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arXiv:1205.0978 · Physical Review A

Arbitrary control of multiple-qubit systems in the symmetric Dicke subspace

Shi‐Biao Zheng

Published Mar 28, 2008• 11 citations
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Abstract

We discuss a general physical mechanism for arbitrary control of the quantum states of multiple qubits in the symmetric Dicke subspace. The qubit-qubit coupling leads to unequal energy spacing in the symmetric Dicke subspace. This allows one to manipulate a prechosen transition with an external driving source, with other transitions remaining off-resonant. Any entangled state in the symmetric Dicke subspace can be created from the initial ground state by tuning the driving source. We illustrate the idea in cavity QED, but it should be applicable to other related systems.

DOI
10.1103/physreva.77.033852

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We discuss a general physical mechanism for arbitrary control of the quantum states of multiple qubits in the symmetric Dicke subspace. The qubit-qubit coupling leads to unequal energy spacing in the symmetric Dicke subspace. This allows one to manipulate a prechosen transition with an external driving source, with other transitions remaining off-resonant. Any entangled state in the symmetric Dicke subspace can be created from the initial ground state by tuning the driving source. We illustrate the idea in cavity QED, but it should be applicable to other related systems.
In this study, the authors explore how to deterministically generate symmetric multi‐qubit Dicke states such as symmetric W‐states, from arbitrary initial states in a cavity quantum electrodynamics (QED) system with the aid of measurement‐based quantum feedback control. The concrete implementation procedures of the feedback strategy, which is constructed in the form of only two constant modes, are presented in detail. In addition, the feasibility of the control scheme in preparing symmetric multi‐qubit Dicke states is explicitly demonstrated by theoretical studies and numerical simulations.
We propose an efficient yet simple protocol to generate arbitrary symmetric entangled states with only global single-qubit rotations in a torn Hilbert space. The system is based on spin-1/2 qubits in a resonator such as atoms in an optical cavity or superconducting qubits coupled to a main bus. By sending light or microwave into the resonator, it induces ac Stark shifts on particular angular-momentum eigenstates (Dicke states) of qubits. Then we are able to generate barriers that hinder transitions between adjacent Dicke states and tear the original Hilbert space into pieces. Therefore, a simple global single-qubit rotation becomes highly nontrivial, and thus generates entanglement among the many-body system. By optimal control of energy shifts on Dicke states, we are able to generate arbitrary symmetric entangled states. We also exemplify that we can create varieties of useful states with near-unity fidelities in only one or very few steps, including W states, spin-squeezed states (SSSs), and Greenberger-Horne-Zeilinger states. Particularly, the SSS can be created by only one step with a squeezing parameter ξ R 2 ∼ 1 / N 0.843 approaching the Heisenberg limit. Our finding establishes a way for universal entanglement generations with only single-qubit drivings where all the multiple-qubit controls are integrated into simply switching on or off microwave. It has direct applications in the variational quantum optimizer, which is available with existing technology. Published by the American Physical Society 2024
A scheme is proposed for implementing the controlled phase gate for three atoms trapped in separated cavities coupled by optical fibers. The energy-level distances of the qubit system become unequal as a consequence of the virtual photon exchange between the atomic qubits, which allows the selective excitation of the qubit system in the symmetric Dicke subspace. The conditional phase shift is produced after a single selective Rabi oscillation and the operation is insensitive to cavity loss and fiber decay.
We present a cavity QED interaction which forces the ground state of a cavity field mode to evolve into an arbitrary quantum state at a prechosen time t∗{t}^{*}t∗. This method does not involve either atom-field state entanglement or the projections characteristic of quantum measurement.
In general, implementing a multi-logical-qubit gate by manipulating quantum states in a decoherence-free subspace (DFS) becomes more complex and difficult when increasing the number of logical qubits. In this work, we propose an idea to realize quantum gates by manipulating quantum states outside their DFS but having the states of the logical qubits remain in their DFS before and after the gate operation. This proposal has the following features: (i) because the states are manipulated outside the DFS, the multiqubit gate implementation can be simplified when compared to realizing a multiqubit gate via manipulating quantum states within the DFS, which usually requires unitary operations over a large DFS, and (ii) because the states of the logical qubits return to the DFS after the gate operation, the errors caused by decoherence during the gate operation are not accumulated for a long-running calculation, and the states of the logical qubits are immune to decoherence when they are stored. Based on this proposal, we then present a way for realizing a multi-target-qubit controlled-not gate using logical qubits encoded in a decoherence-free subspace against collective dephasing. This gate is realized by employing qutrits (three-level quantum systems) placed in a cavity or coupled to a resonator. This proposal has the following advantages: (i) the states of the logical qubits return to their DFS after the gate operation; (ii) the gate can be implemented with only a few basic operations; (iii) the gate operation time is independent of the number of logical qubits; (iv) this gate can be deterministically implemented because no measurement is needed; (v) the intermediate higher-energy level for all qutrits is not occupied during the entire operation, thus decoherence from this level is greatly suppressed; (vi) this proposal is universal and can be applied to realize the proposed gate using natural atoms or artificial atoms (e.g., quantum dots, nitrogen-vacancy centers, and various superconducting qutrits, etc.) placed in a cavity or coupled to a resonator. As an application, we also show how to apply this gate to create a Greenberger-Horne-Zeilinger (GHZ) entangled state of multiple logical qubits encoded in DFS, and further investigate the experimental feasibility for creating the GHZ state of three logical qubits in the DFS, by using six superconducting transmon qutrits coupled to a one-dimensional coplanar waveguide resonator.
We present a scheme to create quantum entanglement between multi-atom Dicke states and two cavity modes by passing N three-level atoms in Λ configuration through a resonant two-mode cavity one by one. We further show that such a scheme can be used to generate arbitrary two-mode N-photon entangled states, arbitrary superposition of Dicke states, and a maximal entangled state of Dicke states. These states may find applications in the demonstration of quantum non-locality, high-precision spectroscopy and quantum information processing.