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What is quantum phase estimation?
Quantum phase estimation (QPE) reads the phase a gate adds to one of its eigenstates as a binary number in counting qubits, using phase kickback and the inverse Fourier transform.
Applied to one of its eigenstates, a gate U leaves the state unchanged except for a phase e^(2πiφ). In phase estimation the counting qubits are put into superposition with H; the j-th counting qubit applies U controlled 2^j times and, through phase kickback, writes the phase onto itself. The inverse QFT turns this pattern into the binary expansion of φ.
In Shor’s algorithm the period is found as the phase of modular multiplication; in quantum chemistry a molecule’s energy is read as the phase of its time evolution. Each extra counting qubit adds one more bit of precision.
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The lesson Phase estimation: measure a gate’s secret lets you try this concept in the browser, with no installation.
Related packages
Related concepts
- Quantum Fourier transform (QFT) · The quantum Fourier transform (QFT) computes the discrete Fourier transform of the amplitudes with H and controlled-phase gates; it underlies period finding and phase estimation.
- Shor’s algorithm · Shor’s algorithm factors large numbers exponentially faster than known classical methods, which is why it threatens RSA encryption.
- VQE (variational quantum eigensolver) · VQE is a hybrid quantum algorithm that approximates the ground-state energy of a molecule by tuning a parameterised quantum circuit in a classical optimisation loop.