Hamiltonian 演化

oracq.algorithms.common.hamiltonian

Hamiltonian decomposition, Pauli evolution, Trotter and truncated Taylor encoding.

oracq.algorithms.common.hamiltonian.trotter_hamsim(terms, final_time, *, steps=2)

First-order Trotter product-formula simulation of the evolution under a Pauli-decomposed Hamiltonian.

For H = sum_j c_j P_j it synthesizes exp(-i*H*t) as the steps-th power of prod_j exp(-i*c_j*P_j*t/steps): each Pauli word is folded, through basis changes and a CNOT chain, into a phase rotation on the last active qubit and then restored in reverse order. The circuit body is a single Repeat(steps) block and is not expanded per step at generation or serialization time; an all-I word consumes no qubits and degenerates to a global phase.

参数:

• terms -- Sequence of (coefficient, Pauli word) pairs; the coefficients are real numbers, converted through float, and the Pauli words are equal-width strings of I/X/Y/Z.

• final_time -- Total evolution time t.

• steps -- Number of repeated steps, at least 1; more steps give a smaller product-formula error.

返回:

A bare unitary operation rather than a block encoding; the registers are target, of word width, and a zero-width signal, and the whole approximates exp(-i*H*t).

返回类型:

Operation

抛出:

ValidationError -- The term sequence is empty, steps is below 1, or the Pauli word widths differ.

oracq.algorithms.common.hamiltonian.taylor_hamiltonian(hamiltonian, time, *, degree=2)

A closable plain Hamiltonian-function block encoding; replaceable by a QSP/HamSim protocol.

参数:

• hamiltonian -- Block encoding of the operator.

• time -- Evolution time, a finite real number.

• degree -- Taylor truncation order, an integer not less than 0; order 0 keeps only the identity term.

返回:

LCU block encoding of the truncated Taylor series, with correctness marked pending.

返回类型:

BlockEncoding

class oracq.algorithms.common.hamiltonian.HermitianProtocol(*args, **kwargs)

基类：Protocol

Access protocol by which the host declares the Hermiticity of an operator.

property hermitian

Whether the operator is declared Hermitian; hamiltonian_simulation accepts only True.

class oracq.algorithms.common.hamiltonian.EvolvableProtocol(*args, **kwargs)

基类：Protocol

Access protocol by which the host declares that an operator can produce its own unitary evolution.

evolution(time)

Return the unitary Operation of this operator for the given evolution time.

The Trotter path requires the returned evolution to need no postselection: apart from target, all public registers are zero width.

参数:

time -- Evolution time, a finite real number.

返回:

The unitary evolution operation of this operator for the given duration.

返回类型:

Operation

class oracq.algorithms.common.hamiltonian.TrotterizableProtocol(*args, **kwargs)

基类：Protocol

Access protocol by which the host declares that an operator decomposes into a Trotter term list.

trotter_list()

Return the TrotterTerm sequence constituting the Hamiltonian; hamiltonian_simulation requires it to be nonempty.

返回:

The product-formula term sequence constituting the Hamiltonian, required to be nonempty.

返回类型:

Sequence[TrotterTerm]

class oracq.algorithms.common.hamiltonian.TrotterTerm(coefficient, operator)

基类：object

A single Hamiltonian term of a product formula: a real coefficient combined with an evolvable operator.

变量:

• coefficient (float) -- Real coefficient of the term; the Trotter path calls operator.evolution with duration coefficient * time / steps.

• operator (object) -- An operator satisfying EvolvableProtocol.

抛出:

ValidationError -- coefficient is not a finite real number, or operator does not satisfy EvolvableProtocol.

coefficient

operator

class oracq.algorithms.common.hamiltonian.PauliOperator(word)

基类：object

A single Pauli word operator; satisfies HermitianProtocol and EvolvableProtocol.

变量:

• word (str) -- A nonempty string of I/X/Y/Z with width at most 64.

• hermitian -- Always True; this is the HermitianProtocol declaration.

抛出:

ValidationError -- word is not a nonempty I/X/Y/Z string, or its width exceeds 64.

word

hermitian = True

block_encoding()

Return the alpha=1.0 block encoding of this Pauli word: per-qubit single-qubit gates plus a zero-width signal.

返回:

The Pauli word block encoding with scale 1.0.

返回类型:

BlockEncoding

evolution(time)

Return the exact unitary evolution of exp(-1j*word*time) (a single term in a single step, with no product-formula error).

参数:

time -- Evolution time, a finite real number.

返回:

The exact unitary evolution operation synthesized in a single term and single step.

返回类型:

Operation

class oracq.algorithms.common.hamiltonian.PauliHamiltonian(terms)

基类：object

A real-coefficient linear combination of equal-width Pauli words; supports both block-encoding and Trotter decomposition access.

变量:

• terms (tuple[tuple[float, str], ...]) -- Tuple of (coefficient, Pauli word) pairs; the coefficients are finite real numbers and all words have equal width.

• hermitian -- Always True; this is the HermitianProtocol declaration.

抛出:

ValidationError -- The term list is empty, a coefficient is not a finite real number, a Pauli word is invalid, or the widths differ.

terms

hermitian = True

block_encoding()

Return the LCU block encoding of the nonzero-coefficient terms; with no nonzero term it degenerates to the zero-operator block encoding.

返回:

LCU block encoding with scale equal to the sum of absolute coefficient values, or the zero operator with no nonzero term.

返回类型:

BlockEncoding

trotter_list()

Wrap each (coefficient, word) into a TrotterTerm and return the tuple.

返回:

Tuple of Trotter terms wrapping each coefficient and Pauli word one by one.

返回类型:

tuple[TrotterTerm, ...]

class oracq.algorithms.common.hamiltonian.EncodedOperator(encoding, hermitian)

基类：object

Host declaration of matrix properties; may represent non-Hermitian operators and does not claim to itself be a unitary.

encoding

hermitian

block_encoding()

Return the block encoding carried at construction.

返回:

The block encoding passed at construction, adapted and validated.

返回类型:

BlockEncoding

oracq.algorithms.common.hamiltonian.hamiltonian_simulation(operator, time, *, method='auto', steps=2, qsp=None)

Currently prefers the decomposable Trotter path; QSP requires the caller to supply an actual implementation.

参数:

• operator -- An operator declaring Hermitian, which must additionally satisfy the Trotter-decomposable or block-encodable protocol.

• time -- Evolution time, a finite real number.

• method -- Path selection, one of auto, trotter or qsp; auto picks by the operator protocol.

• steps -- Number of repeated segments of the Trotter product formula, a positive integer.

• qsp -- An actual implementation of the form qsp(BE, time) returning a BlockEncoding; needed only by the qsp path.

返回:

Block encoding of the evolution exp(-iHt); the Trotter path has scale 1.0.

返回类型:

BlockEncoding