Fast high-fidelity entangling gates for spin qubits in Si double quantum dots

Calderon-Vargas, F. A.; Barron, George S.; Deng, Xiu-Hao; Sigillito, A. J.; Barnes, Edwin; Economou, Sophia E.

doi:10.1103/physrevb.100.035304

Cited by 30 publications

(36 citation statements)

References 32 publications

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“…We consider the isotropic interactions g x (t) = g y (t) = g z (t) = g(t) [65,66] for two-qubit Hamiltonian H d (t) and anisotropic interactions [46] for the single-qubit Hamiltonian H s as…”

Section: Physical Model and Hamiltonianmentioning

confidence: 99%

“…For quantum dot systems, tunable exchange interactions can be built up between spins in two dots. [64][65][66] Before implementing experiments, the relationship between strengths of exchange interactions and gate voltages can be established by empirical formulas with some parameters being predetermined via measurements. Accordingly, the strengths can be controlled by tuning gate voltages in processes of experiments.…”

Section: Experimental Considerationsmentioning

confidence: 99%

“…We assume that two spins in pair (q 1 , q 2 ′ ) ( , ′ = 1, 2) interact with each other through Heisenberg interactions with the same strengths {g (t)| = x, y, z} in three different directions. The Hamiltonian can be written by [46,[64][65][66]…”

Section: Appendix A: Initialization Of Logical Qubitsmentioning

confidence: 99%

“…Generally, state of each logical qubit can be described with a Bell‐state basis as (the initialization of logical qubits in the basis can be found in Appendix A)

\begin{matrix} true \\ right false| 0 false⟩ & = & left \frac{1}{\sqrt{2}} (| ↑ ↑ ⟩ + | ↓ ↓ ⟩), | 1 ⟩ = \frac{1}{\sqrt{2}} (| ↑ ↓ ⟩ + | ↓ ↑ ⟩), \\ right false| 2 false⟩ & = & left \frac{1}{\sqrt{2}} (| ↑ ↑ ⟩ - | ↓ ↓ ⟩), | 3 ⟩ = \frac{1}{\sqrt{2}} (| ↑ ↓ ⟩ - | ↓ ↑ ⟩) \end{matrix}

The singlet state to be prepared reads

false| {normalΨ}_{s} false⟩ = (| 012 ⟩ + false| 120 false⟩ + false| 201 false⟩ - false| 102 false⟩ - false| 210 false⟩ - false| 021 false⟩ false) / \sqrt{6}

. Consider that the spins interact with each other through Heisenberg exchange interactions, the Hamiltonian of the system reads [ 46,64–66 ]

\begin{matrix} true \\ H false(t false) & left = H_{s} + H_{d} (t) \\ H_{normals} & left = \sum_{j = 1}^{3} \sum_{ȷ = x, y, z} \frac{J_{ȷ j}}{4} σ_{ȷ}^{false(q_{j_{1}} false)} \otimes σ_{ȷ}^{false(q_{j_{2}} false)} \end{matrix}

…”

Section: Physical Model and Hamiltonianmentioning

confidence: 99%

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Robust Generation of Logical Qubit Singlet States with Reverse Engineering and Optimal Control with Spin Qubits

et al. 2020

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A protocol is proposed to generate singlet states of three logical qubits constructed by pairs of spins. Single and multiple operations of logical qubits are studied for the construction of an effective Hamiltonian, with which robust control fields are derived with invariant-based reverse engineering and optimal control. Moreover, systematic errors are further compensated by periodic modulation for better robustness. Furthermore, resistance to random noise and decoherence of the protocol is also shown with numerical simulations. Therefore, the protocol may provide useful perspectives for the generation of logical qubit entanglement in spin systems.

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Section: Physical Model and Hamiltonianmentioning

confidence: 99%

Section: Experimental Considerationsmentioning

confidence: 99%

Section: Appendix A: Initialization Of Logical Qubitsmentioning

confidence: 99%

“…Generally, state of each logical qubit can be described with a Bell‐state basis as (the initialization of logical qubits in the basis can be found in Appendix A)

\begin{matrix} true \\ right false| 0 false⟩ & = & left \frac{1}{\sqrt{2}} (| ↑ ↑ ⟩ + | ↓ ↓ ⟩), | 1 ⟩ = \frac{1}{\sqrt{2}} (| ↑ ↓ ⟩ + | ↓ ↑ ⟩), \\ right false| 2 false⟩ & = & left \frac{1}{\sqrt{2}} (| ↑ ↑ ⟩ - | ↓ ↓ ⟩), | 3 ⟩ = \frac{1}{\sqrt{2}} (| ↑ ↓ ⟩ - | ↓ ↑ ⟩) \end{matrix}

The singlet state to be prepared reads

false| {normalΨ}_{s} false⟩ = (| 012 ⟩ + false| 120 false⟩ + false| 201 false⟩ - false| 102 false⟩ - false| 210 false⟩ - false| 021 false⟩ false) / \sqrt{6}

. Consider that the spins interact with each other through Heisenberg exchange interactions, the Hamiltonian of the system reads [ 46,64–66 ]

\begin{matrix} true \\ H false(t false) & left = H_{s} + H_{d} (t) \\ H_{normals} & left = \sum_{j = 1}^{3} \sum_{ȷ = x, y, z} \frac{J_{ȷ j}}{4} σ_{ȷ}^{false(q_{j_{1}} false)} \otimes σ_{ȷ}^{false(q_{j_{2}} false)} \end{matrix}

…”

Section: Physical Model and Hamiltonianmentioning

confidence: 99%

See 2 more Smart Citations

Robust Generation of Logical Qubit Singlet States with Reverse Engineering and Optimal Control with Spin Qubits

et al. 2020

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show abstract

“…To improve the fidelity and robustness of these threequbit gates, it may be advantageous to employ dynamically corrected gates [46]. Provided the noise dynamics are slow compared to the gate times, such methods can lead to substantial improvements in the gate fidelities and robustness of the gates to calibration errors [6,47,48].…”

Section: Outlook and Conclusionmentioning

confidence: 99%

Protocol for a resonantly driven three-qubit Toffoli gate with silicon spin qubits

Gullans

Petta

2019

Phys. Rev. B

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The three-qubit Toffoli gate plays an important role in quantum error correction and complex quantum algorithms such as Shor's factoring algorithm, motivating the search for efficient implementations of this gate. Here we introduce a Toffoli gate suitable for exchange-coupled electron spin qubits in silicon quantum dot arrays. Our protocol is a natural extension of a previously demonstrated resonantly driven CNOT gate for silicon spin qubits. It is based on a single exchange pulse combined with a resonant microwave drive, with an operation time on the order of 100 ns and fidelity exceeding 99%. We analyze the impact of calibration errors and 1/f noise on the gate fidelity and compare the gate performance to Toffoli gates synthesized from two-qubit gates. Our approach is readily generalized to other controlled three-qubit gates such as the Deutsch and Fredkin gates.

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Gate‐Based Protocol Simulations for Quantum Repeaters using Quantum‐Dot Molecules in Switchable Electric Fields

Wilksen,

Lohof,

Willmann

et al. 2024

Adv Quantum Tech

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Electrically controllable quantum‐dot molecules (QDMs) are a promising platform for deterministic entanglement generation and, as such, a resource for quantum‐repeater networks. A microscopic open‐quantum‐systems approach based on a time‐dependent Bloch–Redfield equation is developed to model the generation of entangled spin states with high fidelity. The state preparation is a crucial step in a protocol for deterministic entangled‐photon‐pair generation that is proposed for quantum repeater applications. The theory takes into account the quantum‐dot molecules' electronic properties that are controlled by time‐dependent electric fields as well as dissipation due to electron–phonon interaction. The transition between adiabatic and non‐adiabatic regimes is quantified, which provides insights into the dynamics of adiabatic control of QDM charge states in the presence of dissipative processes. From this, the maximum speed of entangled‐state preparation is inferred under different experimental conditions, which serves as a first step toward simulation of attainable entangled photon‐pair generation rates. The developed formalism opens the possibility for device‐realistic descriptions of repeater protocol implementations.

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Fast high-fidelity entangling gates for spin qubits in Si double quantum dots

Cited by 30 publications

References 32 publications

Robust Generation of Logical Qubit Singlet States with Reverse Engineering and Optimal Control with Spin Qubits

Robust Generation of Logical Qubit Singlet States with Reverse Engineering and Optimal Control with Spin Qubits

Protocol for a resonantly driven three-qubit Toffoli gate with silicon spin qubits

Gate‐Based Protocol Simulations for Quantum Repeaters using Quantum‐Dot Molecules in Switchable Electric Fields

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