Expectation — Hamiltonian and Pauli Expectation Values

API reference for expectation value computation functions. These functions compute the expected value of observable operators with respect to quantum states prepared by quantum programs.

expval_hamiltonian

Computes the expectation value of a Hamiltonian operator with respect to the quantum state prepared by a given program.

Signature

expval_hamiltonian(
    prog: QProg,
    hamiltonian: Hamiltonian,
    shots: int = 1,
    model: NoiseModel = NoiseModel(),
    used_threads: int = 4,
    backend: str = "CPU",
    init_state: list[complex] = []
) -> float

Parameters

Parameter	Type	Description
prog	QProg	Quantum program preparing the state
hamiltonian	Hamiltonian	The Hamiltonian operator
shots	int	Number of measurement shots (default 1)
model	NoiseModel	Noise model for simulation (default ideal)
used_threads	int	Number of parallel threads (default 4)
backend	str	Computation backend: "CPU" or "GPU" (default "CPU")
init_state	list[complex]	Initial state vector to start from instead of |0...0> (new in 0.5.0)

Returns

float — The expectation value $⟨\psi |H|\psi ⟩$ of the Hamiltonian.

Examples

from pyqpanda3.core import H, CNOT, RX, QProg, expval_hamiltonian
from pyqpanda3.hamiltonian import PauliOperator
from pyqpanda3.hamiltonian import Hamiltonian

# Build a state preparation circuit
prog = QProg()
prog << H(0) << CNOT(0, 1) << RX(0, 0.5)

# Define a Hamiltonian: H = 0.5 * Z0 Z1 + 0.3 * X0
pauli_op = PauliOperator({"Z0 Z1": 0.5, "X0": 0.3})
ham = Hamiltonian(pauli_op)

# Compute expectation value
exp_val = expval_hamiltonian(prog, ham, shots=1000)
print(f"Expectation value: {exp_val}")

运行结果：

Expectation value: 0.4387912809451864

Mathematical Background

The expectation value is computed as:

$$⟨H⟩=⟨\psi |H|\psi ⟩=\sum _i{c}_i⟨\psi |P_i|\psi ⟩$$

where $H=\sum _i{c}_i{P}_i$ is the decomposition into Pauli terms.

expval_pauli_operator

Computes the expectation value of a Pauli operator with respect to the quantum state prepared by a given program.

Signature

expval_pauli_operator(
    prog: QProg,
    pauli_operator: PauliOperator,
    shots: int = 1,
    model: NoiseModel = NoiseModel(),
    used_threads: int = 4,
    backend: str = "CPU",
    init_state: list[complex] = []
) -> float

Parameters

Parameter	Type	Description
prog	QProg	Quantum program preparing the state
pauli_operator	PauliOperator	The Pauli operator
shots	int	Number of measurement shots (default 1)
model	NoiseModel	Noise model for simulation (default ideal)
used_threads	int	Number of parallel threads (default 4)
backend	str	Computation backend: "CPU" or "GPU" (default "CPU")
init_state	list[complex]	Initial state vector to start from instead of |0...0> (new in 0.5.0), e.g. a state produced by an earlier simulation and read back via QResult.get_state_vector()

Returns

float — The expectation value of the Pauli operator.

Examples

from pyqpanda3.core import H, QProg, expval_pauli_operator
from pyqpanda3.hamiltonian import PauliOperator

prog = QProg()
prog << H(0)

# Define Pauli operator: Z0
pauli_op = PauliOperator({"Z0": 1.0})

# Compute expectation value (should be ~0 for |+> state)
exp_val = expval_pauli_operator(prog, pauli_op, shots=1000)
print(f"Expectation of Z on |+>: {exp_val}")

运行结果：

Expectation of Z on |+>: 0.0

See Also

• Hamiltonian — Hamiltonian class
• PauliOperator — PauliOperator class
• Simulator — CPUQVM also provides expval methods (deprecated)
• VQCircuit — Variational circuit with gradient computation