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arXiv:cond-mat/0301612 · Physical Review A

Spin-swap gate in the presence of qubit inhomogeneity in a double quantum dot

Xuedong Hu, S. Das Sarma

Published Nov 17, 2003• 13 citations
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Abstract

We study theoretically the effects of qubit inhomogeneity on the quantum logic gate of qubit swap, which is an integral part of the operations of a quantum computer. Our focus here is to construct a robust pulse sequence for swap operation in the simultaneous presence of Zeeman inhomogeneity for quantum dot trapped electron spins and the finite-time ramp-up of exchange coupling in a double dot. We first present a geometric explanation of spin swap operation, mapping the two-qubit operation onto a single-qubit rotation. We then show that in this geometric picture a square-pulse sequence can be easily designed to perform swap in the presence of Zeeman inhomogeneity. Finally, we investigate how finite ramp-up times for the exchange coupling J negatively affect the performance of the swap gate sequence, and show how to correct the problems numerically.

DOI
10.1103/physreva.68.052310

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We study theoretically the effects of qubit inhomogeneity on the quantum logic gate of qubit swap, which is an integral part of the operations of a quantum computer. Our focus here is to construct a robust pulse sequence for swap operation in the simultaneous presence of Zeeman inhomogeneity for quantum dot trapped electron spins and the finite-time ramp-up of exchange coupling in a double dot. We first present a geometric explanation of spin swap operation, mapping the two-qubit operation onto a single-qubit rotation. We then show that in this geometric picture a square-pulse sequence can be easily designed to perform swap in the presence of Zeeman inhomogeneity. Finally, we investigate how finite ramp-up times for the exchange coupling J negatively affect the performance of the swap gate sequence, and show how to correct the problems numerically.
We calculate the effect of an inhomogeneous magnetic field, which is invariably present in an experimental environment, on the exchange energy of a double-quantum-dot artificial molecule, projected to be used as a two-qubit quantum gate in the proposed quantum-dot quantum computer. We use two different theoretical methods to calculate the Hilbert space structure in the presence of the inhomogeneous field: the Heitler-London method, which is carried out analytically, and the molecular orbital method, which is done computationally. Within these approximations we show that the exchange energy J changes slowly when the coupled dots are subject to a magnetic field with a wide range of inhomogeneity, suggesting that swap operations can be performed in such an environment as long as quantum error correction is applied to account for the Zeeman term. We also point out the quantum interference nature of this slow variation in exchange.
We propose a set of universal gate operations for the singlet-triplet qubit realized by two-electron spins in a double quantum dot, in the presence of a fixed inhomogeneous magnetic field. All gate operations are achieved by switching the potential offset between the two dots with an electrical bias, and do not require time-dependent control of the tunnel coupling between the dots. We analyze the two-electron dynamics and calculate the effective qubit rotation angle as a function of the applied electric bias. We present explicit gate sequences for single-qubit rotations about two orthogonal axes, and a CNOT gate sequence, completing the universal gate set.
Spin model plays an important role in the realization of quantum information processing. Quantum entanglement can be constructed, also （swap）n quantum logic gate is available if anisotropy is ignored, when Heisenberg interaction between spins is used; thus a complete quantum computing gate will be realized by combining single-qubit rotation gate. To study the influence of anisotropy on logic gate has high academic value since anisotropy is inevitable in any solid material. In this paper, swap operation in a two-qubit anisotropy XYZ model in the presence of an inhomogeneous magnetic field is discussed. The swap errors caused by the anisotropy parameter ν of the exchange interaction between spins and the inhomogeneous field δ are evaluated. We can see clearly when the swap operation can be approximately used as an ideal swap gate.
A two-electron system confined in two coupled semiconductor quantum dots is investigated as a candidate for performing quantum logic operations with spin qubits. We study different processes of swapping the electron spins by a controlled switching on and off of the exchange interaction. The resulting spin swap corresponds to an elementary operation in quantum-information processing. We perform direct simulations of the time evolution of the two-electron system. Our results show that, in order to obtain the full interchange of spins, the exchange interaction should change smoothly in time. The presence of jumps and spikes in the time characteristics of the confinement potential leads to a considerable increase of the spin-swap time. We propose several mechanisms to modify the exchange interaction by changing the confinement potential profile and discuss their advantages and disadvantages.
The benefit of exchange-only qubits compared to other spin-qubit types is the universal control using only voltage-controlled exchange interactions between neighboring spins. As a compromise, qubit operations have to be constructed from nonorthogonal rotation axes of the Bloch sphere and result in rather long pulsing sequences. This paper aims to develop a faster implementation of single-qubit gates using simultaneous exchange pulses and manifests their potential for the construction of two-qubit gates. We introduce pulse sequences in which single-qubit gates could be executed faster and show that subsequences on three spins in two-qubit gates could be implemented in fewer steps. Our findings can particularly speed up gate sequences for realistic idle times between sequential pulses and we show that this advantage increases with more interconnectivity of the quantum dots. We further demonstrate how a phase operation can introduce a relative phase between the computational and some of the leakage states, which can be advantageous for the construction of two-qubit gates. In addition to our theoretical analysis, we experimentally demonstrate and characterize a simultaneous exchange implementation of X rotations in a Si Ge quantum dot device and compare to the state of the art with sequential exchange pulses.