Optimum phase estimation with two control qubits

• URL: http://arxiv.org/abs/2303.12503v1
• Date: Wed, 22 Mar 2023 12:18:33 GMT
• Title: Optimum phase estimation with two control qubits
• Authors: Peyman Najafi, Pedro C.S. Costa and Dominic W. Berry
• Abstract summary: We show how to measure a phase with a minimum mean-square error using only two control qubits. Our method corresponds to preparing the optimal control state one qubit at a time, while it is simultaneously consumed by the measurement procedure.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Phase estimation is used in many quantum algorithms, particularly in order to estimate energy eigenvalues for quantum systems. When using a single qubit as the probe (used to control the unitary we wish to estimate the eigenvalue of), it is not possible to measure the phase with a minimum mean-square error. In standard methods, there would be a logarithmic (in error) number of control qubits needed in order to achieve this minimum error. Here show how to perform this measurement using only two control qubits, thereby reducing the qubit requirements of the quantum algorithm. Our method corresponds to preparing the optimal control state one qubit at a time, while it is simultaneously consumed by the measurement procedure.

Related papers

• Roadmap to fault tolerant quantum computation using topological qubit arrays [37.024540100400536]
  We describe a device roadmap towards a fault-tolerant quantum computing architecture based on noise-resilient, topologically protected Majorana-based qubits. Our roadmap encompasses four generations of devices: a single-qubit device that enables a measurement-based qubit benchmarking protocol; a two-qubit device that uses measurement-based braiding to perform single-qubit Clifford operations; and an eight-qubit device that can be used to show an improvement of a two-qubit operation when performed on logical qubits.
  arXiv  Detail & Related papers  (2025-02-17T19:00:10Z)
• Low depth amplitude estimation without really trying [1.1005025875011782]
  Quantum amplitude estimation algorithms provide quadratic speedup to Monte-Carlo simulations. They require a circuit depth that scales as inverse of the estimation error. We bypass this limitation by performing the classical Monte-Carlo method on the quantum algorithm itself.
  arXiv  Detail & Related papers  (2024-10-02T01:59:33Z)
• A quantum implementation of high-order power method for estimating geometric entanglement of pure states [39.58317527488534]
  This work presents a quantum adaptation of the iterative higher-order power method for estimating the geometric measure of entanglement of multi-qubit pure states. It is executable on current (hybrid) quantum hardware and does not depend on quantum memory. We study the effect of noise on the algorithm using a simple theoretical model based on the standard depolarising channel.
  arXiv  Detail & Related papers  (2024-05-29T14:40:24Z)
• Certifying almost all quantum states with few single-qubit measurements [0.9558392439655012]
  We show that almost all n-qubit target states can be certified from only O(n2) single-qubit measurements. We show that such verified representations can be used to efficiently predict highly non-local properties.
  arXiv  Detail & Related papers  (2024-04-10T18:21:11Z)
• System Characterization of Dispersive Readout in Superconducting Qubits [37.940693612514984]
  We introduce a single protocol to measure the dispersive shift, resonator linewidth, and drive power used in the dispersive readout of superconducting qubits. We find that the resonator linewidth is poorly controlled with a factor of 2 between the maximum and minimum measured values. We also introduce a protocol for measuring the readout system efficiency using the same power levels as are used in typical qubit readout.
  arXiv  Detail & Related papers  (2024-02-01T08:15:16Z)
• Fast Flux-Activated Leakage Reduction for Superconducting Quantum Circuits [84.60542868688235]
  leakage out of the computational subspace arising from the multi-level structure of qubit implementations. We present a resource-efficient universal leakage reduction unit for superconducting qubits using parametric flux modulation. We demonstrate that using the leakage reduction unit in repeated weight-two stabilizer measurements reduces the total number of detected errors in a scalable fashion.
  arXiv  Detail & Related papers  (2023-09-13T16:21:32Z)
• Determining the ability for universal quantum computing: Testing controllability via dimensional expressivity [39.58317527488534]
  Controllability tests can be used in the design of quantum devices to reduce the number of external controls. We devise a hybrid quantum-classical algorithm based on a parametrized quantum circuit.
  arXiv  Detail & Related papers  (2023-08-01T15:33:41Z)
• On adaptive low-depth quantum algorithms for robust multiple-phase estimation [11.678822620192438]
  We present robust multiple-phase estimation (RMPE) algorithms with Heisenberg-limited scaling. These algorithms are particularly suitable for early fault-tolerant quantum computers.
  arXiv  Detail & Related papers  (2023-03-14T17:38:01Z)
• Optimal Single Qubit Tomography: Realization of Locally Optimal Measurements on a Quantum Computer [0.2621730497733947]
  We implement these measurements on a superconducting quantum computer. Our experiment produces sufficiently low error to allow the saturation of the theoretical limits. The results of the simulations show the robustness of the method in characterizing arbitrary qubit states with different amounts of prior knowledge.
  arXiv  Detail & Related papers  (2023-02-10T09:44:58Z)
• Graph test of controllability in qubit arrays: A systematic way to determine the minimum number of external controls [62.997667081978825]
  We show how to leverage an alternative approach, based on a graph representation of the Hamiltonian, to determine controllability of arrays of coupled qubits. We find that the number of controls can be reduced from five to one for complex qubit-qubit couplings.
  arXiv  Detail & Related papers  (2022-12-09T12:59:44Z)
• Algorithms for quantum simulation at finite energies [0.7734726150561088]
  We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. One is a hybrid quantum algorithm that computes expectation values in a finite energy interval around its mean energy. The other is a quantum-assisted Monte Carlo sampling method to compute other quantities.
  arXiv  Detail & Related papers  (2020-06-04T17:40:29Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.