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Chinese Physics B

Geometric control of concurrence and quantum gate operations in triangular triple quantum dots

Junqing Li, Shuo Dong, Jianhua Wei

Published Jul 7, 2025• 0 citations
Publisher

Abstract

Abstract As an important index to measure the degree of entanglement in quantum systems, concurrence plays an important role in practical research. In this paper, we study the concurrence between two qubits in triangular triple quantum dot structure. Through calculation and simulation, it is found that concurrence is mainly affected by the interdot coupling strength t , Coulomb interaction U , temperature T , and electrode coupling Γ . Through comparative studies with parallel triple quantum dot structures, we demonstrate that the triangular geometry exhibits significantly enhanced concurrence under identical conditions. In addition, under the condition that concurrence exceeds 0.9, the functional relationship between t and U is obtained through simulation, which provides theoretical support for quantum dot regulation under high entanglement. Finally, we demonstrate the feasibility of implementing a three-qubit quantum gate, using the Toffoli gate as a representative example, under the condition that the triangular triple quantum dot system maintains high entanglement.

DOI
10.1088/1674-1056/adec5d

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Abstract As an important index to measure the degree of entanglement in quantum systems, concurrence plays an important role in practical research. In this paper, we study the concurrence between two qubits in triangular triple quantum dot structure. Through calculation and simulation, it is found that concurrence is mainly affected by the interdot coupling strength t , Coulomb interaction U , temperature T , and electrode coupling Γ . Through comparative studies with parallel triple quantum dot structures, we demonstrate that the triangular geometry exhibits significantly enhanced concurrence under identical conditions. In addition, under the condition that concurrence exceeds 0.9, the functional relationship between t and U is obtained through simulation, which provides theoretical support for quantum dot regulation under high entanglement. Finally, we demonstrate the feasibility of implementing a three-qubit quantum gate, using the Toffoli gate as a representative example, under the condition that the triangular triple quantum dot system maintains high entanglement.
Abstract Coherence is a fundamental physical quantity that plays a key role in characterizing the superposition and entanglement of quantum states. In this study, we investigate the coherence properties of a triangular triple-quantum-dot system as functions of coupling strength t , Coulomb repulsion U , and temperature T . We compare the coherence in this triangular configuration with that in a series triple quantum dot structure, and find that the triangular arrangement exhibits significantly enhanced coherence. The effect of an external phase on coherence is also examined, revealing periodic modulation. Furthermore, we analyze the implementation of a CSWAP quantum gate within the triangular triple-quantum-dot platform. Leveraging the high-coherence regime, we decompose the CSWAP gate into a sequence of three CNOT gates and two Toffoli gates. By tuning inter-dot couplings and applying magnetic fields, we realize the CSWAP operation and estimate the required gate time. Triangular triple-quantum-dots are considered a promising platform for quantum computing due to their ability to host chiral spin states and maintain robust quantum coherence, which is essential for high fidelity qubit operations. Our results identify optimal parameter regimes for coherence enhancement and provide a theoretical foundation for implementing advanced quantum gates in chiral qubit architectures, paving the way toward scalable quantum computation.
We consider a model of two interacting always-on, exchange-only qubits for which controlled phase (CPHASE), controlled NOT (CNOT), quantum Fourier transform (QFT) and SWAP operations can be implemented only in a few electrical pulses in a nanosecond time scale. Each qubit is built of three quantum dots (TQD) in a triangular geometry with three electron spins which are always kept coupled by exchange interactions only. The qubit states are encoded in a doublet subspace and are fully electrically controlled by a voltage applied to gate electrodes. The two qubit quantum gates are realized by short electrical pulses which change the triangular symmetry of TQD and switch on exchange interaction between the qubits. We found an optimal configuration to implement the CPHASE gate by a single pulse of the order 2.3 ns. Using this gate, in combination with single qubit operations, we searched for optimal conditions to perform the other gates: CNOT, QFT and SWAP. Our studies take into account environment effects and leakage processes as well. The results suggest that the system can be implemented for fault tolerant quantum computations.
Reliable quantum information processing requires high-fidelity universal manipulation of quantum systems within the characteristic coherence times. Non-adiabatic holonomic quantum computation offers a promising approach to implement fast, universal, and robust quantum logic gates particularly useful in nano-fabricated solid-state architectures, which typically have short coherence times. Here, we propose an experimentally feasible scheme to realize high-speed universal geometric quantum gates in nano-engineered pseudo-spin charge qubits. We use a system of three coupled quantum dots containing a single electron, where two computational states of a double quantum dot charge qubit interact through an intermediate quantum dot. The additional degree of freedom introduced into the qubit makes it possible to create a geometric model system, which allows robust and efficient single-qubit rotations through careful control of the inter-dot tunneling parameters. We demonstrate that a capacitive coupling between two charge qubits permits a family of non-adiabatic holonomic controlled two-qubit entangling gates, and thus provides a promising procedure to maintain entanglement in charge qubits and a pathway toward fault-tolerant universal quantum computation. We estimate the feasibility of the proposed structure by analyzing the gate fidelities to some extent.
We present a model of a qubit built of three coherently coupled quantum dots with three spins in a triangular geometry. The qubit states are encoded in the doublet subspace and they are controlled by a gate voltage, which breaks the triangular symmetry of the system. We show how to prepare the qubit and to perform one-qubit operations. A doublet blockade effect in the current will be discussed. The blockade is related to an asymmetry of transfer rates from the electrodes to different doublet states and is used to read out the dynamics of the qubit state. Our research also presents analysis of the Rabi oscillations, decoherence, and leakage processes in the doublets subspace.
The quantum phase transition and the electronic transport in a triangular quantum dot system are investigated using the numerical renormalization group method. We concentrate on the interplay between the interdot capacitive coupling V and the interdot tunnel coupling t . For small t , three dots form a local spin doublet. As t increases, due to the competition between V and t , there exist two first-order transitions with phase sequence spin-doublet-magnetic frustration phase-orbital spin singlet. When t is absent, the evolutions of the total charge on the dots and the linear conductance are of the typical Coulomb-blockade features with increasing gate voltage. While for sufficient t , the antiferromagnetic spin correlation between dots is enhanced, and the conductance is strongly suppressed for the bonding state is almost doubly occupied.
In semiconductor-based quantum computing, gate operations beyond the two-qubit limit are important, but have remained extremely challenging. The authors realize gate-voltage control of interqubit couplings in a specially designed three-qubit quantum-dot device. They exercise coherent control of both amplitude and phase of a target qubit using the prepared states of two control qubits, and demonstrate the basic functionalities of the universal Toffoli gate. This initial effort to achieve controlled three-qubit operations provides useful insight for research on multiqubit systems in semiconductor devices.