tangelo.toolboxes.circuits package

Subpackages

Submodules

tangelo.toolboxes.circuits.diagonal_coulomb module

Module to generate the rotations to convert the 2-body integrals into a sum of diagonal terms

Refs:

[1] Mario Motta, Erika Ye, Jarrod R. McClean, Zhendong Li, Austin J. Minnich, Ryan Babbush, Garnet Kin-Lic Chan “Low rank representations for quantum simulation of electronic structure”. https://arxiv.org/abs/1808.02625

class tangelo.toolboxes.circuits.diagonal_coulomb.OrbitalRotations

Bases: object

The class that holds the various rotations, operators and coefficients

rotation_gates

The gates to apply to rotate the basis to a diagonal form for a given operator

Type:

list

qubit_operators

The qubit operators to measure from qubit_mapping=”JW” and up_then_down=False. Each is diagonal in the Z basis.

Type:

list

one_body_coefficients

The one-body coefficients corresponding to each operator

Type:

list

constants

The constants corresponding to each operator

Type:

list

two_body_coefficients

The two-body coefficients corresponding to each operator

Type:

list

add_elements(rot_mat, constant=0.0, one_body_coefs=None, two_body_coefs=None)

Add elements to the class for each term to diagonalize a portion of the Hamiltonian

Parameters:

• rot_mat (array) – The unitary rotation matrix

• constant (float) – A constant value for this element

• one_body_coefs (array) – The diagonal coefficients

• two_body_coefs (array) – The two-body coefficients

property n_rotations

tangelo.toolboxes.circuits.diagonal_coulomb.bogoliubov_transform(umat, add_phase=True)

Generate the gates that implement the orbital rotation defined by a given unitary.

The given matrix is decomposed into umat=DU where U is unitary D is a diagonal matrix. If umat is unitary, the values of D will be exp(1j*theta) where theta is real and can be incorporated using add_phase=True. If umat is non-unitary, the values of D will be m*exp(1j*theta) where m and theta are real. m is ignored with only the phase (theta) incorporated in the circuit if add_phase=True.

This implementation uses the circuit outlined in https://arxiv.org/abs/1711.05395

Parameters:

• umat (array) – The square unitary matrix that descibes the basis rotation

• add_phase (bool) – If True, adds PHASE gates according to givens decomposition values D

Returns:

list of Gate – The sequence of Gates that implement the orbital rotation

tangelo.toolboxes.circuits.diagonal_coulomb.get_orbital_rotations(molecule: SecondQuantizedMolecule)

Generate the gates that rotate the orbitals such that each operator is diagonal.

The orbital rotation gates generated are only applicable for qubit_mapping=”JW” and up_then_down=False.

Parameters:

molecule (SecondQuantizedMolecule) – The molecule for which the diagonal representation is requested

Returns:

OrbitalRotations – The class that contains the list of transformation gates and operators to measure

tangelo.toolboxes.circuits.discrete_clock module

Module to generate the circuits necessary to implement discrete clock time Refs:

[1] Jacob Watkins, Nathan Wiebe, Alessandro Roggero, Dean Lee, “Time-dependent Hamiltonian Simulation using Discrete Clock Constructions” arXiv: 2203.11353

tangelo.toolboxes.circuits.discrete_clock.get_adder_circuit(qubit_list: List[int], t: int) → Circuit

Return circuit that takes all bitstrings and add binary(t) to it.

Parameters:

• qubit_list (List[int]) – The qubits to apply the addition of t.

• t (int) – The integer to add

Returns:

Circuit – The circuit that applies the addition of t

tangelo.toolboxes.circuits.discrete_clock.get_discrete_clock_circuit(trotter_func: Callable[[...], Circuit], trotter_kwargs: dict, n_state_qus: int, time: float, n_time_steps: int, mp_order: int) → Circuit

Return discrete clock circuit as described in arXiv: 2203.11353

Parameters:

• trotter_func (Callable[..., Circuit]) – The function that implements the controlled 2nd order trotter time-evolution starting at “t0” for “time” using “n_trotter_steps” using “control”

• trotter_kwargs (dict) – Other keyword arguments for trotter_func.

• n_state_qus (int) – The number of qubits used to represent the state to time-evolve.

• time (float) – The total time to evolve.

• n_time_steps (int) – The number of time steps in the discrete clock.

• mp_order (int) – The multi-product order to use for the time-evolution.

Returns:

Circuit – The time-evolution circuit using the discrete clock construction.

tangelo.toolboxes.circuits.grid_circuits module

Module to generate the circuits for grid based computation

tangelo.toolboxes.circuits.grid_circuits.get_psquared_circuit(dt: float, dx: float, mass: float, qubit_list: List[int], control: int | List[int] = None) → Circuit

Return circuit for p^2/2/m as defined in arXiv:2006.09405 using qft

Parameters:

• dt (float) – Time to evolve.

• dx (float) – Grid spacing.

• mass (float) – The mass used for the time-evolution.

• qubit_list (List[int]) – Qubits to apply circuit to. The order is important depending on lsq_first or msq_first

• control (Union[int, List[int]]) – The control qubits

Returns:

Circuit – The circuit that applies exp(-1j*dt*p^2/2/m)

tangelo.toolboxes.circuits.grid_circuits.get_xsquared_circuit(dt: float, dx: float, fac: float, x0: float, delta: float, qubit_list: List[int], control: None | int | List[int] = None) → Circuit

Return circuit for exp(-1j*dt*[fac*(x - x0)**2 + delta]) as defined in arXiv:2006.09405

Parameters:

• dt (float) – Time to evolve.

• dx (float) – Grid spacing.

• fac (float) – Factor in front of x^2 term.

• x0 (float) – Shift for (x-x0)^2 term

• delta (float) – Constant shift

• qubit_list (List[int]) – Qubits to apply circuit to. The order is important depending on lsq_first or msq_first

• control (Union[int, List[int]]) – The control qubits

Returns:

Circuit – The circuit that applies exp(-1j*dt*[fac*(x-x0)**2 +delta])

tangelo.toolboxes.circuits.lcu module

Module to generate the circuits necessary to implement linear combinations of unitaries Refs:

[1] Dominic W. Berry, Andrew M. Childs, Richard Cleve, Robin Kothari, Rolando D. Somma, “Simulating Hamiltonian dynamics with a truncated Taylor series” arXiv: 1412.4687 Phys. Rev. Lett. 114, 090502 (2015)

tangelo.toolboxes.circuits.lcu.USelectkl(unitaries: List[QubitOperator], n_qubits_sv: int, kmax: int, control: int | List[int] = None) → Circuit

Generate the truncated Taylor series U_{Select} circuit for the list of QubitOperator as defined arXiv:1412.4687 The returned Circuit will have qubits defined in registers |n_qubits_sv>|kmax-1>|n_qubits_u>^{kmax-1}|ancilla> n_qubits_sv is the number of qubits to define the state to propagate. |kmax-1> defines the unary encoding of the Taylor series order. kmax-1 copies of length log2(len(unitaries)) to define the binary encoding of the linear combination of unitaries. Finally, one ancilla qubit to ensure the success of oblivious amplitude amplification. :param unitaries: The list of unitaries that defines the U_{Select} operation :type unitaries: list[QubitOperator] :param n_qubits_sv: The number of qubits in the statevector register :type n_qubits_sv: int :param kmax: The maximum Taylor series order :type kmax: int :param control: Control qubits for operation :type control: int or list[int]

Returns:

Circuit – The circuit that implements the truncated Taylor series U_{Select} operation

tangelo.toolboxes.circuits.lcu.Uprepkl(qu_op: QubitOperator, kmax: int, t: float) → Tuple[Circuit, List[QubitOperator], int]

Generate Uprep circuit using qubit encoding defined in arXiv:1412.4687 :param qu_op: :type qu_op: QubitOperator :param kmax: the order of the truncated Taylor series :type kmax: int :param t: The evolution time :type t: float

Returns:

• Circuit – The Uprep circuit for the truncated Taylor series

• list – the individual QubitOperator unitaries with only the prefactor remaining. i.e. all coefficients are 1, -1, 1j or -1j

• int – The number of repeated applications of the circuit that need to be applied

tangelo.toolboxes.circuits.lcu.get_lcu_qubit_op_info(qu_op: 0) → Tuple[List[int], List[int], float]

Return the operator and auxillary qubit indices and 1-norm for the LCU block decomposition of given QubitOperator. :param qu_op: The qubit operator to decompose into an Linear Combination of Unitaries block encoding. :type qu_op: QubitOperator

Returns:

• List[int] – The qubit operator indices.

• List[int] – The auxillary qubits for the uprep circuit.

• float – The 1-norm of the qubit operator.

tangelo.toolboxes.circuits.lcu.get_oaa_lcu_circuit(qu_op: QubitOperator, control: int | List[int] = None) → Circuit

Apply qu_op using linear combination of unitaries (LCU) with oblivious amplitude amplification (OAA) 1-norm of coefficients must be less than 2. The unitarity of qu_op is not checked by the algorithm :param qu_op: The qu_op to apply. Must be nearly unitary for algorithm to succeed with high probability. :type qu_op: QubitOperator :param control: Control qubit(s) :type control: int or list[int]

Returns:

Circuit – The circuit that implements the linear combination of unitaries for the qu_op

tangelo.toolboxes.circuits.lcu.get_truncated_taylor_series(qu_op: QubitOperator, kmax: int, t: float, control: int | List[int] = None) → Circuit

Generate Circuit to implement the truncated Taylor series algorithm as implemented in arXiv:1412.4687 :param qu_op: The qubit operator to apply the truncated Taylor series exponential :type qu_op: QubitOperator :param kmax: The maximum order of the Taylor series exp{-1j*t*qu_op} = sum_{k}^{kmax}(-1j*t)**k/k! qu_op**k :type kmax: int :param t: The total time to evolve :type t: float :param control: The control qubit(s) :type control: int or list[int]

Returns:

Circuit – the circuit that implements the time-evolution of qu_op for time t with Taylor series kmax

tangelo.toolboxes.circuits.lcu.get_truncated_taylor_series_qubits(qu_op: QubitOperator, kmax: int)

Return the list of qubits used in the Truncated Taylor series circuit :param qu_op: :type qu_op: QubitOperator :param kmax: the order of the truncated Taylor series :type kmax: int

Returns:

List[int] – The list of qubit indices used

tangelo.toolboxes.circuits.lcu.get_unary_prep(kvec: ndarray, kmax: int) → Circuit

Generate the prep circuit for the unary+ancilla part of the Taylor series encoding. This implementation scales linearly with kmax whereas StateVector.initializing_circuit() scaled exponentially.

Parameters:

• kvec (array) – Array representing the coefficients needed to generate unary portion of encoding. Length of array is kmax+2. order “00…000”, “00…001”, “00…011”, …, “01…111”, “1000…”

• kmax (int) – The Taylor series order

Returns:

Circuit – The unary encoding prep circuit

tangelo.toolboxes.circuits.lcu.get_uprep_uselect(qu_op: QubitOperator, control: int | List[int] = None, make_alpha_eq_2: bool = False) → Tuple[Circuit, Circuit, List[int], List[int], float]

Get uprep and (controlled-)uselect circuits along with their corresponding qubits for a QubitOperator. :param qu_op: The qu_op to apply. :type qu_op: QubitOperator :param control: Control qubit(s). :type control: int or list[int] :param make_alpha_eq_2: Make 1-norm equal 2 by adding and subtracting identity terms. Useful for oblivious amplitude amplification

Returns:

• Circuit – Uprep circuit

• Circuit – Uselect circuit

• List[int] – QubitOperator qubits

• List[int] – Auxillary qubits

• float – alpha = 1-norm of coefficients of applied qu_op

tangelo.toolboxes.circuits.lcu.sign_flip(qubit_list: List[int], control: int | List[int] = None) → Circuit

Generate Circuit corresponding to the sign flip of the |0>^n vector for the given qubit_list :param qubit_list: The list of n qubits for which the 2*|0>^n-I operation is generated :type qubit_list: list[int] :param control: Control qubit or list of control qubits. :type control: int or list[int]

Returns:

Circuit – The circuit that generates the sign flip on |0>^n

tangelo.toolboxes.circuits.multiproduct module

Module to generate the circuits necessary to implement multi-product time-evolution Refs:

[1] Guang Hao Low, Vadym Kliuchnikov and Nathan Wiebe, “Well-conditioned multi-product Hamiltonian simulation” arXiv: 1907.11679

tangelo.toolboxes.circuits.multiproduct.get_ajs_kjs(order: int) → Tuple[List[float], List[int], int]

Return aj coefficients and number of steps kj for multi-product order The first two indices of aj coefficients are the portion need to make the one-norm sum to two.

Parameters:

order (int) – The desired order of expansion

Returns:

List[float], List[int], int – aj coefficients, kj steps, number of ancilla qubits needed

tangelo.toolboxes.circuits.multiproduct.get_multi_product_circuit(time: float, order: int, n_state_qus: int, operator: None | QubitOperator | FermionOperator = None, control: int | list = None, second_order_trotter: None | Callable[[...], Circuit] = None, trotter_kwargs: dict | None = None) → Circuit

Return multi-product circuit as defined in arXiv: 1907.11679. Only up to 6th order is currently supported

Parameters:

• time (float) – The time to evolve.

• order (int) – The order of the multi-product expansion

• n_state_qus (int) – The number of qubits in the state to evolve.

• operator (Union[QubitOperator, FermionOperator]) – The operator to evolve in time. Default None

• control (Union[int, List[int]]) – The control qubit(s). Default None

• second_order_trotter (Callable[..., Circuit]) – The callable function that defines the controlled 2nd order time-evolution. Must have arguments “control” and “n_trotter_steps”.

• trotter_kwargs (dict) – Other keyword arguments necessary to evaluate second_order_trotter.

Returns:

Circuit – The circuit representing the time-evolution using the multi-product construction.

tangelo.toolboxes.circuits.qsp module

Module to generate the circuits necessary to implement quantum signal processing (QSP) Hamiltonian Simulation

Ref: [1]: Yulong Dong, Xiang Meng, K. Birgitta Whaley, Lin Lin, “Efficient phase-factor evaluation in quantum signal processing” 2021, arXiv:2002.11649 (https://arxiv.org/abs/2002.11649)

tangelo.toolboxes.circuits.qsp.get_qsp_circuit_no_anc(cua: Circuit, m_qs: List[int], angles: List[float], control: int | List[int] = None, with_z: bool = False) → Circuit

Generate the ancilla free QSP circuit as defined in Fig 16 of https://arxiv.org/abs/2002.11649.

Parameters:

• cua (Circuit) – The controlled unitary (U_A).

• m_qs (List[int]) – The m ancilla qubits used for the Uprep circuit.

• angles (List[float]) – The phases for the QSP circuit.

• control (Union[int, List[int]]) – The control qubit(s).

• with_z (bool) – If True, an extra CZ gate is included. This adds a 1j phase to the operation.

Returns:

Circuit – The ancilla free QSP circuit

tangelo.toolboxes.circuits.qsp.get_qsp_hamiltonian_simulation_circuit(qu_op: QubitOperator, tau: float, eps: float = 0.0001, control: int | List[int] = None, n_attempts: int = 10, method: str = 'laurent', folder: str = None) → Circuit

Returns Quantum Signal Processing (QSP) Hamiltonian simulation circuit for a given QubitOperator for time tau.

The circuits are derived from https://arxiv.org/abs/2002.11649. The list of qubits used for the circuit can be found by qubit_list = get_qs_hamiltonian_simulation_qubit_list(qu_op) qu_op must have it’s spectral range in [-1, 1]. This property is not checked by this function.

Parameters:

• qu_op (QubitOperator) – The qubit operator defining the QSP time-evolution circuit.

• tau (float) – The evolution time.

• eps (float) – The allowed error of the time-evolution. Higher accuracy requires longer circuits, and obtaining the phases can be unstable.

• control (Union[int, List[int]]) – The control qubit(s).

• n_attempts (int) – The number of attempts to calculate the phase factors using pyqsp.

• method (str) – “laurent”: Use laurent polynomial method of pyqsp, “tf”: Use TensorFlow with pyqsp, “QSPPACK”: Use QSPPACK to calculate phases

• folder (str) – Folder that contains QSPPACK.

Returns:

Circuit – The QSP Hamiltonian simulation circuit with oblivious amplitude amplification to ensure very high success probability.

tangelo.toolboxes.circuits.qsp.get_qsp_hamiltonian_simulation_qubit_list(qu_op: QubitOperator) → List[int]

Returns the list of qubits used for the QSP Hamiltonian simulation algorithm

tangelo.toolboxes.circuits.qsp.ham_sim_phases(tau: float, eps: float = 0.01, n_attempts: int = 10, method: str = 'laurent') → Tuple[List[float], List[float]]

Generate the phases required for QSP time-evolution using the pyqsp package

Parameters:

• tau (float) – The evolution time.

• eps (float) – The precision to calculate the factors. Higher precision is more likely to fail.

• n_attempts (int) – The number of attempts to calculate the phase factors. Often multiple tries are required.

• method – “laurent”: Laurent Polynomial method (unstable but fast). “tf” requires TensorFlow installed and is stable but very slow.

Returns:

• List[float] – The phases for Cos(Ht).

• List[float] – The phases for i*Sin(Ht).

tangelo.toolboxes.circuits.qsp.ham_sim_phases_QSPPACK(folder: str, tau: float, eps: float = 1e-07) → Tuple[List[float], List[float]]

Generate the phases required for QSP time-evolution using the QSPPACK package.

QSPPACK is an Matlab/Octave based package that calculates the phase factors. To run this function, a user needs to have: 1) Octave installed and accessible in path. Octave can be found at https://octave.org/ 2) oct2py installed. pip install oct2py 3) QSPPACK downloaded in an accessible folder. Can be found at https://github.com/qsppack/QSPPACK/tree/dev

Parameters:

• folder (str) – The folder location of QSPPACK.

• tau (float) – The evolution time.

• eps (float) – The precision to calculate the factors.

Returns:

• List[float] – The phases for Cos(Ht).

• List[float] – The phases for i*Sin(Ht).

tangelo.toolboxes.circuits.qsp.zero_controlled_cnot(qubit_list: List[int], target: int, control: int | List[int]) → Circuit

Return the circuit for a zero-controlled CNOT gate with possible extra controls on 1.

Parameters:

• qubit_list (List[int]) – The qubits controlled by zero.

• target (int) – The target qubit.

• control (List[int] or int) – The qubits controlled by one.

Returns:

Circuit – The zero controlled cnot circuit with possible extra controls on 1.

Module contents