Is phase estimation limited to zero to two pi, or can it be greater than two pi?
Posted: Sat Aug 26, 2023 5:18 am
Phase estimation in the context of quantum computing is typically concerned with estimating the phase angle of a quantum state, often represented as a complex number. In quantum computing, the phase of a quantum state is usually represented as a value between 0 and 2π radians, corresponding to a full rotation around the unit circle in the complex plane.
The reason for this limitation lies in the periodic nature of quantum states. In quantum mechanics, states that differ by a global phase (an overall phase factor) are considered physically equivalent. Mathematically, this means that any phase angle θ is equivalent to θ + 2π, θ + 4π, and so on. As a result, phase estimation algorithms often give estimates within this range because any phase outside this range can be represented by an equivalent phase within the range of 0 to 2π.
If a phase estimation algorithm were to produce an estimate outside of this range, it could be adjusted to provide an equivalent phase within the 0 to 2π range by taking the modulus (remainder) of the estimated phase with respect to 2π.
However, it's worth noting that quantum algorithms involving phase estimation are typically designed with the understanding that the phase values are confined to this 0 to 2π range, and the algorithms are tailored to make use of this property. If you have a specific context or scenario in mind, please provide more details for a more precise answer.
The reason for this limitation lies in the periodic nature of quantum states. In quantum mechanics, states that differ by a global phase (an overall phase factor) are considered physically equivalent. Mathematically, this means that any phase angle θ is equivalent to θ + 2π, θ + 4π, and so on. As a result, phase estimation algorithms often give estimates within this range because any phase outside this range can be represented by an equivalent phase within the range of 0 to 2π.
If a phase estimation algorithm were to produce an estimate outside of this range, it could be adjusted to provide an equivalent phase within the 0 to 2π range by taking the modulus (remainder) of the estimated phase with respect to 2π.
However, it's worth noting that quantum algorithms involving phase estimation are typically designed with the understanding that the phase values are confined to this 0 to 2π range, and the algorithms are tailored to make use of this property. If you have a specific context or scenario in mind, please provide more details for a more precise answer.