{"backend_name": "ibm_hanoi", "backend_version": "1.3.3", "n_qubits": 27, "basis_gates": ["cx", "id", "rz", "sx", "x"], "gates": [{"name": "id", "parameters": [], "qasm_def": "gate id q { U(0, 0, 0) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]]}, {"name": "rz", "parameters": ["theta"], "qasm_def": "gate rz(theta) q { U(0, 0, theta) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]]}, {"name": "sx", "parameters": [], "qasm_def": "gate sx q { U(pi/2, 3*pi/2, pi/2) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]]}, {"name": "x", "parameters": [], "qasm_def": "gate x q { U(pi, 0, pi) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]]}, {"name": "cx", "parameters": [], "qasm_def": "gate cx q0, q1 { CX q0, q1; }", "coupling_map": [[0, 1], [1, 0], [1, 2], [1, 4], [2, 1], [2, 3], [3, 2], [3, 5], [4, 1], [4, 7], [5, 3], [5, 8], [6, 7], [7, 4], [7, 6], [7, 10], [8, 5], [8, 9], [8, 11], [9, 8], [10, 7], [10, 12], [11, 8], [11, 14], [12, 10], [12, 13], [12, 15], [13, 12], [13, 14], [14, 11], [14, 13], [14, 16], [15, 12], [15, 18], [16, 14], [16, 19], [17, 18], [18, 15], [18, 17], [18, 21], [19, 16], [19, 20], [19, 22], [20, 19], [21, 18], [21, 23], [22, 19], [22, 25], [23, 21], [23, 24], [24, 23], [24, 25], [25, 22], [25, 24], [25, 26], [26, 25]]}, {"name": "reset", "parameters": null, "qasm_def": null}], "local": false, "simulator": false, "conditional": false, "open_pulse": true, "memory": true, "max_shots": 100000, "coupling_map": [[0, 1], [1, 0], [1, 2], [1, 4], [2, 1], [2, 3], [3, 2], [3, 5], [4, 1], [4, 7], [5, 3], [5, 8], [6, 7], [7, 4], [7, 6], [7, 10], [8, 5], [8, 9], [8, 11], [9, 8], [10, 7], [10, 12], [11, 8], [11, 14], [12, 10], [12, 13], [12, 15], [13, 12], [13, 14], [14, 11], [14, 13], [14, 16], [15, 12], [15, 18], [16, 14], [16, 19], [17, 18], [18, 15], [18, 17], [18, 21], [19, 16], [19, 20], [19, 22], [20, 19], [21, 18], [21, 23], [22, 19], [22, 25], [23, 21], [23, 24], [24, 23], [24, 25], [25, 22], [25, 24], [25, 26], [26, 25]], "dynamic_reprate_enabled": true, "supported_instructions": ["cx", "id", "delay", "measure", "reset", "rz", "sx", "x", "if_else", "for_loop", "switch_case"], "rep_delay_range": [0.0, 500.0], "default_rep_delay": 250.0, "max_experiments": 300, "sample_name": "family: Falcon, revision: 5.11", "n_registers": 1, "credits_required": true, "online_date": "2021-04-24T04:00:00+00:00", "description": "27 qubit device", "dt": 0.2222222222222222, "dtm": 0.2222222222222222, "processor_type": {"family": "Falcon", "revision": "5.11"}, "parametric_pulses": ["gaussian", "gaussian_square", "gaussian_square_drag", "drag", "constant"], "allow_q_object": true, "clops": 2341, "clops_h": "None", "clops_v": 2341, "coords": [[1, 2], [2, 2], [2, 3], [2, 4], [3, 2], [3, 4], [4, 1], [4, 2], [4, 4], [4, 5], [5, 2], [5, 4], [6, 2], [6, 3], [6, 4], [7, 2], [7, 4], [8, 1], [8, 2], [8, 4], [8, 5], [9, 2], [9, 4], [10, 2], [10, 3], [10, 4], [11, 4]], "measure_esp_enabled": false, "multi_meas_enabled": true, "parallel_compilation": true, "quantum_volume": 64, "qubit_channel_mapping": [["d0", "u1", "u0", "m0"], ["u4", "u1", "u3", "u8", "u0", "u2", "d1", "m1"], ["u5", "u4", "m2", "u6", "d2", "u2"], ["m3", "u7", "u6", "d3", "u10", "u5"], ["m4", "u13", "u3", "d4", "u8", "u9"], ["u11", "u16", "u7", "d5", "u10", "m5"], ["m6", "d6", "u14", "u12"], ["u14", "u20", "d7", "m7", "u12", "u13", "u15", "u9"], ["u11", "u18", "u16", "u17", "u19", "d8", "u22", "m8"], ["u19", "u17", "m9", "d9"], ["m10", "u20", "d10", "u15", "u24", "u21"], ["u23", "u29", "u18", "m11", "d11", "u22"], ["m12", "u26", "u27", "u32", "u24", "u21", "d12", "u25"], ["u28", "m13", "u30", "u27", "d13", "u25"], ["u23", "u28", "u29", "u30", "u31", "d14", "u34", "m14"], ["u33", "d15", "u26", "u32", "m15", "u37"], ["d16", "u31", "m16", "u35", "u34", "u40"], ["d17", "m17", "u38", "u36"], ["u33", "m18", "d18", "u38", "u36", "u39", "u37", "u44"], ["u41", "m19", "u43", "u40", "u35", "d19", "u42", "u46"], ["u43", "u41", "d20", "m20"], ["d21", "u48", "u45", "u39", "m21", "u44"], ["m22", "u47", "u52", "u42", "u46", "d22"], ["u49", "m23", "u50", "u48", "d23", "u45"], ["m24", "u49", "u50", "u51", "u53", "d24"], ["d25", "u55", "u47", "u52", "u51", "u53", "m25", "u54"], ["d26", "u54", "m26", "u55"]], "supported_features": ["qobj", "parameters", "qasm3"], "timing_constraints": {"acquire_alignment": 16, "granularity": 16, "min_length": 64, "pulse_alignment": 16}, "uchannels_enabled": true, "url": "None", "n_uchannels": 56, "u_channel_lo": [[{"q": 1, "scale": [1.0, 0.0]}], [{"q": 0, "scale": [1.0, 0.0]}], [{"q": 2, "scale": [1.0, 0.0]}], [{"q": 4, "scale": [1.0, 0.0]}], [{"q": 1, "scale": [1.0, 0.0]}], [{"q": 3, "scale": [1.0, 0.0]}], [{"q": 2, "scale": [1.0, 0.0]}], [{"q": 5, "scale": [1.0, 0.0]}], [{"q": 1, "scale": [1.0, 0.0]}], [{"q": 7, "scale": [1.0, 0.0]}], [{"q": 3, "scale": [1.0, 0.0]}], [{"q": 8, "scale": [1.0, 0.0]}], [{"q": 7, "scale": [1.0, 0.0]}], [{"q": 4, "scale": [1.0, 0.0]}], [{"q": 6, "scale": [1.0, 0.0]}], [{"q": 10, "scale": [1.0, 0.0]}], [{"q": 5, "scale": [1.0, 0.0]}], [{"q": 9, "scale": [1.0, 0.0]}], [{"q": 11, "scale": [1.0, 0.0]}], [{"q": 8, "scale": [1.0, 0.0]}], [{"q": 7, "scale": [1.0, 0.0]}], [{"q": 12, "scale": [1.0, 0.0]}], [{"q": 8, "scale": [1.0, 0.0]}], [{"q": 14, "scale": [1.0, 0.0]}], [{"q": 10, "scale": [1.0, 0.0]}], [{"q": 13, "scale": [1.0, 0.0]}], [{"q": 15, "scale": [1.0, 0.0]}], [{"q": 12, "scale": [1.0, 0.0]}], [{"q": 14, "scale": [1.0, 0.0]}], [{"q": 11, "scale": [1.0, 0.0]}], [{"q": 13, "scale": [1.0, 0.0]}], [{"q": 16, "scale": [1.0, 0.0]}], [{"q": 12, "scale": [1.0, 0.0]}], [{"q": 18, "scale": [1.0, 0.0]}], [{"q": 14, "scale": [1.0, 0.0]}], [{"q": 19, "scale": [1.0, 0.0]}], [{"q": 18, "scale": [1.0, 0.0]}], [{"q": 15, "scale": [1.0, 0.0]}], [{"q": 17, "scale": [1.0, 0.0]}], [{"q": 21, "scale": [1.0, 0.0]}], [{"q": 16, "scale": [1.0, 0.0]}], [{"q": 20, "scale": [1.0, 0.0]}], [{"q": 22, "scale": [1.0, 0.0]}], [{"q": 19, "scale": [1.0, 0.0]}], [{"q": 18, "scale": [1.0, 0.0]}], [{"q": 23, "scale": [1.0, 0.0]}], [{"q": 19, "scale": [1.0, 0.0]}], [{"q": 25, "scale": [1.0, 0.0]}], [{"q": 21, "scale": [1.0, 0.0]}], [{"q": 24, "scale": [1.0, 0.0]}], [{"q": 23, "scale": [1.0, 0.0]}], [{"q": 25, "scale": [1.0, 0.0]}], [{"q": 22, "scale": [1.0, 0.0]}], [{"q": 24, "scale": [1.0, 0.0]}], [{"q": 26, "scale": [1.0, 0.0]}], [{"q": 25, "scale": [1.0, 0.0]}]], "meas_levels": [1, 2], "qubit_lo_range": [[4.535164081905799, 5.535164081905799], [4.6551163089924845, 5.6551163089924845], [4.756336131872112, 5.756336131872112], [4.597436340911776, 5.597436340911776], [4.572834663987846, 5.572834663987846], [4.706963312452152, 5.706963312452153], [4.520511438046538, 5.520511438046538], [4.419060559537311, 5.419060559537311], [4.531263329699806, 5.531263329699806], [4.374827459345338, 5.374827459345338], [4.321173620017769, 5.321173620017769], [4.662106273772706, 5.662106273772706], [4.218550303082889, 5.218550303082889], [4.463015970627254, 5.463015970627254], [4.546606913770067, 5.546606913770067], [4.423657069135479, 5.423657069135479], [4.3833666070386235, 5.3833666070386235], [4.722448141289046, 5.722448141289046], [4.467721265556806, 5.467721265556806], [4.502460177949037, 5.502460177949037], [4.595626457655822, 5.595626457655822], [4.339271380594446, 5.339271380594446], [4.419537998954878, 5.419537998954878], [4.420264307231224, 5.420264307231224], [4.491649105460354, 5.491649105460354], [4.3128992412905065, 5.3128992412905065], [4.519586263428441, 5.519586263428441]], "meas_lo_range": [[6.665371582000001, 7.665371582000001], [6.785782665, 7.785782665], [6.673691701, 7.673691701], [6.799234688, 7.799234688], [6.724593267, 7.724593267], [6.735959639000001, 7.735959639000001], [6.844801469, 7.844801469], [6.60075502, 7.60075502], [6.6055231580000004, 7.6055231580000004], [6.833083734000001, 7.833083734000001], [6.662214989000001, 7.662214989000001], [6.720441798, 7.720441798], [6.831941889, 7.831941889], [6.718941369, 7.718941369], [6.774247730000001, 7.774247730000001], [6.774109033, 7.774109033], [6.672388137, 7.672388137], [6.844216288, 7.844216288], [6.610200578000001, 7.610200578000001], [6.606074405, 7.606074405], [6.844557632000001, 7.844557632000001], [6.727958944, 7.727958944], [6.730878403, 7.730878403], [6.780018192, 7.780018192000001], [6.668562946000001, 7.668562946000001], [6.769199002000001, 7.769199002000001], [6.658909981000001, 7.658909981000001]], "meas_kernels": ["hw_qmfk"], "discriminators": ["quadratic_discriminator", "hw_qmfk", "linear_discriminator"], "rep_times": [1000.0], "meas_map": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]], "acquisition_latency": [], "conditional_latency": [], "hamiltonian": {"description": "Qubits are modeled as Duffing oscillators. In this case, the system includes higher energy states, i.e. not just |0> and |1>. The Pauli operators are generalized via the following set of transformations:\n\n$(\\mathbb{I}-\\sigma_{i}^z)/2 \\rightarrow O_i \\equiv b^\\dagger_{i} b_{i}$,\n\n$\\sigma_{+} \\rightarrow b^\\dagger$,\n\n$\\sigma_{-} \\rightarrow b$,\n\n$\\sigma_{i}^X \\rightarrow b^\\dagger_{i} + b_{i}$.\n\nQubits are coupled through resonator buses. The provided Hamiltonian has been projected into the zero excitation subspace of the resonator buses leading to an effective qubit-qubit flip-flop interaction. The qubit resonance frequencies in the Hamiltonian are the cavity dressed frequencies and not exactly what is returned by the backend defaults, which also includes the dressing due to the qubit-qubit interactions.\n\nQuantities are returned in angular frequencies, with units 2*pi*GHz.\n\nWARNING: Currently not all system Hamiltonian information is available to the public, missing values have been replaced with 0.\n", "h_latex": "\\begin{align} \\mathcal{H}/\\hbar = & \\sum_{i=0}^{26}\\left(\\frac{\\omega_{q,i}}{2}(\\mathbb{I}-\\sigma_i^{z})+\\frac{\\Delta_{i}}{2}(O_i^2-O_i)+\\Omega_{d,i}D_i(t)\\sigma_i^{X}\\right) \\\\ & + J_{12,13}(\\sigma_{12}^{+}\\sigma_{13}^{-}+\\sigma_{12}^{-}\\sigma_{13}^{+}) + J_{14,16}(\\sigma_{14}^{+}\\sigma_{16}^{-}+\\sigma_{14}^{-}\\sigma_{16}^{+}) + J_{8,9}(\\sigma_{8}^{+}\\sigma_{9}^{-}+\\sigma_{8}^{-}\\sigma_{9}^{+}) + J_{17,18}(\\sigma_{17}^{+}\\sigma_{18}^{-}+\\sigma_{17}^{-}\\sigma_{18}^{+}) \\\\ & + J_{11,14}(\\sigma_{11}^{+}\\sigma_{14}^{-}+\\sigma_{11}^{-}\\sigma_{14}^{+}) + J_{10,12}(\\sigma_{10}^{+}\\sigma_{12}^{-}+\\sigma_{10}^{-}\\sigma_{12}^{+}) + J_{13,14}(\\sigma_{13}^{+}\\sigma_{14}^{-}+\\sigma_{13}^{-}\\sigma_{14}^{+}) + J_{7,10}(\\sigma_{7}^{+}\\sigma_{10}^{-}+\\sigma_{7}^{-}\\sigma_{10}^{+}) \\\\ & + J_{16,19}(\\sigma_{16}^{+}\\sigma_{19}^{-}+\\sigma_{16}^{-}\\sigma_{19}^{+}) + J_{12,15}(\\sigma_{12}^{+}\\sigma_{15}^{-}+\\sigma_{12}^{-}\\sigma_{15}^{+}) + J_{22,25}(\\sigma_{22}^{+}\\sigma_{25}^{-}+\\sigma_{22}^{-}\\sigma_{25}^{+}) + J_{23,24}(\\sigma_{23}^{+}\\sigma_{24}^{-}+\\sigma_{23}^{-}\\sigma_{24}^{+}) \\\\ & + J_{8,11}(\\sigma_{8}^{+}\\sigma_{11}^{-}+\\sigma_{8}^{-}\\sigma_{11}^{+}) + J_{0,1}(\\sigma_{0}^{+}\\sigma_{1}^{-}+\\sigma_{0}^{-}\\sigma_{1}^{+}) + J_{1,2}(\\sigma_{1}^{+}\\sigma_{2}^{-}+\\sigma_{1}^{-}\\sigma_{2}^{+}) + J_{19,20}(\\sigma_{19}^{+}\\sigma_{20}^{-}+\\sigma_{19}^{-}\\sigma_{20}^{+}) \\\\ & + J_{6,7}(\\sigma_{6}^{+}\\sigma_{7}^{-}+\\sigma_{6}^{-}\\sigma_{7}^{+}) + J_{24,25}(\\sigma_{24}^{+}\\sigma_{25}^{-}+\\sigma_{24}^{-}\\sigma_{25}^{+}) + J_{18,21}(\\sigma_{18}^{+}\\sigma_{21}^{-}+\\sigma_{18}^{-}\\sigma_{21}^{+}) + J_{4,7}(\\sigma_{4}^{+}\\sigma_{7}^{-}+\\sigma_{4}^{-}\\sigma_{7}^{+}) \\\\ & + J_{21,23}(\\sigma_{21}^{+}\\sigma_{23}^{-}+\\sigma_{21}^{-}\\sigma_{23}^{+}) + J_{3,5}(\\sigma_{3}^{+}\\sigma_{5}^{-}+\\sigma_{3}^{-}\\sigma_{5}^{+}) + J_{5,8}(\\sigma_{5}^{+}\\sigma_{8}^{-}+\\sigma_{5}^{-}\\sigma_{8}^{+}) + J_{1,4}(\\sigma_{1}^{+}\\sigma_{4}^{-}+\\sigma_{1}^{-}\\sigma_{4}^{+}) \\\\ & + J_{2,3}(\\sigma_{2}^{+}\\sigma_{3}^{-}+\\sigma_{2}^{-}\\sigma_{3}^{+}) + J_{19,22}(\\sigma_{19}^{+}\\sigma_{22}^{-}+\\sigma_{19}^{-}\\sigma_{22}^{+}) + J_{15,18}(\\sigma_{15}^{+}\\sigma_{18}^{-}+\\sigma_{15}^{-}\\sigma_{18}^{+}) + J_{25,26}(\\sigma_{25}^{+}\\sigma_{26}^{-}+\\sigma_{25}^{-}\\sigma_{26}^{+}) \\\\ & + \\Omega_{d,0}(U_{0}^{(0,1)}(t))\\sigma_{0}^{X} + \\Omega_{d,1}(U_{1}^{(1,0)}(t)+U_{3}^{(1,4)}(t)+U_{2}^{(1,2)}(t))\\sigma_{1}^{X} \\\\ & + \\Omega_{d,2}(U_{5}^{(2,3)}(t)+U_{4}^{(2,1)}(t))\\sigma_{2}^{X} + \\Omega_{d,3}(U_{6}^{(3,2)}(t)+U_{7}^{(3,5)}(t))\\sigma_{3}^{X} \\\\ & + \\Omega_{d,4}(U_{9}^{(4,7)}(t)+U_{8}^{(4,1)}(t))\\sigma_{4}^{X} + \\Omega_{d,5}(U_{11}^{(5,8)}(t)+U_{10}^{(5,3)}(t))\\sigma_{5}^{X} \\\\ & + \\Omega_{d,6}(U_{12}^{(6,7)}(t))\\sigma_{6}^{X} + \\Omega_{d,7}(U_{14}^{(7,6)}(t)+U_{13}^{(7,4)}(t)+U_{15}^{(7,10)}(t))\\sigma_{7}^{X} \\\\ & + \\Omega_{d,8}(U_{18}^{(8,11)}(t)+U_{16}^{(8,5)}(t)+U_{17}^{(8,9)}(t))\\sigma_{8}^{X} + \\Omega_{d,9}(U_{19}^{(9,8)}(t))\\sigma_{9}^{X} \\\\ & + \\Omega_{d,10}(U_{20}^{(10,7)}(t)+U_{21}^{(10,12)}(t))\\sigma_{10}^{X} + \\Omega_{d,11}(U_{22}^{(11,8)}(t)+U_{23}^{(11,14)}(t))\\sigma_{11}^{X} \\\\ & + \\Omega_{d,12}(U_{24}^{(12,10)}(t)+U_{25}^{(12,13)}(t)+U_{26}^{(12,15)}(t))\\sigma_{12}^{X} + \\Omega_{d,13}(U_{28}^{(13,14)}(t)+U_{27}^{(13,12)}(t))\\sigma_{13}^{X} \\\\ & + \\Omega_{d,14}(U_{31}^{(14,16)}(t)+U_{30}^{(14,13)}(t)+U_{29}^{(14,11)}(t))\\sigma_{14}^{X} + \\Omega_{d,15}(U_{33}^{(15,18)}(t)+U_{32}^{(15,12)}(t))\\sigma_{15}^{X} \\\\ & + \\Omega_{d,16}(U_{35}^{(16,19)}(t)+U_{34}^{(16,14)}(t))\\sigma_{16}^{X} + \\Omega_{d,17}(U_{36}^{(17,18)}(t))\\sigma_{17}^{X} \\\\ & + \\Omega_{d,18}(U_{37}^{(18,15)}(t)+U_{39}^{(18,21)}(t)+U_{38}^{(18,17)}(t))\\sigma_{18}^{X} + \\Omega_{d,19}(U_{42}^{(19,22)}(t)+U_{40}^{(19,16)}(t)+U_{41}^{(19,20)}(t))\\sigma_{19}^{X} \\\\ & + \\Omega_{d,20}(U_{43}^{(20,19)}(t))\\sigma_{20}^{X} + \\Omega_{d,21}(U_{44}^{(21,18)}(t)+U_{45}^{(21,23)}(t))\\sigma_{21}^{X} \\\\ & + \\Omega_{d,22}(U_{46}^{(22,19)}(t)+U_{47}^{(22,25)}(t))\\sigma_{22}^{X} + \\Omega_{d,23}(U_{49}^{(23,24)}(t)+U_{48}^{(23,21)}(t))\\sigma_{23}^{X} \\\\ & + \\Omega_{d,24}(U_{50}^{(24,23)}(t)+U_{51}^{(24,25)}(t))\\sigma_{24}^{X} + \\Omega_{d,25}(U_{54}^{(25,26)}(t)+U_{53}^{(25,24)}(t)+U_{52}^{(25,22)}(t))\\sigma_{25}^{X} \\\\ & + \\Omega_{d,26}(U_{55}^{(26,25)}(t))\\sigma_{26}^{X} \\\\ \\end{align}", "h_str": ["_SUM[i,0,26,wq{i}/2*(I{i}-Z{i})]", "_SUM[i,0,26,delta{i}/2*O{i}*O{i}]", "_SUM[i,0,26,-delta{i}/2*O{i}]", "_SUM[i,0,26,omegad{i}*X{i}||D{i}]", "jq12q13*Sp12*Sm13", "jq12q13*Sm12*Sp13", "jq14q16*Sp14*Sm16", "jq14q16*Sm14*Sp16", "jq8q9*Sp8*Sm9", "jq8q9*Sm8*Sp9", "jq17q18*Sp17*Sm18", "jq17q18*Sm17*Sp18", "jq11q14*Sp11*Sm14", "jq11q14*Sm11*Sp14", "jq10q12*Sp10*Sm12", "jq10q12*Sm10*Sp12", "jq13q14*Sp13*Sm14", "jq13q14*Sm13*Sp14", "jq7q10*Sp7*Sm10", "jq7q10*Sm7*Sp10", "jq16q19*Sp16*Sm19", "jq16q19*Sm16*Sp19", "jq12q15*Sp12*Sm15", "jq12q15*Sm12*Sp15", "jq22q25*Sp22*Sm25", "jq22q25*Sm22*Sp25", "jq23q24*Sp23*Sm24", "jq23q24*Sm23*Sp24", "jq8q11*Sp8*Sm11", "jq8q11*Sm8*Sp11", "jq0q1*Sp0*Sm1", "jq0q1*Sm0*Sp1", "jq1q2*Sp1*Sm2", "jq1q2*Sm1*Sp2", "jq19q20*Sp19*Sm20", "jq19q20*Sm19*Sp20", "jq6q7*Sp6*Sm7", "jq6q7*Sm6*Sp7", "jq24q25*Sp24*Sm25", "jq24q25*Sm24*Sp25", "jq18q21*Sp18*Sm21", "jq18q21*Sm18*Sp21", "jq4q7*Sp4*Sm7", "jq4q7*Sm4*Sp7", "jq21q23*Sp21*Sm23", "jq21q23*Sm21*Sp23", "jq3q5*Sp3*Sm5", "jq3q5*Sm3*Sp5", "jq5q8*Sp5*Sm8", "jq5q8*Sm5*Sp8", "jq1q4*Sp1*Sm4", "jq1q4*Sm1*Sp4", "jq2q3*Sp2*Sm3", "jq2q3*Sm2*Sp3", "jq19q22*Sp19*Sm22", "jq19q22*Sm19*Sp22", "jq15q18*Sp15*Sm18", "jq15q18*Sm15*Sp18", "jq25q26*Sp25*Sm26", "jq25q26*Sm25*Sp26", "omegad1*X0||U0", "omegad0*X1||U1", "omegad4*X1||U3", "omegad2*X1||U2", "omegad3*X2||U5", "omegad1*X2||U4", "omegad2*X3||U6", "omegad5*X3||U7", "omegad7*X4||U9", "omegad1*X4||U8", "omegad8*X5||U11", "omegad3*X5||U10", "omegad7*X6||U12", "omegad6*X7||U14", "omegad4*X7||U13", "omegad10*X7||U15", "omegad11*X8||U18", "omegad5*X8||U16", "omegad9*X8||U17", "omegad8*X9||U19", "omegad7*X10||U20", "omegad12*X10||U21", "omegad8*X11||U22", "omegad14*X11||U23", "omegad10*X12||U24", "omegad13*X12||U25", "omegad15*X12||U26", "omegad14*X13||U28", "omegad12*X13||U27", "omegad16*X14||U31", "omegad13*X14||U30", "omegad11*X14||U29", "omegad18*X15||U33", "omegad12*X15||U32", 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