Engineering two-qubit mixed states with weak measurements

Kumar, Parveen; Snizhko, Kyrylo; Gefen, Yuval

doi:10.1103/physrevresearch.2.042014

Cited by 13 publications

(7 citation statements)

References 59 publications

(99 reference statements)

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“…Consider the context of passive (blind) measurement-induced steering, which, in the continuum time limit, leads to Lindbladian dynamics. Then, the addition of Hamiltonian dynamics enriches the variability of steering, allowing, for example, to obtain mixed states by design [35]. It is intriguing to investigate how the addition of Hamiltonian dynamics extends or improves active steering, thus marrying the frameworks of closed-loop quantum control for Hamiltonian-based state preparation and active-decision measurement-based steering.…”

Section: Discussionmentioning

confidence: 99%

Measurement-driven navigation in many-body Hilbert space: Active-decision steering

Herasymenko¹,

Gornyi²,

Gefen³

2021

Preprint

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The challenge of preparing a system in a designated state spans diverse facets of quantum mechanics. To complete this task of steering quantum states, one can employ quantum control through a sequence of generalized measurements which direct the system towards the target state. In an active version of this protocol, the obtained measurement readouts are used to adjust the protocol on-the-go, with a possibility for accelerated performance or fidelity increase. In this work, we consider such active measurement-driven steering as applied to the challenging case of many-body quantum systems. The target states of highest interest would be those with multipartite entanglement. Such state preparation in a measurement-based protocol is limited by the natural constraints for system-detector couplings. We develop a framework for finding such physically feasible couplings, based on parent Hamiltonian construction. For helpful decision-making strategies, we offer Hilbert-space-orientation techniques, comparable to those used in navigation. The first one is to tie the active-decision protocol to the fastest accumulation of the cost function, such as the target state fidelity. We show the potential of 9.5-fold speedup, employing this approach for generating the ground state of the Affleck-Lieb-Kennedy-Tasaki spin chain. The second wayfinding technique is to map out the available measurement actions onto a Quantum State Machine. A decision-making protocol can be based on such a representation, using semiclassical heuristics. This approach has advantages and limitations complementary to the cost function-based method. We give an example of a W-state preparation which is accelerated with this method by a factor of 12.5.

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Section: Discussionmentioning

confidence: 99%

Measurement-driven navigation in many-body Hilbert space: Active-decision steering

Herasymenko¹,

Gornyi²,

Gefen³

2021

Preprint

Self Cite

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“…where |i represent the eigenstates of the charge operator ni and N is the total number of charge states. The Hamiltonian (22) can thus be written in the charge basis {|n 1 , n 2 , n 3 } and its diagonalization gives the eigenvalues which are plotted in Fig. 3 against the external flux φ ext , for three different parameter sets where we have assumed φ ext = φ ext,i , i = 1, 2, 3.…”

Section: Hamiltonian and Eigenspectrummentioning

confidence: 99%

“…Due to an explicit time-dependence, of course, the system stays in the ground state for a shorter period, 1 ns. However, we may prolong this time by employing the ideas from weak measurement theory and quantum Zeno effect [22].…”

Section: Survival and Transition Probabilitiesmentioning

confidence: 99%

The tunable 0−π qubit: Dynamics and relaxation

Rajpoot

Кумари

Joshi

et al. 2021

Int. J. Quantum Inform.

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In this paper, we present a systematic treatment of a [Formula: see text] qubit in the presence of a time-dependent external flux. A gauge-invariant Lagrangian and the corresponding Hamiltonian are obtained. The effect of the flux noise on the qubit relaxation is obtained using the perturbation theory. Under a time-dependent drive of sinusoidal form, the survival probability, and transition probabilities have been studied for different strengths and frequencies. The driven qubit is shown to possess coherent oscillations among two distinct states for a weak to moderate strength close to resonant frequencies of the unperturbed qubit. The parameters can be chosen to prepare the system in its ground state. This feature paves the way to prolong the lifetime by combining ideas from weak measurement and quantum Zeno effect. We believe that this is an important variation of a topologically protected qubit which is tunable.

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“…Various types of measurements have been considered: local projective measurements, local weak measurements that only slightly perturb the system (for their recent applications in other contexts, see, e.g., Refs. [5,[40][41][42][43][44][45][46][47][48][49]), non-local measurements of several sites of the system, and global measurements that act on the many-body system as a whole. The main diagnostic tool for the measurement-induced entanglement transition is the behavior of the entanglement entropy averaged over the measurement runs, but other indicators, such as mutual information or entanglement negativity, have also been used to explore the phenomenon.…”

Section: Introductionmentioning

confidence: 99%

Generalized quantum measurements with matrix product states: Entanglement phase transition and clusterization

Doggen,

Gefen,

Gornyi

et al. 2021

Preprint

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We propose a method, based on matrix product states, for studying the time evolution of manybody quantum lattice systems under continuous and site-resolved measurement. Both the frequency and the strength of generalized measurements can be varied within our scheme, thus allowing us to explore the corresponding two-dimensional phase diagram. The method is applied to one-dimensional chains of nearest-neighbor interacting hard-core bosons. A transition from an entangling to a disentangling (area-law) phase is found. However, by resolving time-dependent density correlations in the monitored system, we find important differences between different regions at the phase boundary. In particular, we observe a peculiar phenomenon of measurement-induced particle clusterization that takes place only for frequent moderately strong measurements, but not for strong infrequent measurements.

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Engineering two-qubit mixed states with weak measurements

Cited by 13 publications

References 59 publications

Measurement-driven navigation in many-body Hilbert space: Active-decision steering

Measurement-driven navigation in many-body Hilbert space: Active-decision steering

The tunable 0−π qubit: Dynamics and relaxation

Generalized quantum measurements with matrix product states: Entanglement phase transition and clusterization

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