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arXiv:0712.3620 · Physical Review Letters

Rapid Measurement of Quantum Systems Using Feedback Control

Joshua Combes, Howard M. Wiseman, Kurt A. Jacobs

Published Apr 22, 2008• 43 citations
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Abstract

We introduce a feedback control algorithm that increases the speed at which a measurement extracts information about a d-dimensional system by a factor that scales as d(2). Generalizing this algorithm, we apply it to a register of n qubits and show an improvement of O(n). We derive analytical bounds on the benefit provided by the feedback and perform simulations that confirm that this speedup is achieved.

DOI
10.1103/physrevlett.100.160503

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•Oct 9, 2018•0 citations
We introduce a feedback control algorithm that increases the speed at which a measurement extracts information about a d-dimensional system by a factor that scales as d(2). Generalizing this algorithm, we apply it to a register of n qubits and show an improvement of O(n). We derive analytical bounds on the benefit provided by the feedback and perform simulations that confirm that this speedup is achieved.
Rapid purification by feedback---specifically, reducing the mean impurity faster than by measurement alone---can be achieved by choosing the eigenbasis of the density matrix to be unbiased relative to the measurement basis. Here we further examine the protocol introduced by Combes and Jacobs [Phys. Rev. Lett. 96, 010504 (2006)] involving continuous measurement of the observable Jz{J}_{z}Jz​ for a DDD-dimensional system. We rigorously rederive the lower bound (2/3)(D+1)(2/3)(D+1)(2/3)(D+1) on the achievable speedup factor and also an upper bound, namely D2/2{D}^{2}/2D2/2, for all feedback protocols that use measurements in unbiased bases. Finally, we extend our results to nnn independent measurements on a register of nnn qubits and derive an upper bound on the achievable speedup factor that scales linearly with nnn.
We consider the use of feedback control during a measurement to increase the rate at which a single qubit is purified, and more generally the rate at which near-pure states may be prepared. We derive the optimal bang-bang algorithm for rapid state preparation from an initially completely mixed state when the measurement basis is unrestricted, and evaluate its performance numerically. We also consider briefly the case in which the measurement basis is fixed with respect to the state to be prepared, and describe the qualitative structure of the optimal bang-bang algorithm.
Measurements are a primitive for characterizing quantum systems. Reducing the time taken to perform a measurement may be beneficial in many areas of quantum information processing. We show that permuting the eigenvalues of the state matrix in the logical basis, using open-loop control, provides an O(n)O(n)O(n) reduction in the measurement time, where nnn is the number of qubits in the register. This reduction is of the same order as the (previously introduced) locally optimal feedback protocol. The advantage of the open-loop protocol is that it is far less difficult experimentally. Because the control commutes with the measured observable at all times, our rapid measurement protocol could be used for characterizing a quantum system, by state or process tomography, or to implement measurement-based quantum error correction.
We consider the use of feedback control during a measurement to increase the rate at which a single qubit is purified, and more generally the rate at which near-pure states may be prepared. We derive the optimal bang-bang algorithm for rapid state preparation from an initially completely mixed state when the measurement basis is unrestricted, and evaluate its performance numerically. We also consider briefly the case in which the measurement basis is fixed with respect to the state to be prepared, and describe the qualitative structure of the optimal bang-bang algorithm.