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arXiv:quant-ph/0410062 · Physical Review A

Controlled phase gate for solid-state charge-qubit architectures

S. G. Schirmer, Daniel K. L. Oi, Andrew D. Greentree

Published Jan 18, 2005• 14 citations
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Abstract

We describe a mechanism for realizing a controlled phase gate for solid-state charge qubits. By augmenting the positionally defined qubit with an auxiliary state, and changing the charge distribution in the three-dot system, we are able to effectively switch the Coulombic interaction, effecting an entangling gate. We consider two architectures, and numerically investigate their robustness to gate noise.

DOI
10.1103/physreva.71.012325

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We describe a mechanism for realizing a controlled phase gate for solid-state charge qubits. By augmenting the positionally defined qubit with an auxiliary state, and changing the charge distribution in the three-dot system, we are able to effectively switch the Coulombic interaction, effecting an entangling gate. We consider two architectures, and numerically investigate their robustness to gate noise.
Exchange-coupled singlet-triplet spin qubits in two gate-defined double quantum dots are considered theoretically. Using charge density operators to describe the double-dot orbital states, we calculate the Coulomb couplings between the qubits and identify optimal bias points for single- and two-qubit operations, as well as convenient idle positions. The same intuitive formulation is used to derive dephasing rates of these qubits due to the fluctuating charge environment, thereby providing the main considerations for a quantum computation architecture that is within current experimental capabilities.
We propose an implementation of the two-qubit gate in a quantum dot spin qubit system which is immune to charge noise problems. Our proposed implementation, if it could be realized in a physical system, would have the advantage of being robust against uncertainties and fluctuations in the tunnel coupling and barrier gate voltage pulse area. The key idea is to introduce an auxiliary dot and use an analog to the stimulated Raman adiabatic passage pulse sequence in three-level atomic systems, often referred to in the context of electron transport in quantum dot systems as Coherent Tunneling by Adiabatic Passage. Spin-dependent tunneling opens the possibility of performing two-qubit gate operations by this method.
In this study, a formal definition, robustness analysis and discussion on the control of a position-based semiconductor charge qubit are presented. Such a qubit can be realized in a chain of coupled quantum dots, forming a register of charge-coupled transistor-like devices, and is intended for CMOS implementation in scalable quantum computers. We discuss the construction and operation of this qubit, its Bloch sphere, and relation with maximally localized Wannier functions which define its position-based nature. We then demonstrate how to build a tight-binding model of single and multiple interacting qubits from first principles of the Schrödinger formalism. We provide all required formulae to calculate the maximally localized functions and the entries of the Hamiltonian matrix in the presence of interaction between qubits. We use three illustrative examples to demonstrate the electrostatic interaction of electrons and discuss how to build a model for many-electron (qubit) system. To conclude this study, we show that charge qubits can be entangled through electrostatic interaction.
Charge noise has been one of the main issues in realizing high fidelity two-qubit quantum gates in semiconductor based qubits. Here, we study the influence of quasistatic noise in quantum dot detuning on the controlled phase gate for spin qubits that defined on a double quantum dot. Analytical expressions for the noise averaged Hamiltonian, exchange interaction, as well as the gate fidelity are derived for weak noise covering experimental relevant regime. We also perform interleaved two-qubit randomized benchmarking analysis for the controlled phase gate and show that an exponential decay of the sequential fidelity is still valid for the weak noise.
We present a theoretical proposal of a tunable charge qubit, hosted in triple quantum dots. The manipulation is solely performed by changing the heights of the two potential barriers between the three dots, while the energies of all three dots are fixed. We have found that when the relative heights of the two barriers are changed, the direction of the axis of rotation in performing single-qubit gates can be varied. On the other hand, the corresponding rotation speed can be tuned by raising or lowering the two barriers at the same time. Our proposal therefore allows for tunability of both the rotation axis and rotating speed for a charge qubit via all-electrical control, which may facilitate realization of quantum algorithms in these devices.