Robust adaptive measurement scheme for qubit-state preparation

Abstract

In this paper, the method of adaptive measurement for qubit-state preparation developed by Jacobs is reconsidered, and an alternative scheme that works even under unknown unitary evolution of the state is shown.The key idea is that the measurement is adaptively changed so that one of the eigenstates of the measured observable is always set between the current and the target states while that eigenstate converges to the target. The most significant feature of this scheme is that the measurement strength can be taken constant, unlike in Jacobs' scheme, which eventually provides fine robustness of the controlled state against the uncertainty of the unitary evolution.

Incoherent Qubit Control Using the Quantum Zeno Effect

“…Measurement-only manipulation has been demonstrated using a fixed measurement basis [15], but unlike Hamiltonian-based methods, implementation of a timedependent measurement basis is lacking. Such a capability is a versatile additional degree of freedom for measurement based protocols, such as rapid state purification [5] and state manipulation [9,10,16], for control by projection into a subspace referred to as quantum Zeno dynamics [17], and for measurement-based quantum computation [18].In this Letter, we present a method to dynamically tune the measurement operator in a circuit-QED system, and use this capability to deterministically and incoherently manipulate the state of an effective qubit. Our method relies on the suppression of coherent evolution via strong measurement, known as the quantum Zeno effect (QZE), which has been observed in many systems [19][20][21][22][23][24][25][26][27][28][29][30].…”

“…Measurement-only manipulation has been demonstrated using a fixed measurement basis [15], but unlike Hamiltonian-based methods, implementation of a timedependent measurement basis is lacking. Such a capability is a versatile additional degree of freedom for measurement based protocols, such as rapid state purification [5] and state manipulation [9,10,16], for control by projection into a subspace referred to as quantum Zeno dynamics [17], and for measurement-based quantum computation [18].…”

Many-body state engineering using measurements and fixed unitary dynamics

“…where J is the inter-well tunnelling and U is the collisional interaction strength ( figure 3(a)). The standard strategies of unitary control [5,6] or control-free engineering [11,12,[14][15][16][17] require modifications in this setting: changing the Hamiltonian parameters abruptly, as for bang-bang control or the SU(2)-decomposition, compromises the lowest-band approximation due to vibrational excitations [9]. Continuous changes impose a speed-limit on achievable operations [7].…”

“…Besides unitary control via the system Hamiltonian, quantum state engineering can also be exerted for a fixed Hamiltonian via the back-action induced by measurements [11][12][13][14][15][16][17][18]. On the one hand, measurement operators that are adapted on previous measurement outcomes can steer a quantum state into a target state [11][12][13].…”

Structure identification and state initialization of spin networks with limited access

“…The continuous measurement is again useful to solve the problem, because it continuously reduces the entropy of the system; furthermore, to overcome the issue that any measurement induces a probabilistic (i.e. non-deterministic) behavior of the system, we employ the adaptive measurement technique [34,35], which is a kind of feedback control that changes the measured observable continuously in time, depending on the past measurement results. It will be actually demonstrated that, in some examples, this method realizes the deterministic stabilization of the target state.…”