# SWAP specific phase components of two qubits

Quantum Computing Asked on January 3, 2022

Is it possible to perform an operation on two qubits with initial states as follows:

$$q_1: 1/sqrt(2)(|0rangle + exp(0.a_1a_2a_3)|1rangle)$$
$$q_2: 1/sqrt(2)(|0rangle + |1rangle)$$

To resultant state:-

$$q_1: 1/sqrt(2)(|0rangle + exp(0.a_1a_2)|1rangle)$$
$$q_2: 1/sqrt(2)(|0rangle + exp(0.a_3)|1rangle)$$

Without knowing the value of $$a_3$$. Where $$a_1,a_2,a_3 ∈ [0, 1].$$

The idea is to shift the phase of $$q_1$$ by $$exp(-0.00a_3)$$ and $$q_2$$ by $$exp(0.a_3)$$ with the unitary operation not being aware of the value of $$a_3$$.

No, it's not possible to extract digits of the phase like that. It would violate the Holevo bound. In general there's no way to "amplify" single small phase differences into big phase differences, because of linearity.

Answered by Craig Gidney on January 3, 2022

## Related Questions

### Why and how is quantum noise predictable?

1  Asked on February 26, 2021

### Are almost-Clifford circuits almost easy to simulate?

1  Asked on February 26, 2021 by forky40

### How is a quantum simulator able to simulate a quantum mechanical properties on a classical computer?

2  Asked on February 26, 2021 by sinestro-38

### How to fix “QiskitChemistryError:PySCF is not installed”

2  Asked on February 25, 2021 by anneahilator

### How to initialize a random state in Qiskit?

2  Asked on February 24, 2021

### Conditional probability between parameter and operator in quantum mechanics?

0  Asked on February 24, 2021

### Tensor product properties used to obtain Kraus operator decomposition of a channel

1  Asked on February 24, 2021 by alexander-pozdneev

### Connection between smooth max-relative entropy and smooth max-information

0  Asked on February 24, 2021

### Recording the time taken by a VQE to find ground state energy

1  Asked on February 23, 2021 by louisl

### Grover search with different diffusion operators

1  Asked on February 23, 2021

### Has any research been done on quantum Zeno machines?

2  Asked on February 22, 2021 by user820789

### Can I adjust the quantum circuit after transpiling it?

1  Asked on February 22, 2021

### Qiskit sample – Portfolio optimization

1  Asked on February 20, 2021 by pavan-kulkarni

### Expectation value of operator – python

1  Asked on February 18, 2021

### How does one create the unitary sending $|0rangle$ into a target quantum state?

3  Asked on February 18, 2021 by bg827

### How can I convert the unitary matrix $e^frac{ipi}{2}$ into a quantum circuit in Qiskit?

1  Asked on February 18, 2021 by physics-world

### Nielsen & Chuang Exercise 6.13: Standard deviation of classical counting algorithm

1  Asked on February 16, 2021

### Post-selection applied to quantum teleportation

1  Asked on February 16, 2021

### Does normalizing a mixed state give a pure state?

2  Asked on February 16, 2021 by eesh-starryn