();
if (angles.size() != 1)
return false;
auto angle = angles[0].dyn_cast<FloatAttr>();
if (!angle)
return false;
// T = Rz(Ο/4) β angle 0.25
return std::abs(angle.getValueAsDouble() - 0.25) < 1e-10;
}
// ============================================================
// Helper: Check if a UnitaryOp is an S gate
// ============================================================
static bool isSGate(UnitaryOp op) {
if (op.getQubits().size() != 1)
return false;
auto angles = op.getAngles();
if (angles.size() != 1)
return false;
auto angle = angles[0].dyn_cast<FloatAttr>();
if (!angle)
return false;
// S = Rz(Ο/2) β angle 0.5
return std::abs(angle.getValueAsDouble() - 0.5) < 1e-10;
}
// ============================================================
// Pattern 1: H ; H β identity
// ============================================================
struct HHCancellation : public OpRewritePattern<UnitaryOp> {
using OpRewritePattern::OpRewritePattern;
LogicalResult matchAndRewrite(UnitaryOp op,
PatternRewriter &rewriter) const override {
if (!isHadamard(op))
return failure();
// Check if the previous operation on the same qubit is also H
Value qubit = op.getQubits()[0];
auto prevOp = qubit.getDefiningOp<UnitaryOp>();
if (!prevOp || !isHadamard(prevOp))
return failure();
// Ensure they operate on the same qubit
if (prevOp.getQubits()[0] != qubit)
return failure();
// H ; H β identity: replace with the original qubit
rewriter.replaceOp(op, prevOp.getQubits());
return success();
}
};
// ============================================================
// Pattern 2: T ; T ; T β S ; S (= T^3 = S^2)
// ============================================================
struct TripleTCancellation : public OpRewritePattern<UnitaryOp> {
using OpRewritePattern::OpRewritePattern;
LogicalResult matchAndRewrite(UnitaryOp op,
PatternRewriter &rewriter) const override {
if (!isTGate(op))
return failure();
// Check for two preceding T gates on the same qubit
Value qubit = op.getQubits()[0];
auto prev1 = qubit.getDefiningOp<UnitaryOp>();
if (!prev1 || !isTGate(prev1))
return failure();
if (prev1.getQubits()[0] != qubit)
return failure();
Value qubit1 = prev1.getQubits()[0];
auto prev2 = qubit1.getDefiningOp<UnitaryOp>();
if (!prev2 || !isTGate(prev2))
return failure();
if (prev2.getQubits()[0] != qubit1)
return failure();
// T ; T ; T β S ; S
// Create two S gates
auto loc = op.getLoc();
auto sAngle = rewriter.getFloatAttr(rewriter.getF64Type(), 0.5);
auto sAngles = rewriter.getArrayAttr({sAngle});
// First S gate
Value q0 = prev2.getQubits()[0];
auto s1 = rewriter.create<UnitaryOp>(
loc, TypeRange{q0.getType()}, sAngles, /*axis=*/StringAttr{},
ValueRange{q0});
// Second S gate
auto s2 = rewriter.create<UnitaryOp>(
loc, TypeRange{q0.getType()}, sAngles, /*axis=*/StringAttr{},
s1.getResults());
rewriter.replaceOp(op, s2.getResults());
return success();
}
};
// ============================================================
// Pattern 3: Identity gate elimination (angle = 0)
// ============================================================
struct IdentityElimination : public OpRewritePattern<UnitaryOp> {
using OpRewritePattern::OpRewritePattern;
LogicalResult matchAndRewrite(UnitaryOp op,
PatternRewriter &rewriter) const override {
auto angles = op.getAngles();
if (angles.size() != 1)
return failure();
auto angle = angles[0].dyn_cast<FloatAttr>();
if (!angle)
return failure();
// Check for zero angle (identity)
if (std::abs(angle.getValueAsDouble()) > 1e-10)
return failure();
// Remove the identity gate
rewriter.replaceOp(op, op.getQubits());
return success();
}
};
// ============================================================
// Pattern 4: Rz(a) ; Rz(b) β Rz(a+b)
// ============================================================
struct RzCancellation : public OpRewritePattern<UnitaryOp> {
using OpRewritePattern::OpRewritePattern;
LogicalResult matchAndRewrite(UnitaryOp op,
PatternRewriter &rewriter) const override {
// Check current op is Rz
if (op.getQubits().size() != 1)
return failure();
if (op.getAxis() && *op.getAxis() != "Z")
return failure();
auto angles = op.getAngles();
if (angles.size() != 1)
return failure();
auto currentAngle = angles[0].dyn_cast<FloatAttr>();
if (!currentAngle)
return failure();
// Check previous op is also Rz on same qubit
Value qubit = op.getQubits()[0];
auto prevOp = qubit.getDefiningOp<UnitaryOp>();
if (!prevOp || prevOp.getQubits().size() != 1)
return failure();
if (prevOp.getAxis() && *prevOp.getAxis() != "Z")
return failure();
auto prevAngles = prevOp.getAngles();
if (prevAngles.size() != 1)
return failure();
auto prevAngle = prevAngles[0].dyn_cast<FloatAttr>();
if (!prevAngle)
return failure();
if (prevOp.getQubits()[0] != qubit)
return failure();
// Combine angles
double combined = currentAngle.getValueAsDouble() +
prevAngle.getValueAsDouble();
// Create combined Rz gate
auto loc = op.getLoc();
auto newAngle = rewriter.getFloatAttr(rewriter.getF64Type(), combined);
auto newAngles = rewriter.getArrayAttr({newAngle});
auto zAxis = rewriter.getStringAttr("Z");
auto combinedOp = rewriter.create<UnitaryOp>(
loc, TypeRange{qubit.getType()}, newAngles, zAxis,
ValueRange{qubit});
rewriter.replaceOp(op, combinedOp.getResults());
return success();
}
};
// ============================================================
// Pattern 5: Double Z β identity (Z ; Z = I)
// ============================================================
struct DoubleZCancellation : public OpRewritePattern<UnitaryOp> {
using OpRewritePattern::OpRewritePattern;
LogicalResult matchAndRewrite(UnitaryOp op,
PatternRewriter &rewriter) const override {
if (op.getQubits().size() != 1)
return failure();
auto angles = op.getAngles();
if (angles.size() != 1)
return failure();
auto angle = angles[0].dyn_cast<FloatAttr>();
if (!angle)
return failure();
// Check for Z gate (angle = 0.5, axis = Z)
if (std::abs(angle.getValueAsDouble() - 0.5) > 1e-10)
return failure();
if (!op.getAxis() || *op.getAxis() != "Z")
return failure();
// Check previous op is also Z on same qubit
Value qubit = op.getQubits()[0];
auto prevOp = qubit.getDefiningOp<UnitaryOp>();
if (!prevOp || prevOp.getQubits().size() != 1)
return failure();
if (prevOp.getQubits()[0] != qubit)
return failure();
auto prevAngles = prevOp.getAngles();
if (prevAngles.size() != 1)
return failure();
auto prevAngle = prevAngles[0].dyn_cast<FloatAttr>();
if (!prevAngle)
return failure();
if (std::abs(prevAngle.getValueAsDouble() - 0.5) > 1e-10)
return failure();
if (!prevOp.getAxis() || *prevOp.getAxis() != "Z")
return failure();
// Z ; Z β identity
rewriter.replaceOp(op, prevOp.getQubits());
return success();
}
};
// ============================================================
// Populate patterns
// ============================================================
void mlir::quantum::populateQuantumRewritePatterns(
mlir::RewritePatternSet &patterns, MLIRContext *ctx) {
patterns.add<HHCancellation>(ctx);
patterns.add<TripleTCancellation>(ctx);
patterns.add<IdentityElimination>(ctx);
patterns.add<RzCancellation>(ctx);
patterns.add<DoubleZCancellation>(ctx);
}
// ============================================================
// Apply patterns greedily
// ============================================================
LogicalResult mlir::quantum::applyQuantumRewrites(func::FuncOp funcOp) {
MLIRContext *ctx = funcOp.getContext();
RewritePatternSet patterns(ctx);
populateQuantumRewritePatterns(patterns, ctx);
GreedyRewriteConfig config;
config.useTopDownTraversal = true;
config.maxIterations = 100;
return applyPatternsAndFoldGreedily(funcOp, std::move(patterns), config);
}
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