Simulation of molecule in Qiskit using DMET and SQD

Simulation of molecule in Qiskit using DMET and SQD Ask Question Asked 4 days ago Modified 4 days ago Viewed 34 times 0 I need some help with quantum chemistry calculations I’m running using Qiskit. I am trying to simulate a benzene molecule using Density Matrix Embedding Theory (DMET) together with Sample-based Quantum Diagonalization (SQD). In this framework, the molecule is divided into smaller fragments — in this case, six C–H fragments. The Hamiltonian of the full system is decomposed into smaller fragment Hamiltonians, which can then be solved independently. The DMET procedure converges when the sum of the traces of the one-particle reduced density matrices over all fragments equals the total number of electrons in the system. The problem is encoded into a quantum circuit using the LUCJ ansatz implemented in ffsim. More details about DMET can be found in this paper: https://pubs.acs.org/doi/full/10.1021/acs.jctc.6b00316 The issue is that, when I run a noiseless quantum simulation, I do not obtain a stable solution. When I solve the same problem classically using a CCSD solver, all fragments give identical energies and particle numbers, as expected from symmetry. However, in the quantum simulation, the fragment energies and particle numbers differ slightly, with discrepancies on the order of 0.001. Although these differences seem small, they are large enough to prevent DMET convergence. I want to emphasize that the simulation is completely noiseless. Does anyone have suggestions on how I could improve the accuracy or stability of the simulation? Here is a relevant snippet of my code showing how the quantum simulation is set up. t1 = mycc.t1 #T1 operator obtained from a previous CCSD calculation t2 = mycc.t2 #T2 operator obtained from a previous CCSD calculation n_reps = 1 #number of repetitions of the LUCJ ansatz alpha_alpha_indices = [(p, p + 1) for p in range(norbs_as - 1)] alpha_beta_indices = None fake_backend = FakeFez() simulator = AerSimulator() pass_manager, alpha_beta_indices = ffsim.qiskit.generate_lucj_pass_manager( backend = fake_backend, norb = norbs_as, #number of spatial orbitals connectivity = 'heavy-hex', interaction_pairs = (alpha_alpha_indices,alpha_beta_indices), optimization_level = 3, ) print(alpha_beta_indices) ucj_op = ffsim.UCJOpSpinBalanced.from_t_amplitudes( t2=t2, t1=t1, n_reps=n_reps, interaction_pairs=(alpha_alpha_indices, alpha_beta_indices), optimize=True, options=dict(maxiter=1000), ) qubits = QuantumRegister(2*norbs_as, name='q') circuit = QuantumCircuit(qubits) hf = ffsim.qiskit.PrepareHartreeFockJW(norbs_as,(nelec_as//2,nelec_as//2)) circuit.append(hf,qubits) circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op),qubits) circuit.measure_all() print('Original circuit',circuit.count_ops(),'num_qubits:',circuit.num_qubits) isa_circuit = pass_manager.run(circuit) print('Transpiled circuit',isa_circuit.count_ops(),'num_qubits:',isa_circuit.num_qubits) job = simulator.run(isa_circuit,shots = 100_000) primitive_result = job.result() counts = primitive_result.get_counts(0) On the other hand, when I run the same simulation on real quantum hardware, the solution is much more stable across the different fragments and DMET convergence is achieved. This is very strange, since the hardware simulation is noisy, yet it performs better than the noiseless simulation. Here is the code for the simulation in real hardware: t1 = mycc.t1 #T1 operator obtained from a previous CCSD calculation t2 = mycc.t2 #T2 operator obtained from a previous CCSD calculation n_reps = 1 #number of repetitions of the LUCJ ansatz alpha_alpha_indices = [(p, p + 1) for p in range(norbs_as - 1)] alpha_beta_indices = None service = QiskitRuntimeService(token='---') backend = service.backend('ibm_fez') pass_manager, alpha_beta_indices = ffsim.qiskit.generate_lucj_pass_manager( backend = backend, norb = norbs_as, #number of spatial orbitals connectivity = 'heavy-hex', interaction_pairs = (alpha_alpha_indices,alpha_beta_indices), optimization_level = 0, ) print(alpha_beta_indices) ucj_op = ffsim.UCJOpSpinBalanced.from_t_amplitudes( t2=t2, t1=t1, n_reps=n_reps, interaction_pairs=(alpha_alpha_indices, alpha_beta_indices), optimize=True, options=dict(maxiter=1000), ) qubits = QuantumRegister(2*norbs_as, name='q') circuit = QuantumCircuit(qubits) hf = ffsim.qiskit.PrepareHartreeFockJW(norbs_as,(nelec_as//2,nelec_as//2)) circuit.append(hf,qubits) circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op),qubits) circuit.measure_all() print('Original circuit',circuit.count_ops(),'num_qubits:',circuit.num_qubits) sampler = Sampler(mode=backend) sampler.options.dynamical_decoupling.enable = True isa_circuit = pass_manager.run(circuit) print('Transpiled circuit',isa_circuit.count_ops(),'num_qubits:',isa_circuit.num_qubits) job = sampler.run([isa_circuit], shots = 10_000) primitive_result = job.result() pub_result = primitive_result[0] counts = pub_result.data.meas.get_counts() Any comments or insights on this issue are very appreciated. Thank you. qiskitchemistry Share Improve this question Follow asked May 11 at 21:45 Daniel 111 1 bronze badge Hi, try to set in the simulation an optimization level = 0 instead of 3. I believe (but is a hypothesis) the transpiler is breaking the symmetry. Could you give me some feedback if this was the issue? :) –  Enrique Anguiano Vara Commented May 12 at 21:06 Add a comment Know someone who can answer? Share a link to this question via email, Twitter, or Facebook. Your Answer Sign up or log in Sign up using Google Sign up using Email and Password Post as a guest Name Email Required, but never shown Post Your Answer By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions qiskitchemistry See similar questions with these tags. 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