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arXiv:2501.13289 · Journal of Applied Physics

Effects of valley splitting on resonant-tunneling readout of spin qubits

Tetsufumi Tanamoto, Keiji Ono

Published Apr 25, 2025• 0 citations
arXivHTMLPDF

Abstract

The effect of valley splitting on the readout of qubit states is theoretically investigated in a three-quantum-dot (QD) system. A single unit of the three-QD system consists of qubit-QDs and a channel-QD that is connected to a conventional transistor. The nonlinear source–drain current characteristics under resonant-tunneling effects are used to distinguish different qubit states. Using nonequilibrium Green functions, the current formula for the three-QD system is derived when each QD has two valley energy levels. Two valley states in each QD are considered to be affected by variations in the fabrication process. We found that when valley splitting is smaller than Zeeman splitting, the current nonlinearity can improve the readout, provided that the nonuniformity of the valley energy levels is small. Conversely, when the valley splitting is larger than the Zeeman splitting, the nonuniformity degraded the readout. In both cases, we showed that there are regions where the measurement time tmeas is much less than the decoherence time tdec such that tdec/tmeas>100. This suggests that less than 1% measurement error is anticipated, which opens up the possibility of implementing surface codes even in the presence of valley splitting.

DOI
10.1063/5.0260516

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•Jan 1, 2015•0 citations
The effect of valley splitting on the readout of qubit states is theoretically investigated in a three-quantum-dot (QD) system. A single unit of the three-QD system consists of qubit-QDs and a channel-QD that is connected to a conventional transistor. The nonlinear source–drain current characteristics under resonant-tunneling effects are used to distinguish different qubit states. Using nonequilibrium Green functions, the current formula for the three-QD system is derived when each QD has two valley energy levels. Two valley states in each QD are considered to be affected by variations in the fabrication process. We found that when valley splitting is smaller than Zeeman splitting, the current nonlinearity can improve the readout, provided that the nonuniformity of the valley energy levels is small. Conversely, when the valley splitting is larger than the Zeeman splitting, the nonuniformity degraded the readout. In both cases, we showed that there are regions where the measurement time tmeas is much less than the decoherence time tdec such that tdec/tmeas>100. This suggests that less than 1% measurement error is anticipated, which opens up the possibility of implementing surface codes even in the presence of valley splitting.
Spin qubit systems are one of the promising candidates for quantum computing. The quantum dot (QD) arrays are intensively investigated by many researchers. Because the energy-difference between the up-spin and down-spin states is very small, the detection of the qubit state is of prime importance in this field. Moreover, many wires are required to control qubit systems. Therefore, the integration of qubits and wires is also an important issue. In this study, the measurement process of QD arrays is theoretically investigated using resonant tunneling, controlled by a conventional transistor. It is shown that the number of possible measurements during coherence time can exceed a hundred under the backaction of the measurements owing to the nonlinear characteristics of resonant tunneling. It is also discussed to read out the measurement results by the conventional transistor.
In spin qubit arrays the exchange coupling can be harnessed to implement two-qubit gates and to realize intermediate-range qubit connectivity along a spin bus. In this work, we propose a scheme to characterize the exchange coupling between electrons in adjacent quantum dots. We investigate theoretically the transmission of a microwave resonator coupled to a triple quantum dot occupied by two electrons. We assume that the right quantum dot (QD) is always occupied by one electron while the second electron can tunnel between the left and center QDs. If the two electrons are in adjacent dots they interact via the exchange coupling. By means of analytical calculations we show that the transmission profile of the resonator directly reveals the value of the exchange coupling strength between two electrons. From perturbation theory up to second order we conclude that the exchange can still be identified in the presence of magnetic gradients. A valley splitting comparable to the interdot tunnel coupling will lead to further modifications of the cavity transmission dips that also depend on the valley phases.
Charge separation from the (4,0)(4,0)(4,0) to the (3,1)(3,1)(3,1) state in a Si/SiGe double quantum dot is commonly used for initialization of spin qubits and Pauli-spin-blockade readout. It was used in recent experiments involving creation of the (3,1)(3,1)(3,1) singlet, and subsequent shuttling of one of the electrons. We present a theoretical description of the process of charge separation and singlet-triplet mixing, arriving at expressions for the singlet return probability that take into account experimentally observed finite probabilities of the creation of singlets with various patterns of valley occupations. In our analysis we focus on magnetic fields for which the electron spin Zeeman splitting is close to the valley splitting in one of the dots, when the spin-valley coupling causes a strong renormalization of the frequency of oscillations of singlet return probability. The latter effect has been recently used to perform valley splitting mapping by shuttling of one quantum dot to various locations with respect to the other. We give a detailed description of singlet-triplet dynamics near these spin-valley resonances and compare the results of calculations with measurements on double quantum dots in two distinct Si/SiGe heterostructures. Comparison of theory with experiments in which the presence of a few valley occupation patterns is visible, gives insight into the valley dependence of ggg-factors in these structures, providing support for a recently proposed theoretical model of this dependence. We also discuss how dephasing of singlet return probability oscillations near the spin-valley resonances is affected by valley splitting fluctuations caused by electric field noise.
Controlling the energy scales of a quantum system is essential for defining robust qubits. In silicon spin qubits, the nearly degenerate conduction-band valleys create a leakage channel from the single-spin computational basis, posing a challenge to scaling and to shuttling-based architectures. Here, we measure the relevant energy scales of single-electron spin qubits in buried silicon quantum wells co-designed for low disorder and high valley splitting. Across a linear array of four quantum dots with an average orbital energy of 2.4(2) meV, we report an average single-electron valley splitting of 0.40(6) meV and an average two-electron singlet-triplet splitting of 0.24(7) meV. In three dots, we observe a strong correlation between valley splitting and orbital energy, with an average linear coefficient of ≈0.22\approx 0.22≈0.22 (meV/meV), demonstrating that electrostatic confinement can increase the valley splitting by several hundred microelectronvolts. In contrast, the remaining dot exhibits the highest valley splitting of 0.76(2) meV and low correlation, suggesting excellent characteristics for spin-qubit operation. Our findings demonstrate that strong confinement can be exploited in buried quantum wells to effectively enhance the valley splitting, thereby establishing a viable path toward the realization of shuttling and sparse-occupation-based architectures in low-disorder heterostructures.
Advanced tensor network numerical methods are used to explore the fidelity of repeated SWAP operations on a system comprising 20--100 quantum dot spin qubits in the presence of valley leakage and electrostatic crosstalk. The fidelity of SWAP gates is largely unaffected by Zeeman splitting and valley splitting, except when these parameters come into resonance. The fidelity remains independent of the overall valley phase for valley eigenstates, while for generic valley states, some minor corrections arise. We analyze the fidelity scaling for long qubit chains without valley effects, where crosstalk represents the only error source.
This thesis addresses the concept of quantum computing with semiconductor quantum dots. The basic unit of a quantum computer is a quantum mechanical two-level system, the so-called quantum bit (qubit). The qubit can be defined as the spin of an electron confined in a quantum dot or as a two-dimensional subspace of the Hilbert space for several spins. Some semiconductors have several minima in their conduction band, socalled valleys. A two-dimensional valley degree of freedom can also be considered as a qubit. In this thesis, quantum registers storing spin as well as valley qubits are described theoretically. Virtual hopping yields an exchange interaction between neighboring quantum dots, which reduces the energy of antisymmetric spin-valley states according to the Pauli principle. Considering the spin and the valley degrees of freedom of two electrons in neighboring quantum dots as qubits, the exchange interaction is a four-qubit interaction. In this thesis, it will be shown that it is, nevertheless, possible to generate a universal two-qubit gate for spin qubits or for valley qubits by combining the exchange interaction and individual single-qubit gates. The exchange interaction in this two-electron double quantum dot directly provides a universal two-qubit gate for one spin and one valley qubit as well. For this, the qubits are defined as suitable subspaces, spanned by the singlet and one triplet state of the spin and the valley states, respectively, Using those gates, arbitrary quantum operations can be performed for single-spin and single-valley qubits in the same quantum register, where in one double quantum dot the quantum states are restricted to the singlet-triplet subspace. While in this register single-spin and single-valley rotations are required, these gates are dispensable in a quantum register storing spin and valley singlet-triplet qubits. The single-qubit operations, in this case, can be provided by the exchange interaction and a gradient in the energy splitting of spin and valley states when the spin qubit is stored in a double quantum dot with spin degrees of freedom only and when the spin states in the double quantum dot which stores the valley qubit are polarized. For providing the two-qubit gate, the spin and the valley qubits need to be stored in the same double quantum dot. The crucial task for this register is to interchange the spin of a spin-only and a spin-valley quantum dot in order to switch between the single-qubit and the two-qubit operation mode. This interchanging of the spin can be achieved by a valley-depending virtual hopping between the quantum dots. Furthermore, echo sequences for a so-called exchange-only qubit are considered. An exchange-only qubit is defined as a subspace in a system of three electron spins in a triple quantum dot. An inhomogeneous magnetic field, which may be caused by nuclear spins in the semiconductor, can lead to decoherence and leakage, i.e., the state might leave the qubit subspace. Suppressing this effect by an echo sequence which consists of pulses interchanging neighboring spin states, so-called SWAP gates, was proposed. Controllability over these quantum operations is provided via the exchange interaction. In this thesis, the performance of different such sequences is investigated. The analysis shows that optimization strategies developed for single spin echoes can be adapted for the three spin system. The echo sequences can be different in their order of applied SWAP gates interchanging the spins in the first and second dots or in the second and third dots. The noise suppression performance depends slightly on this order of SWAP gates. For two spins in a double quantum dot a scheme for quantum state tomography is presented. The corresponding measurement operators are constructed from a set of mutually unbiased bases of the four-dimensional two-qubit Hilbert space. These measurements are represented by short sequences of no more than three elementary quantum gates and projective measurements by the well-established spin-to-charge conversion.