def test_build_fail_1(): dimH = 11 Oh0 = Odn2(dimH, qo.QO.T_COMPLEX) - Ocos(dimH, qo.QO.T_COMPLEX) rs = qo.ReducedSystem(Oh0, dipole=Osin(dimH, qo.QO.T_COMPLEX)) # -- Run with OpenCL kernel kernelCL = OpenCLKernel(rs) kernelCL.compile()
def test_divergence_1(): config = { 'dimH': 13, 'EC': 1, 'Omega': 3, 'y_0': 0.02, 't_bath': 0.0, 'tr': (0, 20, 0.001), 't_rho0': [0], } pf = 1.0 / config['EC'] * config['Omega'] ** 2 Oh0 = 0.5 * config['EC'] * Odn2(config['dimH'], qo.QO.T_COMPLEX) \ - pf * Ocos(config['dimH'], qo.QO.T_COMPLEX) rs = qo.ReducedSystem(Oh0, dipole=Osin(config['dimH'], qo.QO.T_COMPLEX)) # -- Run with QuTip kernel = QutipKernel(rs) kernel.compile() kernel.sync(t_bath=config['t_bath'], y_0=config['y_0'], state=rs.thermal_state(T=config['t_rho0'])) tlist = qo.time_gatter(*config['tr']) (_, _, tstate, _) = kernel.run(tlist) # -- Run with OpenCL kernel kernelCL = OpenCLKernel(rs) kernelCL.optimize_jumps = True kernelCL.compile() kernelCL.sync(t_bath=config['t_bath'], y_0=config['y_0'], state=rs.thermal_state(T=config['t_rho0'])) tlist_cl, resultCL = kernelCL.reader_rho_t(kernelCL.run(config['tr'], steps_chunk_size=1e4)) # -- compare all states at all times assert_allclose(tlist, tlist_cl) assert_allclose(resultCL, tstate, **qo.QO.TEST_TOLS)
def test_two_level_T_driving(): """ two level system at finite temperature with time dependent hamiltonian compared to reference implementation. """ REF_TOL = 0.0001 OMEGA = 2.0 tr = (0, 1.0, 0.001) y_0 = 0.5 t_bath = 1.0 h0 = [0, 0, 0, OMEGA] states = [[1.0, 0.0, 0.0, 0.0]] * 3 param = np.array([(0.0, 0.0), (1.0, 2.0), (1.0, 2.5)], dtype=np.dtype([ ('A', np.float32), ('b', np.float32), ])) kernel = OpenCLKernel(ReducedSystem(h0, [ 0, 1, 1, 0, ])) kernel.t_sysparam = param.dtype kernel.ht_coeff = [lambda t, p: p['A'] * np.sin(p['b'] * t / np.pi)] kernel.compile() kernel.sync(state=states, y_0=y_0, t_bath=t_bath, sysparam=param, htl=[[1, 1, 1, 1]]) tf, rhof = kernel.reader_tfinal_rho(kernel.run(tr, steps_chunk_size=1234)) # test final time assert np.isclose(tf, tr[1]) # reference result (_, fstate, _, _) = opmesolve([h0, [[1, 1, 1, 1], kernel.ht_coeff[0]]], states, t_bath=t_bath, y_0=y_0, tw=[OMEGA], tr=tr, kernel="QuTip", args=param) # test against reference assert_allclose(rhof[0], fstate[0], **QOP.TEST_TOLS) assert_allclose(rhof[1], fstate[1], **QOP.TEST_TOLS) assert_allclose(rhof[2], fstate[2], **QOP.TEST_TOLS)
def test_two_level_TZero(): """ most simple dissipative case. two level system with at T=0: d rho / dt = -i[H,rho] + y_0 \\Omega^3 D[A(\\Omega)] """ REF_TOL = 0.0001 OMEGA = 2.0 tr = (0, 1.0, 0.001) y_0 = [0.5, 0.5, 0.25] h0 = [0, 0, 0, OMEGA] states = [ # T=inf [0.5, 0.0, 0.0, 0.5], # T=0 [1.0, 0.0, 0.0, 0.0], # T=t + coherence [0.75, 0.5, 0.5, 0.25], ] kernel = OpenCLKernel(ReducedSystem(h0, [ 0, 1, 1, 0, ])) kernel.compile() kernel.sync(state=states, y_0=y_0, t_bath=0) tf, rhof = kernel.reader_tfinal_rho(kernel.run(tr)) # test final time assert np.isclose(tf, tr[1]) # reference result (_, fstate, _, _) = opmesolve(h0, states, t_bath=0, y_0=y_0, tw=[OMEGA], tr=tr, kernel="QuTip") # test against reference assert_allclose(rhof[0], fstate[0], **QOP.TEST_TOLS) assert_allclose(rhof[1], fstate[1], **QOP.TEST_TOLS) assert_allclose(rhof[2], fstate[2], **QOP.TEST_TOLS)
def test_thermalization(): """ in this test we setup a harmonic oscillator H = \Omega n such that it couples thru x operator D = x = a^\dagger + a and check whether a list of ground states thermalize correctly. Testes Kernels: - QuTip - OpenCL """ # system parameters dimH = 5 t_bath = [0.0, 0.2, 1.0, 1.5] y_0 = 1.25 Omega = 1.0 tr = (0, 4.00, 0.005) state0 = np.zeros(dimH**2, dtype=np.complex64).reshape((dimH, dimH)) state0[0, 0] = 1 Ee = [Omega * k for k in range(dimH)] tlist = time_gatter(tr[0], tr[1], tr[2]) # operators Oa = op_a(dimH) Oad = Oa.conj().T On = Oad @ Oa Ox = Oa + Oad # reduced system rs = ReducedSystem(Omega * On) # the expected mean occupation numbers # # <E> = Tr(H rho_th) = Tr(H sum_i p_i e^(beta*Omega*i)) # expected_En = [ sum(e_i * p_i for (e_i, p_i) in zip(Ee, thermal_dist(Ee, t))) for t in t_bath ] # -- Run with QuTip kernel = QutipKernel(rs) kernel.compile() kernel.sync(t_bath=t_bath, y_0=y_0, state=[state0] * 4) tlist = time_gatter(tr[0], tr[1], tr[2]) (_, _, tstate, _) = kernel.run(tlist) # test whether states have thermalized En = np.trace(tstate[-1, :] @ On, axis1=1, axis2=2).real assert np.allclose(expected_En, En, **QOP.TEST_TOLS) # -- Run with OpenCL kernel kernelCL = OpenCLKernel(rs) kernelCL.compile() kernelCL.sync(t_bath=t_bath, y_0=y_0, state=state0.flatten()) tlist_cl, resultCL = kernelCL.reader_rho_t(kernelCL.run(tr)) # test whether states have thermalized assert_allclose(tlist, tlist_cl) EnCL = np.trace(resultCL[-1, :] @ On, axis1=1, axis2=2).real assert np.allclose(expected_En, EnCL, **QOP.TEST_TOLS), "{}".format(expected_En - EnCL)
def test_dork(): """ three level system at finite temperature with time dependent hamiltonian compared to reference implementation. """ h0 = np.diag([ 1, 2, 3, 7, 9, 15, 27, 30, ]) rs = ReducedSystem(h0) kernel = OpenCLKernel(rs) kernel.compile() kernel.sync(state=rs.thermal_state(0), t_bath=1, y_0=1) rs = ReducedSystem(h0).create_rs_dipole_ladder() kernel = OpenCLKernel(rs) kernel.compile() kernel.sync(state=rs.thermal_state(0), t_bath=1, y_0=1)
def test_time_gatter(): """ in this test two debug buffers are injected into the OpenCL kernel: 1. Time Buffer - to read out internal time at each time step 2. Index Buffer - to read out internal output index at each time step. we compare the values, chunkwise, against expected times and indices. Also, the run() generator yields a triplet which we also test in this test. """ rs = ReducedSystem([0, 0, 0, 1], [0, 1, 1, 0]) kernel = OpenCLKernel(rs) kernel.c_debug_hook_1 = "time_gatter[2*n+get_global_id(0)] = t + 1337 * get_global_id(0);\n" \ + "index_gatter[2*n+get_global_id(0)] = __out_len * n + __in_offset;\n" # we want 5 steps & two systems, we use a buffer of shape (7, 2) to check # whether the kernel overflow the 5 expected items. h_time = np.zeros((7, 2), dtype=np.float32) b_time = kernel.arr_to_buf(h_time) h_gatter = np.zeros((7, 2), dtype=np.int32) b_gatter = kernel.arr_to_buf(h_gatter) # hook & compile kernel.cl_debug_buffers = [ ('__global float *time_gatter', b_time), ('__global int *index_gatter', b_gatter), ] kernel.compile() # syn kernel.sync(state=[1, 0, 0, 0], y_0=1, t_bath=[1, 1]) expected_cl_tlists = [ np.array([.000, .001, .002, .003, 0.004]), np.array([.005, .006, .007, .008, 0.009]), np.array([.010, .011, .012]), ] expected_tlists = [ np.array([.001, .002, .003, .004, 0.005]), np.array([.006, .007, .008, .009, 0.010]), np.array([.011, .012, .013]), ] dt = 0.001 # the first index (0) is allready occupied by the initial state # given at kernel.sync we therefore expect the idx to start from 1. current_index = 1 run_kwargs = {'steps_chunk_size': 5, 'parallel': False} for j, (idx, tlist, rho_eb) in enumerate(kernel.run((0, 0.013, dt), **run_kwargs)): # -- test index assert idx[0] == current_index i1 = idx[1] - idx[0] current_index += i1 + 1 # -- test time used inside the kernel # note: we measure the time before increasing it, thus # we expect a lattice like 0, 1, 2, 3 while the yielde # tlist should be 1, 2, 3, 4 as tlist corresponds to the # time at which the state rho_eb is. expected_tlist_cl = expected_cl_tlists[j] l = len(expected_tlist_cl) cl.enqueue_copy(kernel.queue, h_time, b_time) assert_allclose(expected_tlist_cl, h_time[:l, 0]) assert_allclose(expected_tlist_cl + 1337, h_time[:l, 1]) # test that buffer did not overflow assert_allclose(np.zeros(7 - l), h_time[l:, 0]) assert_allclose(np.zeros(7 - l), h_time[l:, 1]) # reset time buffer h_time = np.zeros_like(h_time) b_time = kernel.arr_to_buf(h_time) kernel.cl_debug_buffers[0] = (kernel.cl_debug_buffers[0], b_time) # -- test time yielded from python expected_tlist = expected_tlists[j] l = len(expected_tlist) assert_allclose(expected_tlist, tlist) # -- test index gatter cl.enqueue_copy(kernel.queue, h_gatter, b_gatter) expected_gatter = np.arange(l * 2).reshape((l, 2)) * 4 assert_allclose(expected_gatter, h_gatter[0:len(expected_gatter)]) expected_empty_gatter = np.zeros((7 - l) * 2).reshape((7 - l, 2)) assert_allclose(expected_empty_gatter, h_gatter[len(expected_gatter):]) # reset gatter buffer h_gatter = np.zeros_like(h_gatter) b_gatter = kernel.arr_to_buf(h_gatter) kernel.cl_debug_buffers[1] = (kernel.cl_debug_buffers[1], b_gatter) # test rho_eb assert rho_eb.shape[0] == l
def test_four_level_T(): """ four level system at finite temperature T - all possible jumps - no dipole - eigenbase - compare optimized and non-optimized vs. reference """ REF_TOL = 0.0001 tr = (0, 1.0, 0.001) t_bath = [1.0, 0.5] y_0 = [1.3, 2.4] h0 = [ 0.0, 0, 0, 0, 0, 1.0, 0, 0, 0, 0, 2.0, 0, 0, 0, 0, 6.0, ] states = [ [ # T=0 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ], [ # some weird state 0.4, 0.4, 0.6, 0.3, 0.4, 0.3, 0.2, 0.2, 0.6, 0.2, 0.1, 0.6, 0.3, 0.2, 0.6, 0.2, ] ] sys = ReducedSystem(h0) kernel = OpenCLKernel(sys) kernel.optimize_jumps = True kernel.compile() kernel.sync(state=states, y_0=y_0, t_bath=t_bath) tf, rhof = kernel.reader_tfinal_rho(kernel.run(tr, steps_chunk_size=1111)) # test final time assert np.isclose(tf, tr[1]) kernel2 = OpenCLKernel(sys) kernel2.optimize_jumps = False kernel2.compile() kernel2.sync(state=states, y_0=y_0, t_bath=t_bath) tf, rhof2 = kernel.reader_tfinal_rho(kernel2.run(tr)) # test final time assert np.isclose(tf, tr[1]) # reference result (_, fstate, _, _) = opmesolve(h0, states, t_bath=t_bath, y_0=y_0, tr=tr, kernel="QuTip") # test against reference assert_allclose(rhof[0], fstate[0], **QOP.TEST_TOLS) assert_allclose(rhof[1], fstate[1], **QOP.TEST_TOLS) assert_allclose(rhof2[0], fstate[0], **QOP.TEST_TOLS) assert_allclose(rhof2[1], fstate[1], **QOP.TEST_TOLS)
def test_three_level_T(): """ three level system at finite temperature. - two jumps (1*Omega, 2*Omega) - no dipole - eigenbase - compare optimized vs. reference """ REF_TOL = 0.0001 OMEGA = 2.0 tr = (0, 0.5, 0.001) tw = [OMEGA, 2 * OMEGA] t_bath = 1.0 h0 = [ 0.0, 0, 0, 0, OMEGA, 0, 0, 0, 2 * OMEGA, ] states = [ [ # T=inf 1.0 / 3.0, 0.0, 0.0, 0.0, 1.0 / 3.0, 0.0, 0.0, 0.0, 1.0 / 3.0 ], [ # T=0 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], [ # T=t + coherence 0.4, 0.4 + 0.25j, 0.6 - 0.5j, 0.4 - 0.25j, 0.2, -0.2j, 0.6 + 0.5j, 0.2j, 0.4 ] ] sys = ReducedSystem(h0, [ 0, 1, 1, 1, 0, 1, 1, 1, 0, ]) kernel = OpenCLKernel(sys) assert kernel.optimize_jumps kernel.compile() kernel.sync(state=states, y_0=1.0, t_bath=t_bath) tf, rhof = kernel.reader_tfinal_rho(kernel.run(tr)) # test final time assert np.isclose(tf, tr[1]) # reference result (_, fstate, _, _) = opmesolve(h0, states, t_bath=t_bath, y_0=1.0, tw=tw, tr=tr, kernel="QuTip") # test against reference assert_allclose(rhof[0], fstate[0], **QOP.TEST_TOLS) assert_allclose(rhof[1], fstate[1], **QOP.TEST_TOLS) assert_allclose(rhof[2], fstate[2], **QOP.TEST_TOLS)
def test_two_level_T(): """ most simple dissipative case at finite temperature: two level system at T > 0: d rho / dt = -i[H,rho] + y_0 * \Omega^3 * (1 + N(\\Omega)) * D[A(\\Omega)] + y_0 * \Omega^3 * N(\\Omega) * D[A^\\dagger(\\Omega)] - single jump - no dipole - eigenbase - compared optimized vs. reference """ REF_TOL = 0.0001 OMEGA = 2.0 tr = (0, 1.0, 0.001) y_0 = 0.5 t_bath = 1.0 h0 = [0, 0, 0, OMEGA] states = [ [ # T=inf 0.5, 0.2 - 0.4j, 0.2 + 0.4j, 0.5 ], [ # T=0 1.0, 0.0, 0.0, 0.0 ] ] kernel = OpenCLKernel(ReducedSystem(h0, [ 0, 1, 1, 0, ])) kernel.compile() kernel.sync(state=states, y_0=y_0, t_bath=t_bath) tf, rhof = kernel.reader_tfinal_rho(kernel.run(tr)) # test final time assert np.isclose(tf, tr[1]) # reference result (_, fstate, _, _) = opmesolve(h0, states, t_bath=t_bath, y_0=y_0, tw=[OMEGA], tr=tr, kernel="QuTip") # test against reference assert_allclose(rhof[0], fstate[0], **QOP.TEST_TOLS) assert_allclose(rhof[1], fstate[1], **QOP.TEST_TOLS)
def test_three_level_TZero(): """ two different annihilation processes A(Omega), A(2*Omega) at T=0: - two possible jumps - no dipole - eigenbase - compared optimized vs. reference """ REF_TOL = 0.0001 OMEGA = 2.0 tr = (0, 0.1, 0.001) tw = [OMEGA, 2 * OMEGA] h0 = [ 0.0, 0, 0, 0, OMEGA, 0, 0, 0, 2 * OMEGA, ] states = [ [ # T=inf 1.0 / 3.0, 0.0, 0.0, 0.0, 1.0 / 3.0, 0.0, 0.0, 0.0, 1.0 / 3.0 ], [ # T=0 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], [ # T=t + coherence 0.4, 0.4, 0.6, 0.4, 0.2, 0.2, 0.6, 0.2, 0.4 ] ] sys = ReducedSystem(h0, [ 0, 1, 1, 1, 0, 1, 1, 1, 0, ]) kernel = OpenCLKernel(sys) kernel.compile() kernel.sync(state=states, y_0=1.0, t_bath=0) tf, rhof = kernel.reader_tfinal_rho(kernel.run(tr)) # test final time assert np.isclose(tf, tr[1]) # reference result (_, fstate, _, _) = opmesolve(h0, states, t_bath=0, y_0=1.0, tw=tw, tr=tr, kernel="QuTip") # test against reference assert_allclose(rhof[0], fstate[0], **QOP.TEST_TOLS) assert_allclose(rhof[1], fstate[1], **QOP.TEST_TOLS) assert_allclose(rhof[2], fstate[2], **QOP.TEST_TOLS)
def test_von_neumann(): """ integrate von Neumann equation to test the following: - reduced system with no transitions => von Neumann - evolve multiple states - all states at all times t should be recorded and be available in `result.tstate` - we test some physical properties of the results i) desity operator properties at all t ii) behavior of coherent elements (rotatation at certain w_ij) """ PRECISION_DT_ANGLE = 6 tr = (0.0, 13.37, 0.01) h0 = [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 5.5, ] # dipole coupling = 0 => no dissipative dynamics system = ReducedSystem(h0, np.zeros_like(h0)) kernel = OpenCLKernel(system) kernel.compile() # we confige a state whith 3 coherent elements. # we expect that the diagonal elements are constant # in time while the coherent elements rotate at # the transition frrquency, meaning # # d arg(<0|rho(t)|1>) * dt d = (w_1 - w_0) * 0.1 = 0.1 # d arg(<0|rho(t)|2>) * dt d = (w_2 - w_0) * 0.1 = 0.3 # d arg(<2|rho(t)|3>) * dt d = (w_3 - w_2) * 0.1 = 0.25 # expect_w10, expect_w20, expect_w32 = 1.0, 3.0, 2.5 ground_state = [ 0.7, 0.25, 0.5, 0.0, 0.25, 0.2, 0.0, 0.0, 0.5, 0.0, 0.0, 0.3, 0.0, 0.0, 0.3, 0.1 ] # this groundstate should be stationary. gs2 = [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ] # note that for y_0=0.0 the dissipator would vanish as well. kernel.sync(state=[ground_state, gs2], t_bath=0, y_0=1.0) tlist, ts = kernel.reader_rho_t(kernel.run(tr)) # test times assert_allclose(np.arange(tr[0], tr[1] + tr[2], tr[2]), tlist) assert tstate_rho_hermitian(ts) assert tstate_rho_trace(1.0, ts) # test diagonal elements, r_00(t+dt) - r_00(t) = 0 for all t assert np.allclose(ts[:, 0, 0, 0][:-1] - ts[:, 0, 0, 0][1:], 0) assert np.allclose(ts[:, 0, 1, 1][:-1] - ts[:, 0, 1, 1][1:], 0) assert np.allclose(ts[:, 0, 2, 2][:-1] - ts[:, 0, 2, 2][1:], 0) assert np.allclose(ts[:, 0, 3, 3][:-1] - ts[:, 0, 3, 3][1:], 0) # test rotation of coherent elements by # calulating(r_01(t+dt) - r_01(t))/dt r10 = np.round( (np.angle(ts[:, 0, 1, 0][:-1]) - np.angle(ts[:, 0, 1, 0][1:])) % np.pi, PRECISION_DT_ANGLE) assert np.all(r10 == expect_w10 * tr[2]) r20 = np.round( (np.angle(ts[:, 0, 2, 0][:-1]) - np.angle(ts[:, 0, 2, 0][1:])) % np.pi, PRECISION_DT_ANGLE) assert np.all(r20 == expect_w20 * tr[2]) r32 = np.round( (np.angle(ts[:, 0, 3, 2][:-1]) - np.angle(ts[:, 0, 3, 2][1:])) % np.pi, PRECISION_DT_ANGLE) assert np.all(r32 == expect_w32 * tr[2])
def test_von_neumann_basis(): """ we integrate a system which is not provided in eigenbase. two states are tests: 1. stationary (and pure) state |i><i| 2. some non stationary state test checks basic integrator and density operator properties and compares the result against QuTip reference solver. """ REF_TOL = 0.0001 tr = (0, 1, 0.001) h0 = [ 1, 1.5, 0, 1.5, 1.42, 3, 0, 3, 2.11, ] ev, s = np.linalg.eigh(np.array(h0).reshape((3, 3))) s = s.T rho1 = np.outer(s[0].conj().T, s[0]) rho2 = np.array([0.5, 0, 0, 0, 0.5, 0, 0, 0, 0], dtype=np.complex64).reshape((3, 3)) states = [rho1, rho2] system = ReducedSystem(h0) kernel = OpenCLKernel(system) kernel.compile() # we archive von Neumann by setting global damping to y_0= # which leads to supression of dissipative terms kernel.sync(state=states, y_0=0, t_bath=0) tlist, ts = kernel.reader_rho_t(kernel.run(tr)) # test times assert_allclose(np.arange(tr[0], tr[1] + tr[2], tr[2]), tlist) # test density operator assert tstate_rho_hermitian(ts[1:2]) assert tstate_rho_trace(1.0, ts) # test stationary state assert_allclose(ts[-1][0], rho1, **QOP.TEST_TOLS) # test against reference (_, fstate, _, _) = opmesolve(h0, states, 0, 0, tw=[], tr=tr, kernel="QuTip") assert_allclose(ts[-1][0], fstate[0], **QOP.TEST_TOLS) assert_allclose(ts[-1][1], fstate[1], **QOP.TEST_TOLS)
def test_complex_dipole_complex(): """ test whether complex components in dipole operator are interpreted correctly. """ # system parameters dimH = 5 t_bath = [0.0, 0.2, 0.5, 0.6] y_0 = 0.15 Omega = 1.4 tr = (0, 16.52, 0.005) state0 = np.zeros(dimH**2).reshape((dimH, dimH)) state0[0, 0] = 1 # operators Oa = op_a(dimH) Oad = Oa.conj().T On = Oad @ Oa Ox = Oa + Oad # non-complex dipole dipole = [ 0, 2 + 1j, 0, 3 - np.pi * 0.1j, 0, 2 - 1j, 0, -1j, 0, 4, 0, 1j, 0, 5, 0, 3 + np.pi * 0.1j, 0, 5, 0, 6j, 0, 4, 0, -6j, 0, ] # reduced system rs = ReducedSystem(Omega * On, dipole=dipole) # -- Run with QuTip kernel = QutipKernel(rs) kernel.compile() kernel.sync(t_bath=t_bath, y_0=y_0, state=[state0] * 4) tlist = time_gatter(*tr) (_, _, tstate, _) = kernel.run(tlist) # -- Run with OpenCL kernel kernelCL = OpenCLKernel(rs) kernelCL.compile() kernelCL.sync(t_bath=t_bath, y_0=y_0, state=state0.flatten()) tlist_cl, resultCL = kernelCL.reader_rho_t( kernelCL.run(tr, steps_chunk_size=132)) # -- compare all states at all times assert_allclose(tlist, tlist_cl) assert_allclose(resultCL, tstate, atol=1e-5, rtol=1e-7)
#!/usr/local/bin/python3 import numpy as np import qoptical as qo from qoptical.kernel_opencl import OpenCLKernel if __name__ == "__main__": qo.QO.DEBUG = True # two state system rs = qo.ReducedSystem([0, 0, 0, 1], dipole=[0, 1, 1, 0]) # three states at different temperatures rho0 = rs.thermal_state(T=[0, 0.1, 0.2, 0.3]) kernel = OpenCLKernel(system=rs) kernel.compile() kernel.sync(state=rho0, t_bath=[0, 0, 0, 15], y_0=0.5) runner = kernel.run((0, 200, 0.0005)) tf, rhof = kernel.reader_tfinal_rho(runner) print(tf, np.round(rhof, 3)) rhoth = rs.thermal_state(T=[0, 0, 0, 15]) print(tf, np.round(rhoth, 3))