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Haiqu.mps_loading(mps, shape=‘plr’, num_layers=2, truncation_cutoff=1e-06, fine_tuning_iterations=20, name=None)

Generate a quantum circuit that prepares a quantum state from matrix product state (MPS). The MPS is normalized in the process, and expect physical index to be of size 2. Given a MPS, this method creates a Data Loading job that runs in the Haiqu cloud. The result of this job is a circuit which can be used to supply the state to a quantum algorithm for processing. Two MPS formats are supported:
  1. Standard form (only site tensors): 
    │     │     │     │        │
A₁ ── A₂ ── A₃ ── A₄ ─ ⋯ ─ Aₙ
  2. Vidal form (site and bond tensors): 
    │           │           │              │
Γ₁ ── Λ₁ ── Γ₂ ── Λ₂ ── Γ₃ ── Λ₃ ─ ⋯ ─ Γₙ
The complexity and quality of the generated circuit can be controlled by the num_layers, truncation_cutoff, and fine_tuning_iterations parameters. Passing the MPS with high bond dimension may degrade the quality and synthesis time.
  • Parameters:
    • mps (Sequence) — The MPS in either standard or Vidal form. Standard form expects a list of rank-3 site tensors (one per each qubit). Vidal form is a tuple of site and bond tensors, where bonds tensors are rank-1 or diagonal rank-2 tensors. The MPS type is determined automatically. Standard form includes left- and right-canonical forms, while Vidal form includes central canonical form.
    • shape (str) — shape of site tensors of the MPS. Site tensors are rank-3 tensors. Shape defines the order of axes in it. p - physical index, l - left index, r - right index. Defaults to “plr”, which is standard order in Qiskit.
    • num_layers (int) — The number of layers in the generated circuit. More layers can improve the quality of the output vector at the cost of a deeper circuit. Defaults to 2.
    • truncation_cutoff (Real) — The entanglement cutoff for later layers. Increasing this threshold may result in a smaller (but more approximate) circuit. Defaults to 1e-6.
    • fine_tuning_iterations (int) — The maximum number of fine-tuning iterations to perform after each layer is added. Increasing this limit may improve the quality of the circuit by using more classical resources. Defaults to 20.
    • name (str | None) — The name for the job and the produced circuit. If None (default), a name will be automatically generated.
  • Returns: The Data Loading job that will generate the circuit from the MPS.
  • Return type: DataLoadingJobModel

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Examples

Loading Qiskit MPS: 
>>> qc = qiskit.QuantumCircuit(2)
>>> qc.h(0)
>>> qc.cx(0, 1)  # prepare test Bell state
>>> qc.save_matrix_product_state(label="mps")
>>> mps = AerSimulator().run(qc).result().data(0)["mps"]  # get MPS from Aer Simulator
>>> job = haiqu.mps_loading(mps)
>>> mps_gate = job.result()
>>> print(f"MPS was loaded with fidelity {job.fidelity:.3f}")
MPS was loaded with fidelity 1.000
>>> mps_qc = qiskit.QuantumCircuit(2)
>>> mps_qc.compose(mps_gate, inplace=True)
>>> print(haiqu.statevector_run(mps_qc).result())  # confirm the Bell state was loaded
[array([0.70710678+0.j, 0.        +0.j, 0.        +0.j, 0.70710678+0.j])]
Preparing a ground state of a Hamiltonian: 
>>> import quimb.tensor as qtn  # !pip install quimb (if not present)
>>> H = qtn.MPO_ham_heis(4, j=1.0, cyclic=False)  # Heisenberg hamiltonian
>>> dmrg = qtn.DMRG2(H, bond_dims=[4, 8])
>>> dmrg.solve(tol=1e-12)  # find the ground state
>>> job = haiqu.mps_loading(dmrg.state.arrays, shape="lpr")  # Quimb uses another shape
>>> heis_gs = qiskit.QuantumCircuit(4)
>>> heis_gs.compose(job.result(), inplace=True)  # circuit preparing the ground state
>>> print(f"Ground state was loaded with fidelity {job.fidelity:.3f}")
Ground state was loaded with fidelity 1.000