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.[1]
  2. The QPE scheme can be applied as a subroutine to design many quantum algorithms.[1]
  3. The proposed controlled-unitary gate can be directly utilized to implement the circuit of the QPE scheme for the QPE algorithm.[1]
  4. Moreover, we can consider the controlled-unitary gate as the basic module of a multi-qubit QPE scheme for scalability.[1]
  5. In this video, Postdoctoral Researcher Ben Criger (QuTech) talks you through an algorithm to estimate these relative phases: Quantum phase estimation.[2]
  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.[2]
  7. This can be achieved by incorporating phase estimation algorithm into the hybrid quantum-classical computation scheme, where quantum block is trained classically.[3]
  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).[4]
  9. The phase estimation algorithm is a quantum subroutine useful for finding the eigenvalue corresponding to an eigenvector \(u\) of some unitary operator.[5]
  10. Quantum Phase Estimation is a quantum algorithm that estimates the phase of a unitary operator.[6]
  11. In general applications, current QPE algorithms either suffer an exponential time overload or require a set of - notoriously quite fragile - GHZ states.[7]
  12. These limitations have prevented so far the demonstration of QPE beyond proof-of-principles.[7]
  13. Here we propose a new QPE algorithm that scales linearly with time and is implemented with a cascade of Gaussian spin states (GSS).[7]
  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.[7]
  15. The Phase Estimation Algorithm (PEA) is an important quantum algorithm used independently or as a key subroutine in other quantum algorithms.[8]
  16. Phase estimation is an abstract concept but a crucial part of period finding in Shor’s Algorithm.[9]
  17. Phase estimation is about finding the eigenvalue of a unitary operator.[9]
  18. We consider the quantum phase estimation algorithm and present two distribution schemes for the algorithm.[10]
  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.[11]
  20. We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing.[12]
  21. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine its scaling in circuit depth and width.[12]
  22. The corresponding quantum circuit requires asymptotically lower depth and width (number of qubits) than quantum phase estimation.[12]
  23. QPE is a very important subroutine used in many quantum algorithms of practical importance.[13]
  24. The QPE using qudits has certain advantages when compared to the version using qubits.[13]
  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.[13]
  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.[13]
  27. The objective of quantum phase estimation can be to estimate the eigenphases of eigenvectors of a unitary operator.[14]
  28. Furthermore, a system implementing phase estimation of multiple eigenvalues of a unitary operator may facilitate a quantum speed up of computational tasks.[14]
  29. 1 depicts an example phase estimation system 100.[14]
  30. The phase estimation system 100 may include a quantum circuit 102, and a phase learning subsystem 104.[14]
  31. Abstract : We study numerically the effects of static imperfections and residual couplings between qubits for the quantum phase estimation algorithm with two qubits.[15]

소스

  1. ↑ 1.0 1.1 1.2 1.3 Photonic scheme of quantum phase estimation for quantum algorithms via cross-Kerr nonlinearities under decoherence effect
  2. ↑ 2.0 2.1 Quantum Phase estimation
  3. ↑ Phase estimation algorithm for quantum states classification with NISQ devices
  4. ↑ Imperfect Distributed Quantum Phase Estimation
  5. ↑ Phase Estimation Algorithm — Grove 1.7.0 documentation
  6. ↑ Quantum Phase Estimation in Qiskit — Quantum Computing UK
  7. ↑ 7.0 7.1 7.2 7.3 Quantum Phase Estimation Algorithm with Gaussian Spin States
  8. ↑ Quantum Phase Estimation with Time‐Frequency Qudits in a Single Photon
  9. ↑ 9.0 9.1 QC — Phase estimation in Shor’s Algorithm
  10. ↑ Imperfect Distributed Quantum Phase Estimation
  11. ↑ IBM Quantum Experience
  12. ↑ 12.0 12.1 12.2 Faster phase estimation
  13. ↑ 13.0 13.1 13.2 13.3 "Quantum Phase Estimation and Arbitrary Accuracy Iterative Phase Estima" by Vamsi Parasa and Marek Perkowski
  14. ↑ 14.0 14.1 14.2 14.3 WO2017116446A1 - Quantum phase estimation of multiple eigenvalues - Google Patents
  15. ↑ Quantum phase estimation algorithm in presence of static imperfections

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