g#dZddlmZddlZddlZddlmZddlmZddl Z ddl m Z ddl mZddlmZmZdd lmZd d lmZmZejr dd l mZdd lmZGddeZddZdS)z#The Suzuki-Trotter product formula.) annotationsN)Callable)chain)ParameterExpression)QuantumCircuit) SparsePauliOpPauli) deprecate_arg)ProductFormulareorder_paulis)ParameterValueType)PauliEvolutionGateceZdZdZeddddd d d!fd Zd"dZedZxZ S)# SuzukiTrottera The (higher order) Suzuki-Trotter product formula. The Suzuki-Trotter formulas improve the error of the Lie-Trotter approximation. For example, the second order decomposition is .. math:: e^{A + B} \approx e^{B/2} e^{A} e^{B/2}. Higher order decompositions are based on recursions, see Ref. [1] for more details. In this implementation, the operators are provided as sum terms of a Pauli operator. For example, in the second order Suzuki-Trotter decomposition we approximate .. math:: e^{-it(XI + ZZ)} = e^{-it/2 XI}e^{-it ZZ}e^{-it/2 XI} + \mathcal{O}(t^3). References: [1]: D. Berry, G. Ahokas, R. Cleve and B. Sanders, "Efficient quantum algorithms for simulating sparse Hamiltonians" (2006). `arXiv:quant-ph/0508139 `_ [2]: N. Hatano and M. Suzuki, "Finding Exponential Product Formulas of Higher Orders" (2005). `arXiv:math-ph/0506007 `_ atomic_evolutionz1.4c^|duo)ttj|jdkS)N)leninspect signature parameters)callables _/granary/edev/quantum/lib/python3.11/site-packages/qiskit/synthesis/evolution/suzuki_trotter.pyzSuzukiTrotter.Bs184#7$= !(++6 7 71 <zkThe 'Callable[[Pauli | SparsePauliOp, float], QuantumCircuit]' signature of the 'atomic_evolution' argumentzInstead you should update your 'atomic_evolution' function to be of the following type: 'Callable[[QuantumCircuit, Pauli | SparsePauliOp, float], None]'.)namesince predicatedeprecation_descriptionadditional_msgrr FrNTorderintrepsinsert_barriersbool cx_structurestrCallable[[Pauli | SparsePauliOp, float], QuantumCircuit] | Callable[[QuantumCircuit, Pauli | SparsePauliOp, float], None] | Nonewrappreserve_orderreturnNonec |dkr|dzdkrtd|dt|||||||dS)aV Args: order: The order of the product formula. reps: The number of time steps. insert_barriers: Whether to insert barriers between the atomic evolutions. cx_structure: How to arrange the CX gates for the Pauli evolutions, can be ``"chain"``, where next neighbor connections are used, or ``"fountain"``, where all qubits are connected to one. This only takes effect when ``atomic_evolution is None``. atomic_evolution: A function to apply the evolution of a single :class:`.Pauli`, or :class:`.SparsePauliOp` of only commuting terms, to a circuit. The function takes in three arguments: the circuit to append the evolution to, the Pauli operator to evolve, and the evolution time. By default, a single Pauli evolution is decomposed into a chain of ``CX`` gates and a single ``RZ`` gate. Alternatively, the function can also take Pauli operator and evolution time as inputs and returns the circuit that will be appended to the overall circuit being built. wrap: Whether to wrap the atomic evolutions into custom gate objects. This only takes effect when ``atomic_evolution is None``. preserve_order: If ``False``, allows reordering the terms of the operator to potentially yield a shallower evolution circuit. Not relevant when synthesizing operator with a single term. Raises: ValueError: If order is not even r rzfSuzuki product formulae are symmetric and therefore only defined for when the order is 1 or even, not .)r+N) ValueErrorsuper__init__) selfr"r$r%r'rr*r+ __class__s rr2zSuzukiTrotter.__init__?sj 199aA8=AAA        )      r evolutionr/list[tuple[str, list[int], ParameterValueType]]c.|j}|jfdt|trfd|D}nd|D}j|}jttj|z}|S)aExpand the Hamiltonian into a Suzuki-Trotter sequence of sparse gates. For example, the Hamiltonian ``H = IX + ZZ`` for an evolution time ``t`` and 1 repetition for an order 2 formula would get decomposed into a list of 3-tuples containing ``(pauli, indices, rz_rotation_angle)``, that is: .. code-block:: text ("X", [0], t), ("ZZ", [0, 1], 2t), ("X", [0], t) Note that the rotation angle contains a factor of 2, such that that evolution of a Pauli :math:`P` over time :math:`t`, which is :math:`e^{itP}`, is represented by ``(P, indices, 2 * t)``. For ``N`` repetitions, this sequence would be repeated ``N`` times and the coefficients divided by ``N``. Args: evolution: The evolution gate to expand. Returns: The Pauli network implementing the Trotter expansion. cvfd|D}jst|S|S)NcXg|]&\}}}||t|zdzjz f'Sr) real_or_failr$).0pauliindicescoeffr3times r z@SuzukiTrotter.expand..to_sparse_list..sO)E7Ee!4!4t!;a!?$)!KLr)to_sparse_listr+r )operatorpaulisr3r@s rrBz,SuzukiTrotter.expand..to_sparse_lists\-5-D-D-F-FF& .%f---Mrc&g|] }|SrF)r<rCrBs rrAz(SuzukiTrotter.expand..s#PPP(^^H55PPPrcg|]}|gSrFrF)r<ops rrAz(SuzukiTrotter.expand..sFFFbbTFFFr) rCr@ isinstancelist_recurser"r$r from_iterable)r3r5 operators non_commutingproduct_formula flattenedr@rBs` @@rexpandzSuzukiTrotter.expands4& ~       i & & GPPPPiPPPMMGFNN9,E,EFFFM-- MBBIU%8%I%I J JJ rc~|dkr|S|dkr?d|ddD}|dg}||ztt|zSdddd|dz z zz z dt|dz fd|Dz}t|dz fd|D}||z|zS)Nr rc&g|]}d|DS)c&g|]\}}}|||dz fSr:rF)r<labelqubitsr?s rrAz5SuzukiTrotter._recurse...s*OOO0Dvu%+OOOrrF)r<rDs rrAz*SuzukiTrotter._recurse..s7POOOOrc,g|]}fd|DS)c(g|]\}}}|||zfSrFrFr<rUrVr? reductions rrAz5SuzukiTrotter._recurse...s,[[[.s?\[[[TZ[[[rc,g|]}fd|DS)c4g|]\}}}|||ddzz zfS)r rXrFr[s rrAz5SuzukiTrotter._recurse...sD0E65Q]1B(CDrrFr]s rrAz*SuzukiTrotter._recurse..sL  4:r)rJreversedrrK)r"grouped_paulishalvesfullouterinnerr\s @rrKzSuzukiTrotter._recurses. A::! ! aZZ,SbS1F#2&'DD=4(8(8#9#99 9QqEAI!778I .. "0E"**  #1   E5=5( (r)rr FrNFT)r"r#r$r#r%r&r'r(rr)r*r&r+r&r,r-)r5rr,r6) __name__ __module__ __qualname____doc__r r2rQ staticmethodrK __classcell__)r4s@rrr#s6] == * V     %# #4 4 4 4 4 4   4 l3333j))\)))))rrdc t|tr|S|tjtjz}t tj||krtj|Std|d)zReturn real if close, otherwise fail. Unbound parameters are left unchanged. Based on NumPy's ``real_if_close``, i.e. ``tol`` is in terms of machine precision for float. zEncountered complex value z, but expected real.) rIrnpfinfofloatepsabsimagrealr0)valuetolabstols rr;r;st %,-- 28E??& &F 275>>V##wu~~ M%MMM N NNr)rl)ri __future__rrtypingcollections.abcr itertoolsrnumpyrn"qiskit.circuit.parameterexpressionrqiskit.circuit.quantumcircuitrqiskit.quantum_info.operatorsrr qiskit.utils.deprecationr rOr r TYPE_CHECKINGr&qiskit.circuit.library.pauli_evolutionrrr;rFrrrsN*)"""""" $$$$$$BBBBBB888888>>>>>>>>222222;;;;;;;; J@@@@@@IIIIIIu)u)u)u)u)Nu)u)u)p O O O O O Or