Quantum phase estimation algorithm

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1. The main aim of the QPE scheme is to estimate the phase of an unknown eigenvalue, corresponding to an eigenstate of an arbitrary unitary operation.
2. The QPE scheme can be applied as a subroutine to design many quantum algorithms.
3. The proposed controlled-unitary gate can be directly utilized to implement the circuit of the QPE scheme for the QPE algorithm.
4. Moreover, we can consider the controlled-unitary gate as the basic module of a multi-qubit QPE scheme for scalability.
5. In this video, Postdoctoral Researcher Ben Criger (QuTech) talks you through an algorithm to estimate these relative phases: Quantum phase estimation.
6. After a short discussion on the precision of phase estimation, Ben introduces the concept of binary fractions, which comes in handy in the rest of the example.
7. This can be achieved by incorporating phase estimation algorithm into the hybrid quantum-classical computation scheme, where quantum block is trained classically.
8. 2, we will explain the quantum phase estimation algorithm (Sect. 2.1), non-local controlled operations (Sect. 2.2) and the distributed quantum Fourier transform (Sect. 2.3).
9. The phase estimation algorithm is a quantum subroutine useful for finding the eigenvalue corresponding to an eigenvector \(u\) of some unitary operator.
10. Quantum Phase Estimation is a quantum algorithm that estimates the phase of a unitary operator.
11. In general applications, current QPE algorithms either suffer an exponential time overload or require a set of - notoriously quite fragile - GHZ states.
12. These limitations have prevented so far the demonstration of QPE beyond proof-of-principles.
13. Here we propose a new QPE algorithm that scales linearly with time and is implemented with a cascade of Gaussian spin states (GSS).
14. We show that our protocol achieves a QPE sensitivity overcoming previous bounds, including those obtained with GHZ states, and is robustly resistant to several sources of noise and decoherence.
15. The Phase Estimation Algorithm (PEA) is an important quantum algorithm used independently or as a key subroutine in other quantum algorithms.
16. Phase estimation is an abstract concept but a crucial part of period finding in Shor’s Algorithm.
17. Phase estimation is about finding the eigenvalue of a unitary operator.
18. We consider the quantum phase estimation algorithm and present two distribution schemes for the algorithm.
19. If we want to measure a more complex observable, such as the energy described by a Hamiltonian H , we resort to quantum phase estimation.
20. We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing.
21. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine its scaling in circuit depth and width.
22. The corresponding quantum circuit requires asymptotically lower depth and width (number of qubits) than quantum phase estimation.
23. QPE is a very important subroutine used in many quantum algorithms of practical importance.
24. The QPE using qudits has certain advantages when compared to the version using qubits.
25. The QPE using qudits is more accurate and requires lesser number of qudits (as the value of the radix d increases) to estimate the phase up to a given accuracy with a given success probability.
26. Since the existing quantum computer implementations use only few qubits, it is important to have alternative versions of the QPE which use as few qubits as possible.
27. The objective of quantum phase estimation can be to estimate the eigenphases of eigenvectors of a unitary operator.
28. Furthermore, a system implementing phase estimation of multiple eigenvalues of a unitary operator may facilitate a quantum speed up of computational tasks.
29. 1 depicts an example phase estimation system 100.
30. The phase estimation system 100 may include a quantum circuit 102, and a phase learning subsystem 104.
31. Abstract : We study numerically the effects of static imperfections and residual couplings between qubits for the quantum phase estimation algorithm with two qubits.

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• ID : Q2835770

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• [{'LOWER': 'quantum'}, {'LOWER': 'phase'}, {'LOWER': 'estimation'}, {'LEMMA': 'algorithm'}]