"""Quantum state vectors The quantum state of :math:`n` quantum bits is represented as a 1D array of complex numbers of length :math:`2^n`; the components of the state vector in the computational basis. The computational basis for :math:`n` qubits is ordered by the number represented by the associated classical bitstring. """ import numpy as np __all__ = ["from_classical", "is_normalized", "num_qubits", "zero"] # type: ignore def from_classical(bitstring): """Return a quantum state corresponding to a classical bitstring. Parameters ---------- bitstring : sequence of bits Can be a string like "01011", or a sequence of integers. Returns ------- state : ndarray[(2**n,), complex] The state vector in the computational basis. Has :math:`2^n` components. """ bitstring = "".join(map(str, bitstring)) n_qubits = len(bitstring) try: index = int(bitstring, base=2) except ValueError: raise ValueError("Input is not a classical bitstring") from None state = np.zeros(1 << n_qubits, dtype=complex) state[index] = 1 return state def zero(n: int): """Return the zero state on 'n' qubits.""" state = np.zeros(1 << n, dtype=complex) state[0] = 1 return state def num_qubits(state): """Return the number of qubits in the state. Raises ValueError if 'state' does not have a shape that is an integer power of 2. """ _check_valid_state(state) return state.shape[0].bit_length() - 1 def is_normalized(state: np.ndarray) -> bool: """Return True if and only if 'state' is normalized.""" return np.allclose(np.linalg.norm(state), 1) def _check_valid_state(state): if not ( # is an array isinstance(state, np.ndarray) # is complex and np.issubdtype(state.dtype, np.complex128) # is a vector and len(state.shape) == 1 # has size 2**n, n > 1 and np.log2(state.shape[0]).is_integer() and state.shape[0].bit_length() > 1 and is_normalized(state) ): raise ValueError("State is not valid")

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