Session F28: Architectures for Semiconducting Quantum Computing

Long-range exchange coupling for spin qubits

To scale the arrays of single-electron quantum dots arrays it is necessary to realize long-range spin coupling. In the talk I will present our study of multielectron quantum dots and demonstrate they mediate exchange interaction. In addition I will discuss tunability of multielectron coupler and argue that it can also be used to transfer the electrons between non-neighboring dots.   

Exchange coupling of spin qubits via a multielectron quantum dot

We present a theoretical description for the effective exchange interaction between distant spin qubits mediated by a multielectron quantum dot. Our model is used to interpret experimentally observed exchange interactions between singlet-triplet qubits in such a configuration. We show that a non-zero spin correlation energy for the mediator dot is required to explain key features of the measured exchange profile. The competition between the standard singlet-favouring exchange and the triplet-favouring exchange results in a sweet-spot where the interaction is resistant to charge noise on gate voltages. We argue that multielectron quantum dots are a promising avenue for fast, noise-resistant coupling of spin qubits.   

Negative exchange interactions in few-electron double quantum dots

In a recent experiment, it was shown that negative exchange interactions can arise when a single-electron quantum dot is coupled to a larger quantum dot containing on the order of one hundred electrons. The origin of this negative exchange can be traced to the larger quantum dot exhibiting a spin triplet rather than singlet ground state. Here, we show using a microscopic model based on the configuration interaction (CI) method that both triplet and singlet ground states are realized depending on the number of electrons. In the case of only four electrons, a full CI calculation reveals that triplet ground states occur for sufficiently large dots. These results hold for symmetric and asymmetric quantum dots in both Si and GaAs, showing that negative exchange interactions are robust in few-electron double quantum dots and do not require large numbers of electrons.   

Synchronized High-Fidelity Two-Qubit Gates in Double Quantum Dots

While single-qubit gates with fidelities exceeding 99% for spin qubits in natural silicon and 99.9% in isotopically purified silicon have been demonstrated [1], the fidelity of two-qubit gates is still subject to several limitations. Motivated by recent experiments [2], we theoretically describe a high-fidelity controlled-NOT gate using the exchange interaction between the spins in neighboring quantum dots subject to a magnetic field gradient. We find an optimal gate sequence and present a synchronization method which avoids detrimental spin flips when the control qubit is in state 0. Furthermore, we identify systematic phase mismatches accumulated during the gate. We show that by synchronizing the resonant and off-resonant transitions and compensating unintended phases, the overall gate fidelity can be increased significantly. Numerical simulations also demonstrate a high tolerance against charge noise due to a partial intrinsic refocussing mechanism.

[1] J. Yoneda et al., arXiv:1708.01454.
[2] D. M. Zajac, A. J. Sigillito, M. Russ, F. Borjans, J. M. Taylor, G. Burkard, and J. R. Petta, arXiv:1708.03530.   

Entangling silicon spin qubits in a hybrid dot-donor system

Quantum bits realized in hybrid systems harness the optimal features of multiple types of quantum systems. Silicon provides a particularly attractive platform for realizing hybrid semiconductor qubits, as it supports both nuclear and electron spin qubits in well-isolated atomic impurities as well as highly tunable quantum dot-based spin qubits. Recent experiments [1,2] combine the favorable properties of both systems to demonstrate full coherent control of a hybrid singlet-triplet qubit via exchange and an intrinsic magnetic gradient provided by the donor hyperfine interaction. In order to couple these qubits, we theoretically consider the capacitive interaction in the presence of hyperfine coupling and identify regimes of operation relevant for experiments. We also extend this analysis to investigate the electron spin-mediated interaction between the nuclear spins as a potential mechanism for entangling gates.

[1] P. Harvey-Collard et al., Nat. Commun. 8, 1029 (2017).
[2] M. Rudolph et al., 2016 IEEE International Electron Devices Meeting (IEDM), 34.1.1 (2016).   

High-Fidelity and Robust Two-Qubit Gates for Quantum-Dot Spin Qubits in Silicon

A two-qubit controlled-NOT (CNOT) gate, realized by a controlled-phase (C-phase) gate together with some single-qubit gates, has been experimentally implemented recently for quantum-dot spin qubits in isotopically purified silicon, a promising solid-state system for practical quantum computation. In the experiments, the single-qubit gates have been demonstrated with fault-tolerant control-fidelity, but the infidelity of the two-qubit C-phase gate is, primarily due to the electrical noise, still higher than the required error threshold for fault-tolerant quantum computation (FTQC). Here, by taking the realistic system parameters and the experimental constraints on the control pulses into account, we construct experimentally realizable high-fidelity CNOT gates robust against the electrical noise with the experimentally measured 1/ f^1.01 noise spectrum and against the uncertainty in the interdot tunnel coupling amplitude. Our optimal CNOT gate has about two orders of magnitude improvement in gate infidelity over the ideal C-phase gate. Furthermore, within the same control framework, high-fidelity and robust single-qubit gates can also be constructed, paving the way for large-scale FTQC.   

A pulse sequence designed for robust CNOT gates in SiMOS quantum dots

We theoretically analyze the errors in one- and two-qubit gates in a silicon MOS semiconductor double quantum dot setup [1], and present a pulse sequence which can suppress the errors in exchange coupling due to charge noise to within the acceptable rate for fault-tolerance using ideal local rotations. In practice, the overall fidelity of the pulse sequence will be limited only by the quality of the single-qubit gates available: the CNOT infidelity comes out to be ~10x the infidelity of the single-qubit operations.

For a realistic case, we model the errors and show that a naive implementation of our pulse sequence which uses uncorrected noisy one-qubit gates implemented by pulsing the ESR line can implement a perfect entangler two-qubit gate with a fidelity close to 99.9%, using experimental parameters. Our pulse sequence is simple and we expect an experimental implementation would be straightforward. We also evaluate the performance of this gate against 1/f noise, and analyze the effects of nonadiabaticy during finite rise periods, and compare our results against the existing adiabatic protocol presented in [1].


[1] M. Veldhorst et al, Nature 526, 410-414 (2015)   

Achieving high fidelity single qubit gates in strongly driven silicon quantum dot qubits

Performing qubit gate operations as quickly as possible can be important for minimizing the effects of decoherence. For resonant gating, this requires applying a strong ac drive. However, strong driving can present control challenges by causing leakage as well as theoretical challenges because the rotating-wave approximation can break down. Here we analyze resonant X rotations of silicon quantum double dot hybrid and charge qubits in the presence of 1/f charge noise, typical for semiconducting devices. We obtain analytical formulas for optimal driving parameters, as well as the system evolution. We show that, by exploiting strong driving, gate fidelities in both qubits can be above 99.9%.

This work has been supported in part by ARO (W911NF-12-0607, W911NF-17-1-02747), NSF (PHY-1104660), the University of Wisconsin-Madison, and the Vannevar Bush Faculty Fellowship program sponsored by the Basic Research Office of the Assistant Secretary of Defense for Research and Engineering and funded by the Office of Naval Research through grant N00014-15-1-0029. The views and conclusions contained in this work are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office (ARO), or the U.S. Government.   

Compressed Optimization of Device Architectures (CODA) for Semiconductor Quantum Devices

Recent advances in nanotechnology have enabled researchers to control quantum mechanical objects with unprecedented accuracy. As these devices become larger and more complex, the ability to design them such that they can be simply controlled becomes a daunting task. Here, we introduce a protocol for the Compressed Optimization of Device Architectures (CODA) and apply it to semiconducting quantum dot qubit devices. CODA leads to a metric for benchmarking device performance and optimizing device designs, and provides a scheme for automating the control of gate operations. We demonstrate the CODA protocol through simulations of up to eight quantum dots in devices. This work was supported in part by ARO (W911NF-12-1-0607, W911NF-17-1-0274), and NSF (PHY-1104660). The authors gratefully acknowledge support from the Sandia National Laboratories Truman Fellowship Program, which is funded by the Laboratory Directed Research and Development (LDRD) Program. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for DOE's National Nuclear Security Administration under contract DE-NA0003525, SAND Number: SAND2017-11688 A.   

Measurement-free Implementations of Small-Scale Surface Codes for Quantum Dot Qubits

In quantum dot spin qubits, readout is typically much slower than gate operations, and conventional surface code implementations that rely on syndrome measurements could therefore be challenging. However, fast and accurate reset of quantum dot qubits can be achieved via tunneling to a reservoir. Here, we propose small-scale surface code implementations for which syndrome measurements are replaced by a combination of Toffoli gates and qubit reset. For quantum dot qubits, this enables much faster error correction than measurement-based schemes, but requires additional ancilla qubits and nonlocal interactions. We have performed numerical simulations of two different coding schemes, obtaining error thresholds on the orders of 10^-2 for a 1D architecture that only corrects bit-flip errors, and 10^-4 for a 2D architecture that corrects bit and phase-flip errors. We have also demonstrated that when the measurement time is about 10 times the gate time, our method begins producing a higher threshold than the measurement-based method.

The authors acknowledge support from the Vannevar Bush Faculty Fellowship program sponsored by the Basic Research Office of the Assistant Secretary of Defense for Research and Engineering and funded by the Office of Naval Research through grant N00014-15-1-0029.   

Demonstration of a hole quantum dot in Ge/SiGe

Heavy holes in Ge/SiGe quantum well heterostructures have potential advantages as spin-based qubits including all electrical control through intrinsic spin-orbit coupling, the possibility of isotopic enrichment, and the absence of valley states. Recently high-mobility material suitable to host spin qubits has become available. We will report on experiments which demonstrate the formation of a gate-controlled lateral quantum dot in undoped Ge/SiGe heterostructure quantum wells. Details of the device fabrication and low-temperature characterization of the quantum dot will be presented. These results, demonstrating confinement of holes in this material system, are the first step toward achieving heavy hole-based spin qubits in a lateral quantum dot device design in germanium. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.   

Light-mass hole-spins in a Ge quantum well as qubits

Electrons bound to quantum dots provide well defined (spin 1/2) physical qubits. Under strong spin-orbit coupling spin qubits are expected to suffer rapid dephasing from charge noise; however, recent experiments have effectively employed spin-orbit coupling in coherent quantum gates. Here we show that hole spins in a Si_1-xGe_x/Ge/ Si_1-xGe_x quantum well possess highly desirable properties as qubits, including a high natural abundance of nuclear spin-0 isotopes, a large (~100 meV) intrinsic splitting between the light and heavy hole bands, and a very light (~0.05m₀) effective mass. We employ ab initio methods to determine the band structure of strained Ge quantum wells as a function of x, and we discuss the advantages and challenges of using Ge hole spins as qubits.   

A Gate-driven Entanglement Switch, Magic Angles, and a Decoherence Free Subspace in Acceptor Spin Qubits in Si

Electrical control of quantum bits could pave the way for fast, low-power, scalable quantum computation. It was recently shown that an acceptor spin qubit in Si, based on holes rather than electrons, offers full electrical control, fast operations with long relaxation and dephasing times, and entanglement based on dipole-dipole interactions. The two-qubit operations are limited by the dipole-dipole interaction itself, since it can only be turned off by deactivating one of the qubits. The other limiting factor is the relaxation time T₁, which is difficult to enhance if fast operations are desired using purely electrical means. Here we show theoretically that an appropriate fixed magnetic field in-plane orientation allows to electrically switch two-qubit coupling on and off while enhancing the relaxation time T₁ near a decoherence free subspace. This magic angle stems from the interplay of the T_d symmetry of the acceptor in the Si lattice and the spin-3/2 characteristic of hole systems. Our findings can be directly applied to state-of-the-art acceptor based architectures, for which we propose suitable protocols to practically achieve full electrical tunability of entanglement and the realization of a decoherence-free subspace. arXiv:1706.08858