cqlib-core 0.1.0-beta.5

// This code is part of Cqlib.
//
// (C) Copyright China Telecom Quantum Group 2026
//
// This code is licensed under the Apache License, Version 2.0. You may
// obtain a copy of this license in the LICENSE.txt file in the root directory
// of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
//
// Any modifications or derivative works of this code must retain this
// copyright notice, and modified files need to carry a notice indicating
// that they have been altered from the originals.

rule decompose_mci0_to_i {
    match { MCI[0] 0 }
    rewrite { I 0 }
}

rule decompose_mch0_to_h {
    match { MCH[0] 0 }
    rewrite { H 0 }
}

rule decompose_mch0_to_rx_ry {
    match { MCH[0] 0 }
    rewrite { RY(π/2) 0, RX(π) 0, GPhase(π/2) }
}

rule decompose_mcrx0_to_rx {
    match { MCRX[0](theta) 0 }
    rewrite { RX(theta) 0 }
}

rule decompose_mcrxx0_to_rxx {
    match { MCRXX[0](theta) 0 1 }
    rewrite { RXX(theta) 0 1 }
}

rule decompose_mcrxx0_to_rx_ry_rzz {
    match { MCRXX[0](theta) 0 1 }
    rewrite { RY(-π/2) 0, RY(-π/2) 1, RZZ(theta) 0 1, RY(π/2) 1, RY(π/2) 0 }
}

rule decompose_mcrxy0_to_rxy {
    match { MCRXY[0](theta, phi) 0 }
    rewrite { RXY(theta, phi) 0 }
}

rule decompose_mcrxy0_to_rx_ry {
    match { MCRXY[0](theta, phi) 0 }
    rewrite { RX(-π/2) 0, RY(-phi) 0, RX(theta) 0, RY(phi) 0, RX(π/2) 0 }
}

rule decompose_mcry0_to_ry {
    match { MCRY[0](theta) 0 }
    rewrite { RY(theta) 0 }
}

rule decompose_mcryy0_to_ryy {
    match { MCRYY[0](theta) 0 1 }
    rewrite { RYY(theta) 0 1 }
}

rule decompose_mcryy0_to_rx_ry_rzz {
    match { MCRYY[0](theta) 0 1 }
    rewrite { RX(π/2) 0, RX(π/2) 1, RZZ(theta) 0 1, RX(-π/2) 1, RX(-π/2) 0 }
}

rule decompose_mcrz0_to_rz {
    match { MCRZ[0](theta) 0 }
    rewrite { RZ(theta) 0 }
}

rule decompose_mcrz0_to_rx_ry {
    match { MCRZ[0](theta) 0 }
    rewrite { RX(-π/2) 0, RY(theta) 0, RX(π/2) 0 }
}

rule decompose_mcrzx0_to_rzx {
    match { MCRZX[0](theta) 0 1 }
    rewrite { RZX(theta) 0 1 }
}

rule decompose_mcrzx0_to_rx_ry_rzz {
    match { MCRZX[0](theta) 0 1 }
    rewrite { RY(-π/2) 1, RZZ(theta) 0 1, RY(π/2) 1 }
}

rule decompose_mcrzz0_to_rzz {
    match { MCRZZ[0](theta) 0 1 }
    rewrite { RZZ(theta) 0 1 }
}

rule decompose_mcs0_to_s {
    match { MCS[0] 0 }
    rewrite { S 0 }
}

rule decompose_mcs0_to_rx_ry {
    match { MCS[0] 0 }
    rewrite { RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, GPhase(π/4) }
}

rule decompose_mcsdg0_to_sdg {
    match { MCSDG[0] 0 }
    rewrite { SDG 0 }
}

rule decompose_mcsdg0_to_rx_ry {
    match { MCSDG[0] 0 }
    rewrite { RX(-π/2) 0, RY(-π/2) 0, RX(π/2) 0, GPhase(-π/4) }
}

rule decompose_mcswap0_to_swap {
    match { MCSWAP[0] 0 1 }
    rewrite { SWAP 0 1 }
}

rule decompose_mcswap0_to_rx_ry_rzz {
    match { MCSWAP[0] 0 1 }
    rewrite { RY(-π/2) 0, RY(-π/2) 1, RZZ(π/2) 0 1, RY(π/2) 1, RY(π/2) 0, RX(π/2) 0, RX(π/2) 1, RZZ(π/2) 0 1, RX(-π/2) 1, RX(-π/2) 0, RZZ(π/2) 0 1, GPhase(π/4) }
}

rule decompose_mct0_to_t {
    match { MCT[0] 0 }
    rewrite { T 0 }
}

rule decompose_mct0_to_rx_ry {
    match { MCT[0] 0 }
    rewrite { RX(-π/2) 0, RY(π/4) 0, RX(π/2) 0, GPhase(π/8) }
}

rule decompose_mctdg0_to_tdg {
    match { MCTDG[0] 0 }
    rewrite { TDG 0 }
}

rule decompose_mctdg0_to_rx_ry {
    match { MCTDG[0] 0 }
    rewrite { RX(-π/2) 0, RY(-π/4) 0, RX(π/2) 0, GPhase(-π/8) }
}

rule decompose_mcu0_to_u {
    match { MCU[0](theta, phi, lambda) 0 }
    rewrite { U(theta, phi, lambda) 0 }
}

rule decompose_mcu0_to_rx_ry {
    match { MCU[0](theta, phi, lambda) 0 }
    rewrite { RX(-π/2) 0, RY(lambda - π/2) 0, RX(theta) 0, RY(phi + π/2) 0, RX(π/2) 0, GPhase((phi + lambda) / 2) }
}

rule decompose_mcx0_to_x {
    match { MCX[0] 0 }
    rewrite { X 0 }
}

rule decompose_mcx0_to_rx {
    match { MCX[0] 0 }
    rewrite { RX(π) 0, GPhase(π/2) }
}

rule decompose_mcxy0_to_xy {
    match { MCXY[0](theta) 0 }
    rewrite { XY(theta) 0 }
}

rule decompose_mcxy0_to_rx_ry {
    match { MCXY[0](phi) 0 }
    rewrite { RX(-π/2) 0, RY(-phi) 0, RX(π) 0, RY(phi) 0, RX(π/2) 0 }
}

rule decompose_mcx2p0_to_x2p {
    match { MCX2P[0] 0 }
    rewrite { X2P 0 }
}

rule decompose_mcx2p0_to_rx {
    match { MCX2P[0] 0 }
    rewrite { RX(π/2) 0 }
}

rule decompose_mcx2m0_to_x2m {
    match { MCX2M[0] 0 }
    rewrite { X2M 0 }
}

rule decompose_mcx2m0_to_rx {
    match { MCX2M[0] 0 }
    rewrite { RX(-π/2) 0 }
}

rule decompose_mcxy2p0_to_xy2p {
    match { MCXY2P[0](theta) 0 }
    rewrite { XY2P(theta) 0 }
}

rule decompose_mcxy2p0_to_rx_ry {
    match { MCXY2P[0](phi) 0 }
    rewrite { RX(-π/2) 0, RY(-phi) 0, RX(π/2) 0, RY(phi) 0, RX(π/2) 0 }
}

rule decompose_mcxy2m0_to_xy2m {
    match { MCXY2M[0](theta) 0 }
    rewrite { XY2M(theta) 0 }
}

rule decompose_mcxy2m0_to_rx_ry {
    match { MCXY2M[0](phi) 0 }
    rewrite { RX(-π/2) 0, RY(-phi) 0, RX(-π/2) 0, RY(phi) 0, RX(π/2) 0 }
}

rule decompose_mcy0_to_y {
    match { MCY[0] 0 }
    rewrite { Y 0 }
}

rule decompose_mcy0_to_ry {
    match { MCY[0] 0 }
    rewrite { RY(π) 0, GPhase(π/2) }
}

rule decompose_mcy2p0_to_y2p {
    match { MCY2P[0] 0 }
    rewrite { Y2P 0 }
}

rule decompose_mcy2p0_to_ry {
    match { MCY2P[0] 0 }
    rewrite { RY(π/2) 0 }
}

rule decompose_mcy2m0_to_y2m {
    match { MCY2M[0] 0 }
    rewrite { Y2M 0 }
}

rule decompose_mcy2m0_to_ry {
    match { MCY2M[0] 0 }
    rewrite { RY(-π/2) 0 }
}

rule decompose_mcz0_to_z {
    match { MCZ[0] 0 }
    rewrite { Z 0 }
}

rule decompose_mcz0_to_rx_ry {
    match { MCZ[0] 0 }
    rewrite { RX(-π/2) 0, RY(π) 0, RX(π/2) 0, GPhase(π/2) }
}

rule decompose_mcphase0_to_phase {
    match { MCPhase[0](theta) 0 }
    rewrite { Phase(theta) 0 }
}

rule decompose_mcphase0_to_rx_ry {
    match { MCPhase[0](theta) 0 }
    rewrite { RX(-π/2) 0, RY(theta) 0, RX(π/2) 0, GPhase(theta/2) }
}

rule decompose_mccx0_to_cx {
    match { MCCX[0] 0 1 }
    rewrite { CX 0 1 }
}

rule decompose_mccx0_to_rx_ry_rzz {
    match { MCCX[0] 0 1 }
    rewrite { RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(5*π/4) }
}

rule decompose_mcccx0_to_ccx {
    match { MCCCX[0] 0 1 2 }
    rewrite { CCX 0 1 2 }
}

rule decompose_mcccx0_to_rx_ry_rzz {
    match { MCCCX[0] 0 1 2 }
    rewrite {
        RY(π/2) 2, RX(π) 2, GPhase(π/2),
        RY(π/2) 2, RX(π) 2, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, RZZ(-π/2) 1 2, RY(π/2) 2, RX(π) 2, GPhase(π),
        RX(-π/2) 2, RY(-π/4) 2, RX(π/2) 2, GPhase(-π/8),
        RY(π/2) 2, RX(π) 2, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, RZZ(-π/2) 0 2, RY(π/2) 2, RX(π) 2, GPhase(π),
        RX(-π/2) 2, RY(π/4) 2, RX(π/2) 2, GPhase(π/8),
        RY(π/2) 2, RX(π) 2, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, RZZ(-π/2) 1 2, RY(π/2) 2, RX(π) 2, GPhase(π),
        RX(-π/2) 2, RY(-π/4) 2, RX(π/2) 2, GPhase(-π/8),
        RY(π/2) 2, RX(π) 2, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, RZZ(-π/2) 0 2, RY(π/2) 2, RX(π) 2, GPhase(π),
        RX(-π/2) 1, RY(π/4) 1, RX(π/2) 1, GPhase(π/8),
        RX(-π/2) 2, RY(π/4) 2, RX(π/2) 2, GPhase(π/8),
        RY(π/2) 2, RX(π) 2, GPhase(π/2),
        RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(π),
        RX(-π/2) 0, RY(π/4) 0, RX(π/2) 0, GPhase(π/8),
        RX(-π/2) 1, RY(-π/4) 1, RX(π/2) 1, GPhase(-π/8),
        RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(π/2)
    }
}

rule decompose_mccy0_to_cy {
    match { MCCY[0] 0 1 }
    rewrite { CY 0 1 }
}

rule decompose_mccy0_to_rx_ry_rzz {
    match { MCCY[0] 0 1 }
    rewrite { RX(-π/2) 1, RY(-π/2) 1, RX(π/2) 1, RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, GPhase(5*π/4) }
}

rule decompose_mccz0_to_cz {
    match { MCCZ[0] 0 1 }
    rewrite { CZ 0 1 }
}

rule decompose_mccz0_to_rx_ry_rzz {
    match { MCCZ[0] 0 1 }
    rewrite { RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, GPhase(π/4) }
}

rule decompose_mcfsim0_to_fsim {
    match { MCFSIM[0](theta, phi) 0 1 }
    rewrite { FSIM(theta, phi) 0 1 }
}

rule decompose_mcfsim0_to_rx_ry_rzz {
    match { MCFSIM[0](theta, phi) 0 1 }
    rewrite { RY(-π/2) 0, RY(-π/2) 1, RZZ(theta) 0 1, RY(π/2) 1, RY(π/2) 0, RX(π/2) 0, RX(π/2) 1, RZZ(theta) 0 1, RX(-π/2) 1, RX(-π/2) 0, GPhase(-phi/4), RX(-π/2) 0, RY(-phi/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(-phi/2) 1, RX(π/2) 1, RZZ(phi/2) 0 1 }
}

rule decompose_mcx1_to_cx {
    match { MCX[1] 0 1 }
    rewrite { CX 0 1 }
}

rule decompose_mcx1_to_rx_ry_rzz {
    match { MCX[1] 0 1 }
    rewrite { RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(5*π/4) }
}

rule decompose_mcx2_to_ccx {
    match { MCX[2] 0 1 2 }
    rewrite { CCX 0 1 2 }
}

rule decompose_mcx2_to_rx_ry_rzz {
    match { MCX[2] 0 1 2 }
    rewrite {
        RY(π/2) 2, RX(π) 2, GPhase(π/2),
        RY(π/2) 2, RX(π) 2, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, RZZ(-π/2) 1 2, RY(π/2) 2, RX(π) 2, GPhase(π),
        RX(-π/2) 2, RY(-π/4) 2, RX(π/2) 2, GPhase(-π/8),
        RY(π/2) 2, RX(π) 2, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, RZZ(-π/2) 0 2, RY(π/2) 2, RX(π) 2, GPhase(π),
        RX(-π/2) 2, RY(π/4) 2, RX(π/2) 2, GPhase(π/8),
        RY(π/2) 2, RX(π) 2, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, RZZ(-π/2) 1 2, RY(π/2) 2, RX(π) 2, GPhase(π),
        RX(-π/2) 2, RY(-π/4) 2, RX(π/2) 2, GPhase(-π/8),
        RY(π/2) 2, RX(π) 2, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, RZZ(-π/2) 0 2, RY(π/2) 2, RX(π) 2, GPhase(π),
        RX(-π/2) 1, RY(π/4) 1, RX(π/2) 1, GPhase(π/8),
        RX(-π/2) 2, RY(π/4) 2, RX(π/2) 2, GPhase(π/8),
        RY(π/2) 2, RX(π) 2, GPhase(π/2),
        RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(π),
        RX(-π/2) 0, RY(π/4) 0, RX(π/2) 0, GPhase(π/8),
        RX(-π/2) 1, RY(-π/4) 1, RX(π/2) 1, GPhase(-π/8),
        RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(π/2)
    }
}

rule decompose_mcy1_to_cy {
    match { MCY[1] 0 1 }
    rewrite { CY 0 1 }
}

rule decompose_mcy1_to_rx_ry_rzz {
    match { MCY[1] 0 1 }
    rewrite { RX(-π/2) 1, RY(-π/2) 1, RX(π/2) 1, RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, GPhase(5*π/4) }
}

rule decompose_mcz1_to_cz {
    match { MCZ[1] 0 1 }
    rewrite { CZ 0 1 }
}

rule decompose_mcz1_to_rx_ry_rzz {
    match { MCZ[1] 0 1 }
    rewrite { RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, GPhase(π/4) }
}

rule decompose_mcrx1_to_crx {
    match { MCRX[1](theta) 0 1 }
    rewrite { CRX(theta) 0 1 }
}

rule decompose_mcrx1_to_rx_ry_rzz {
    match { MCRX[1](theta) 0 1 }
    rewrite { RX(theta/2) 1, RY(-π/2) 1, RZZ(-theta/2) 0 1, RY(π/2) 1 }
}

rule decompose_mcry1_to_cry {
    match { MCRY[1](theta) 0 1 }
    rewrite { CRY(theta) 0 1 }
}

rule decompose_mcry1_to_rx_ry_rzz {
    match { MCRY[1](theta) 0 1 }
    rewrite { RY(theta/2) 1, RX(π/2) 1, RZZ(-theta/2) 0 1, RX(-π/2) 1 }
}

rule decompose_mcrz1_to_crz {
    match { MCRZ[1](theta) 0 1 }
    rewrite { CRZ(theta) 0 1 }
}

rule decompose_mcrz1_to_rx_ry_rzz {
    match { MCRZ[1](theta) 0 1 }
    rewrite { RX(-π/2) 1, RY(theta/2) 1, RX(π/2) 1, RZZ(-theta/2) 0 1 }
}

rule decompose_mcy2_to_ccx {
    match { MCY[2] 0 1 2 }
    rewrite { SDG 2, CCX 0 1 2, S 2 }
}

rule decompose_mcy2_to_rx_ry_rzz {
    match { MCY[2] 0 1 2 }
    rewrite {
        RX(-π/2) 2, RY(-π/2) 2, RX(π/2) 2, GPhase(-π/4),
        RY(π/2) 2, RX(π) 2, GPhase(π/2),
        RY(π/2) 2, RX(π) 2, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, RZZ(-π/2) 1 2, RY(π/2) 2, RX(π) 2, GPhase(π),
        RX(-π/2) 2, RY(-π/4) 2, RX(π/2) 2, GPhase(-π/8),
        RY(π/2) 2, RX(π) 2, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, RZZ(-π/2) 0 2, RY(π/2) 2, RX(π) 2, GPhase(π),
        RX(-π/2) 2, RY(π/4) 2, RX(π/2) 2, GPhase(π/8),
        RY(π/2) 2, RX(π) 2, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, RZZ(-π/2) 1 2, RY(π/2) 2, RX(π) 2, GPhase(π),
        RX(-π/2) 2, RY(-π/4) 2, RX(π/2) 2, GPhase(-π/8),
        RY(π/2) 2, RX(π) 2, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, RZZ(-π/2) 0 2, RY(π/2) 2, RX(π) 2, GPhase(π),
        RX(-π/2) 1, RY(π/4) 1, RX(π/2) 1, GPhase(π/8),
        RX(-π/2) 2, RY(π/4) 2, RX(π/2) 2, GPhase(π/8),
        RY(π/2) 2, RX(π) 2, GPhase(π/2),
        RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(π),
        RX(-π/2) 0, RY(π/4) 0, RX(π/2) 0, GPhase(π/8),
        RX(-π/2) 1, RY(-π/4) 1, RX(π/2) 1, GPhase(-π/8),
        RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(π),
        RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, GPhase(-π/4)
    }
}

rule decompose_mcz2_to_ccx {
    match { MCZ[2] 0 1 2 }
    rewrite { H 2, CCX 0 1 2, H 2 }
}

rule decompose_mcz2_to_rx_ry_rzz {
    match { MCZ[2] 0 1 2 }
    rewrite {
        RY(π/2) 2, RX(π) 2, GPhase(π/2),
        RY(π/2) 2, RX(π) 2, GPhase(π/2),
        RY(π/2) 2, RX(π) 2, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, RZZ(-π/2) 1 2, RY(π/2) 2, RX(π) 2, GPhase(π),
        RX(-π/2) 2, RY(-π/4) 2, RX(π/2) 2, GPhase(-π/8),
        RY(π/2) 2, RX(π) 2, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, RZZ(-π/2) 0 2, RY(π/2) 2, RX(π) 2, GPhase(π),
        RX(-π/2) 2, RY(π/4) 2, RX(π/2) 2, GPhase(π/8),
        RY(π/2) 2, RX(π) 2, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, RZZ(-π/2) 1 2, RY(π/2) 2, RX(π) 2, GPhase(π),
        RX(-π/2) 2, RY(-π/4) 2, RX(π/2) 2, GPhase(-π/8),
        RY(π/2) 2, RX(π) 2, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 2, RY(π/2) 2, RX(π/2) 2, RZZ(-π/2) 0 2, RY(π/2) 2, RX(π) 2, GPhase(π),
        RX(-π/2) 1, RY(π/4) 1, RX(π/2) 1, GPhase(π/8),
        RX(-π/2) 2, RY(π/4) 2, RX(π/2) 2, GPhase(π/8),
        RY(π/2) 2, RX(π) 2, GPhase(π/2),
        RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(π),
        RX(-π/2) 0, RY(π/4) 0, RX(π/2) 0, GPhase(π/8),
        RX(-π/2) 1, RY(-π/4) 1, RX(π/2) 1, GPhase(-π/8),
        RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(π),
        RY(π/2) 2, RX(π) 2
    }
}

rule decompose_mcs1_to_phase_cx {
    match { MCS[1] 0 1 }
    rewrite { Phase(π/4) 0, Phase(π/4) 1, CX 0 1, Phase(-π/4) 1, CX 0 1 }
}

rule decompose_mcs1_to_rx_ry_rzz {
    match { MCS[1] 0 1 }
    rewrite { RX(-π/2) 0, RY(π/4) 0, RX(π/2) 0, GPhase(π/8), RX(-π/2) 1, RY(π/4) 1, RX(π/2) 1, GPhase(π/8), RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(π), RX(-π/2) 1, RY(-π/4) 1, RX(π/2) 1, GPhase(-π/8), RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(3*π/2) }
}

rule decompose_mcsdg1_to_phase_cx {
    match { MCSDG[1] 0 1 }
    rewrite { Phase(-π/4) 0, Phase(-π/4) 1, CX 0 1, Phase(π/4) 1, CX 0 1 }
}

rule decompose_mcsdg1_to_rx_ry_rzz {
    match { MCSDG[1] 0 1 }
    rewrite { RX(-π/2) 0, RY(-π/4) 0, RX(π/2) 0, GPhase(-π/8), RX(-π/2) 1, RY(-π/4) 1, RX(π/2) 1, GPhase(-π/8), RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(π), RX(-π/2) 1, RY(π/4) 1, RX(π/2) 1, GPhase(π/8), RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(3*π/2) }
}

rule decompose_mct1_to_phase_cx {
    match { MCT[1] 0 1 }
    rewrite { Phase(π/8) 0, Phase(π/8) 1, CX 0 1, Phase(-π/8) 1, CX 0 1 }
}

rule decompose_mct1_to_rx_ry_rzz {
    match { MCT[1] 0 1 }
    rewrite { RX(-π/2) 0, RY(π/8) 0, RX(π/2) 0, GPhase(π/16), RX(-π/2) 1, RY(π/8) 1, RX(π/2) 1, GPhase(π/16), RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(π), RX(-π/2) 1, RY(-π/8) 1, RX(π/2) 1, GPhase(-π/16), RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(3*π/2) }
}

rule decompose_mctdg1_to_phase_cx {
    match { MCTDG[1] 0 1 }
    rewrite { Phase(-π/8) 0, Phase(-π/8) 1, CX 0 1, Phase(π/8) 1, CX 0 1 }
}

rule decompose_mctdg1_to_rx_ry_rzz {
    match { MCTDG[1] 0 1 }
    rewrite { RX(-π/2) 0, RY(-π/8) 0, RX(π/2) 0, GPhase(-π/16), RX(-π/2) 1, RY(-π/8) 1, RX(π/2) 1, GPhase(-π/16), RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(π), RX(-π/2) 1, RY(π/8) 1, RX(π/2) 1, GPhase(π/16), RY(π/2) 1, RX(π) 1, RX(-π/2) 0, RY(π/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(π/2) 1, RX(π/2) 1, RZZ(-π/2) 0 1, RY(π/2) 1, RX(π) 1, GPhase(3*π/2) }
}

rule decompose_mcphase1_to_phase_cx {
    match { MCPhase[1](theta) 0 1 }
    rewrite { Phase(theta/2) 0, Phase(theta/2) 1, CX 0 1, Phase(-theta/2) 1, CX 0 1 }
}

rule decompose_mcphase1_to_rx_ry_rzz {
    match { MCPhase[1](theta) 0 1 }
    rewrite { RX(-π/2) 0, RY(theta/2) 0, RX(π/2) 0, RX(-π/2) 1, RY(theta/2) 1, RX(π/2) 1, RZZ(-theta/2) 0 1, GPhase(theta/4) }
}

rule decompose_mcphase1_to_rz_cx {
    match { MCPhase[1](theta) 0 1 }
    rewrite { RZ(theta/2) 0, CX 0 1, RZ(-theta/2) 1, CX 0 1, RZ(theta/2) 1, GPhase(theta/4) }
}

rule decompose_mcphase1_to_rz_x2p_cz {
    match { MCPhase[1](theta) 0 1 }
    rewrite {
        RZ(theta/2) 0,
        RZ(π/2) 1, X2P 1, RZ(π) 1,
        CZ 0 1,
        X2P 1, RZ(π) 1, RZ(-theta/2) 1,
        X2P 1, RZ(π) 1,
        CZ 0 1,
        X2P 1, RZ(π/2) 1, RZ(theta/2) 1,
        GPhase(theta/4)
    }
}

rule decompose_mcphase2_to_parity_phase {
    match { MCPhase[2](theta) 0 1 2 }
    rewrite {
        Phase(theta/4) 0,
        Phase(theta/4) 1,
        CX 0 1, Phase(-theta/4) 1, CX 0 1,
        Phase(theta/4) 2,
        CX 0 2, Phase(-theta/4) 2, CX 0 2,
        CX 1 2, Phase(-theta/4) 2, CX 1 2,
        CX 0 2, CX 1 2, Phase(theta/4) 2, CX 1 2, CX 0 2
    }
}

rule decompose_mcswap1_to_ccx {
    match { MCSWAP[1] 0 1 2 }
    rewrite { CCX 0 1 2, CCX 0 2 1, CCX 0 1 2 }
}

rule decompose_mcswap1_to_rz_x2p_cz {
    match { MCSWAP[1] 0 1 2 }
    rewrite {
        X2P 1,
        CZ 2 1,
        RZ(-π) 1, X2P 1, RZ(-π/4) 1,
        X2P 2, RZ(-3*π/4) 2, X2P 2,
        CZ 0 2,
        X2P 2, RZ(5*π/4) 2, X2P 2, RZ(π) 2,
        CZ 1 2,
        X2P 1, RZ(π) 1,
        X2P 2, RZ(3*π/4) 2, X2P 2, RZ(π) 2,
        CZ 0 2,
        CZ 0 1,
        RZ(π/4) 0,
        X2P 1, RZ(3*π/4) 1, X2P 1, RZ(π) 1,
        CZ 0 1,
        X2P 2, RZ(5*π/4) 2, X2P 2, RZ(π/2) 2,
        CZ 2 1,
        X2P 1, RZ(π/2) 1,
        GPhase(11*π/8)
    }
}

rule decompose_mcswap1_to_rz_x2p_cx {
    match { MCSWAP[1] 0 1 2 }
    rewrite {
        X2P 1,
        RZ(π/4) 2, X2P 2, RZ(π/2) 2,
        CX 1 2,
        RZ(-π) 1, X2P 1, RZ(-3*π/4) 1,
        RZ(π/2) 2, X2P 2, RZ(-π/4) 2, X2P 2, RZ(π/4) 2,
        CX 0 2, RZ(π/4) 2,
        CX 1 2, RZ(-π/4) 2,
        CX 0 2,
        CX 0 1, RZ(π/4) 0, RZ(-π/4) 1,
        CX 0 1,
        RZ(3*π/4) 2, X2P 2, RZ(π/2) 2,
        CX 2 1,
        GPhase(3*π/8)
    }
}

rule decompose_mcswap1_to_rx_ry_rzz {
    match { MCSWAP[1] 0 1 2 }
    rewrite {
        RY(π/2) 1, RX(π) 1,
        RZZ(π/2) 2 1,
        RY(π/2) 1, RX(-π/2) 1,
        RY(π/2) 2, RX(π/2) 2,
        RZZ(π/4) 1 2,
        RY(-π/2) 1, RX(π/4) 1,
        RZZ(π/2) 0 1,
        RX(π/2) 0, RY(π/2) 0, RX(-π/2) 0,
        RX(-π/2) 1,
        RX(-π/2) 2, RY(π/4) 2, RX(-π/2) 2,
        RZZ(π/4) 1 2,
        RY(-π/2) 1, RX(π/4) 1,
        RZZ(π/2) 0 1,
        RX(π/2) 0, RY(π/2) 0, RX(π/2) 0,
        RX(π/2) 1, RY(π/2) 1, RX(-π/2) 1,
        RX(-π/2) 2, RY(π/4) 2, RX(-π/2) 2,
        RZZ(π/4) 0 2,
        RX(π/2) 0, RY(π/4) 0, RX(π/2) 0,
        RY(π/2) 2, RX(-3*π/4) 2,
        RZZ(π/2) 2 1,
        RY(π/2) 1, RX(π/2) 1,
        RX(π/2) 2, RY(π/2) 2, RX(-π/2) 2,
        GPhase(π/8)
    }
}

rule decompose_mcrzz1_to_ccx_crz {
    match { MCRZZ[1](theta) 0 1 2 }
    rewrite { CCX 0 1 2, CRZ(theta) 0 2, CCX 0 1 2 }
}

rule decompose_mcrxx1_to_ccx_crz {
    match { MCRXX[1](theta) 0 1 2 }
    rewrite { H 1, H 2, CCX 0 1 2, CRZ(theta) 0 2, CCX 0 1 2, H 1, H 2 }
}

rule decompose_mcryy1_to_ccx_crz {
    match { MCRYY[1](theta) 0 1 2 }
    rewrite { RX(π/2) 1, RX(π/2) 2, CCX 0 1 2, CRZ(theta) 0 2, CCX 0 1 2, RX(-π/2) 1, RX(-π/2) 2 }
}

rule decompose_mcrzx1_to_ccx_crz {
    match { MCRZX[1](theta) 0 1 2 }
    rewrite { H 2, CCX 0 1 2, CRZ(theta) 0 2, CCX 0 1 2, H 2 }
}

rule decompose_mcx3_to_parity_phase {
    match { MCX[3] 0 1 2 3 }
    rewrite {
        H 3,
        RZ(π/8) 0,
        RZ(π/8) 1,
        CX 0 1, RZ(-π/8) 1, CX 0 1,
        RZ(π/8) 2,
        CX 0 2, RZ(-π/8) 2, CX 0 2,
        CX 1 2, RZ(-π/8) 2, CX 1 2,
        CX 0 2, CX 1 2, RZ(π/8) 2, CX 1 2, CX 0 2,
        RZ(π/8) 3,
        CX 0 3, RZ(-π/8) 3, CX 0 3,
        CX 1 3, RZ(-π/8) 3, CX 1 3,
        CX 0 3, CX 1 3, RZ(π/8) 3, CX 1 3, CX 0 3,
        CX 2 3, RZ(-π/8) 3, CX 2 3,
        CX 0 3, CX 2 3, RZ(π/8) 3, CX 2 3, CX 0 3,
        CX 1 3, CX 2 3, RZ(π/8) 3, CX 2 3, CX 1 3,
        CX 0 3, CX 1 3, CX 2 3, RZ(-π/8) 3, CX 2 3, CX 1 3, CX 0 3,
        H 3, GPhase(π/16) }
}