quantum gate directory
Phase Oracle
Symbol
$O_f^\pm$
Qubits: $n$ Dimension: $p$
hermitian
Description:
Encodes a Boolean function as phases on computational basis states.
Alternate notations:
- $U_f^\pm$
- $\mathcal{O}_f^\pm$
SDK Support
| SDK | Name |
|---|---|
| Qiskit |
qiskit.circuit.library.PhaseOracleGate
ⓘ
|
| PennyLane | — ⓘ |
| Cirq | — |
| Q# | — |
| PyQuil | — |
| Braket | — |
| BQSKit | — |
| Qibo | — |
| pytket | — ⓘ |
| Stim | — |
| OpenQASM | — |
Groups
This gate is contained in the following groups:
A phase oracle is a variant of the standard oracle that acts on a single register $|x\rangle$, encoding the value of a classical Boolean function $f: \{0, 1\}^n \to \{0, 1\}$ as a relative phase: $$ |x\rangle \xmapsto{O_f^\pm} (-1)^{f(x)}|x\rangle $$ This construction is particularly useful in algorithms like Grover's search, where interference between states allows the amplitudes of marked states to be amplified.
Properties
- Diagonal in the computational basis; unitary and Hermitian for Boolean $f$.
- Can be implemented from a standard oracle via phase kickback.
Usage
- Grover search and amplitude amplification.
- Encoding classical predicates into quantum phases.
References
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