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arXiv:1707.07929 · Physical Review A

Magic angle for barrier-controlled double quantum dots

Xu-Chen Yang, Xin Wang

Published Jan 9, 2018• 6 citations
arXivHTMLPDF

Abstract

We show that the exchange interaction of a singlet-triplet spin qubit confined in double quantum dots, when being controlled by the barrier method, is insensitive to a charged impurity lying along certain directions away from the center of the double-dot system. These directions differ from the polar axis of the double dots by the magic angle, equaling $arccos\left(1/\sqrt{3}\right)\ensuremath{\approx}54.{7}^{\ensuremath{\circ}}$, a value previously found in atomic physics and nuclear magnetic resonance. This phenomenon can be understood from an expansion of the additional Coulomb interaction created by the impurity, but also relies on the fact that the exchange interaction solely depends on the tunnel coupling in the barrier-control scheme. Our results suggest that for a scaled-up qubit array, when all pairs of double dots rotate their respective polar axes from the same reference line by the magic angle, crosstalk between qubits can be eliminated, allowing clean single-qubit operations. While our model is a rather simplified version of actual experiments, our results suggest that it is possible to minimize unwanted couplings by judiciously designing the layout of the qubits.

DOI
10.1103/physreva.97.012304

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We show that the exchange interaction of a singlet-triplet spin qubit confined in double quantum dots, when being controlled by the barrier method, is insensitive to a charged impurity lying along certain directions away from the center of the double-dot system. These directions differ from the polar axis of the double dots by the magic angle, equaling arccos(1/3)\ensuremath≈54.7\ensuremath∘arccos\left(1/\sqrt{3}\right)\ensuremath{\approx}54.{7}^{\ensuremath{\circ}}arccos(1/3​)\ensuremath≈54.7\ensuremath∘, a value previously found in atomic physics and nuclear magnetic resonance. This phenomenon can be understood from an expansion of the additional Coulomb interaction created by the impurity, but also relies on the fact that the exchange interaction solely depends on the tunnel coupling in the barrier-control scheme. Our results suggest that for a scaled-up qubit array, when all pairs of double dots rotate their respective polar axes from the same reference line by the magic angle, crosstalk between qubits can be eliminated, allowing clean single-qubit operations. While our model is a rather simplified version of actual experiments, our results suggest that it is possible to minimize unwanted couplings by judiciously designing the layout of the qubits.
It has been recently demonstrated that a singlet-triplet spin qubit in semiconductor double quantum dots can be controlled by changing the height of the potential barrier between the two dots (``barrier control''), which has led to a considerable reduction of charge noises as compared with the traditional tilt control method. In this paper we show, through a molecular-orbital-theoretic calculation of double quantum dots influenced by a charged impurity, that the relative charge noise for a system under the barrier control not only is smaller than that for the tilt control but actually decreases as a function of an increasing exchange interaction. This is understood as a combined consequence of the greatly suppressed detuning noise when the two dots are symmetrically operated, as well as an enhancement of the interdot hopping energy of an electron when the barrier is lowered which in turn reduces the relative charge noise at large exchange interaction values. We have also studied the response of the qubit to charged impurities at different locations and found that the improvement of barrier control is least for impurities equidistant from the two dots due to the small detuning noise they cause but is otherwise significant along other directions.
It has been recently demonstrated that a singlet-triplet spin qubit in semiconductor double quantum dots can be controlled by changing the height of the potential barrier between the two dots (barrier control), which has led to a considerable reduction of charge noises as compared to the traditional tilt control method. In this paper we show, through a molecular-orbital-theoretic calculation of double quantum dots influenced by a charged impurity, that the relative charge noise for a system under the barrier control not only is smaller than that for the tilt control, but actually decreases as a function of an increasing exchange interaction. This is understood as a combined consequence of the greatly suppressed detuning noise when the two dots are symmetrically operated, as well as an enhancement of the inter-dot hopping energy of an electron when the barrier is lowered which in turn reduces the relative charge noise at large exchange interaction values. We have also studied the response of the qubit to charged impurities at different locations, and found that the improvement of barrier control is least for impurities equidistant from the two dots due to the small detuning noise they cause, but is otherwise significant along other directions.
We theoretically consider the effects of having unintentional charged impurities in laterally coupled two-dimensional double (GaAs) quantum-dot systems, where each dot contains one or two electrons and a single charged impurity. Using molecular orbital and configuration interaction methods, we calculate the effect of the impurity on the two-electron energy spectrum of each individual dot as well as on the spectrum of the coupled-double-dot two-electron system. We find that the singlet-triplet exchange splitting between the two lowest-energy states, both for the individual dots and the coupled-dot system, depends sensitively on the location of the impurity and its coupling strength (i.e. the effective charge). A strong electron-impurity coupling breaks down the equality of the two doubly occupied singlets in the left and the right dots, leading to a mixing between different spin singlets. As a result, the maximally entangled qubit states are no longer fully obtained in the zero-magnetic-field case. Moreover, a repulsive impurity results in a triplet-singlet transition as the impurity effective charge increases or the impurity position changes. We comment on the impurity effect in spin qubit operations in the double-dot system based on our numerical results.
A two-level quantum system is the building block of a quantum computer. This pair of quantum states defines the computational unit of a quantum computer, and it is called a quantum bit or qubit in analogy to the bit that is the binary unit of a classical computer. The spin of a single electron naturally defines such a two-level quantum system. A quantum dot can be tuned to the single-electron regime, and an array of singly occupied quantum dots provides a multi-qubit register. This thesis describes the multielectron encoding of a spin qubit using a pair or a trio of quantum dots, and it analyzes the coherence properties and manipulation protocols of this system. The singlet-triplet qubit, coded using the singlet state and the spinless triplet state of a pair of singly occupied quantum dots, can be controlled all electrically when applying voltages to gates close to the quantum dot structure. Rapid, subnanosecond modifications of the double quantum dot's charge configuration have been realized successfully. A small magnetic field gradient across the double quantum dot enables universal qubit control. Two modifications of the normal singlet-triplet encoding are introduced. (1) The six-electron configuration of a double quantum dot encodes a singlet-triplet qubit in the same way as for the two-electron double quantum dot. Two electrons at each quantum dot are irrelevant for the qubit manipulations because they are paired in a singlet state; the remaining two electrons encode the qubit. The qubit's wave function is immune to charge noise at moderate out-of-plane magnetic fields. (2) A singlet-triplet qubit encoded using two quantum dots of different sizes has an orbital state degeneracy of the singlet state and the spinless triplet state at finite out-of-plane magnetic fields. Spin-orbit interactions lift this state degeneracy, while the magnitude of the state coupling is determined by the size difference of the QDs. This setup enables the manipulations of singlet-triplet qubits without the need for magnetic field gradients. Finally, two-qubit gates between singlet-triplet qubits are proposed that use mediated exchange interactions via one quantum state. These operations are well controlled and highly noise insensitive. Orbital interactions alone can control spin qubits coded in a three electron Hilbert space. For example, the exchange-only qubit is encoded using three singly occupied quantum dots. The exchange interactions of two quantum dot pairs need to be modified to manipulate this qubit. The noise sensitivity of the exchange-only qubit is discussed. Alternatively, a three-electron qubit at a double quantum dot can be operated when single electrons are transferred between the quantum dots. Fast, subnanosecond manipulations of the double quantum dot's charge configuration are required to realize single-qubit gates. A novel two-qubit pulse gate for the three-electron double quantum dot qubit is proposed.
In the semiconductor double quantum dot singlet-triplet qubit architecture, the decoherence caused by the qubit's charge environment poses a serious obstacle towards large scale quantum computing. The effects of the charge decoherence can be mitigated by operating the qubit in the so-called sweet spot regions where it is insensitive to electrical noise. In this paper, we propose singlet-triplet qubits based on two quantum dots of different sizes. Such asymmetric double quantum dot systems allow the implementation of exchange gates with controllable exchange splitting JJJ operated in the doubly occupied charge region of the larger dot, where the qubit has high resilience to charge noise. In the larger dot, JJJ can be quenched to a value smaller than the intradot tunneling using magnetic fields, while the smaller dot and its larger splitting can be used in the projective readout of the qubit.
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.