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Communications in Theoretical Physics

Robust Quantum Computing in Decoherence-Free Subspaces with Double-Dot Spin Qubits

Zhi‐Bo Feng, Chunli Zhang, Yun-Qing Zhou

Published Feb 1, 2014• 2 citations
Publisher

Abstract

We present a scheme for implementing robust quantum gates in decoherence-free subspaces (DFSs) with double-dot spin qubits. Through the resonator-assisted interaction, the controllable interqubit couplings can be achieved only by adjusting the qubit transition frequencies. We construct a set of logic gates on the DFS-encoded qubits to eliminate the collective noise effects, and thus the gate fidelities can be enhanced remarkably. This proposal may offer a potential approach to realize the robust quantum computing with spin qubits.

DOI
10.1088/0253-6102/61/2/06

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We present a scheme for implementing robust quantum gates in decoherence-free subspaces (DFSs) with double-dot spin qubits. Through the resonator-assisted interaction, the controllable interqubit couplings can be achieved only by adjusting the qubit transition frequencies. We construct a set of logic gates on the DFS-encoded qubits to eliminate the collective noise effects, and thus the gate fidelities can be enhanced remarkably. This proposal may offer a potential approach to realize the robust quantum computing with spin qubits.
A general scheme to perform universal, fault-tolerant quantum computation within decoherence-free subspaces (DFSs) is presented. At most two-qubit interactions are required, and the system remains within the DFS throughout the entire implementation of a quantum gate. We show explicitly how to perform universal computation on clusters of the four-qubit DFS encoding one logical qubit each under spatially symmetric (collective) decoherence. Our results have immediate relevance to quantum computer implementations in which quantum logic is implemented through exchange interactions, such as the recently proposed spin-spin coupled quantum dot arrays and donor-atom arrays.
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 show how to efficiently exploit decoherence free subspaces (DFSs), which are immune to collective noise, for realizing quantum repeaters with long-lived quantum memories. Our setup consists of an assembly of simple modules and we show how to implement them in systems of cold, neutral atoms in arrays of dipole traps. We develop methods for realizing robust gate operations on qubits encoded in a DFS using collisional interactions between the atoms. We also give a detailed analysis of the performance and stability of all required gate operations and emphasize that all modules can be realized with current or near future experimental technology.
An approach is presented for directly constructing cn-Not multi-qubit logic gates using quantum dots. In addition, error-avoiding codes in the projected subspace are discussed, offering a potentially robust scheme for protecting against decoherence. The following general conditions were found: (1) a projected subspace can always be constructed, in which decoherence effects can be cancelled by adjusting the interaction coupling time, enabling error-correction to be performed. This subspace is closed for the projected states. (2) The necessary and sufficient conditions for a decoherence-free subspace are that the second term in the subdynamic equation, be equal to zero. Commonly formulated conditions for a decoherence-free subspace are shown to be particular approximations of this condition, including the so-called Born–Markovian approximation.
Abstract A scheme for implementing the non-adiabatic holonomic quantum computation in decoherence-free subspaces is proposed with the interactions between a microcavity and quantum dots. A universal set of quantum gates can be constructed on the encoded logical qubits with high fidelities. The current scheme can suppress both local and collective noises, which is very important for achieving universal quantum computation. Discussions about the gate fidelities with the experimental parameters show that our schemes can be implemented in current experimental technology. Therefore, our scenario offers a method for universal and robust solid-state quantum computation.