High-fidelity gates in quantum dot spin qubits

Abstract

Several logical qubits and quantum gates have been proposed for semiconductor quantum dots controlled by voltages applied to top gates. The different schemes can be difficult to compare meaningfully. Here we develop a theoretical framework to evaluate disparate qubit-gating schemes on an equal footing. We apply the procedure to two types of double-dot qubits: the singlet-triplet and the semiconducting quantum dot hybrid qubit. We investigate three quantum gates that flip the qubit state: a DC pulsed gate, an AC gate based on logical qubit resonance, and a gate-like process known as stimulated Raman adiabatic passage. These gates are all mediated by an exchange interaction that is controlled experimentally using the interdot tunnel coupling g and the detuning e, which sets the energy difference between the dots. Our procedure has two steps. First, we optimize the gate fidelity (f) for fixed g as a function of the other control parameters; this yields an f opt (g) that is universal for different types of gates. Next, we identify physical constraints on the control parameters; this yields an upper bound f max that is specific to the qubit-gate combination. We show that similar gate fidelities (∼ 99:5%) should be attainable for singlet-triplet qubits in isotopically purified Si, and for hybrid qubits in natural Si. Considerably lower fidelities are obtained for GaAs devices, due to the fluctuating magnetic fields ΔB produced by nuclear spins.quantum computing | Heisenberg exchange | decoherence T he fundamental building block of a quantum information processor is a two-state quantum system, or qubit. Solid-state qubits based on electrons confined in top-gated quantum dots in semiconductor heterostructures (1) are promising, due to the promise of manipulability and the overall maturity of semiconductor technology. In a charge qubit, the information is stored in the location of an electron in a double quantum dot. Because charge qubits are subject to strong Coulomb interactions, they can be manipulated quickly, at gigahertz frequencies, using control electronics (2-5); however, they also couple strongly to environmental noise sources, such as thermally activated charges on materials defects, leading to short, subnanosecond decoherence times (6). Spin qubits, which couple more weakly to environmental noise, have much longer coherence times (1, 7-15). However, because magnetic couplings are weak, gate operations between spin qubits are slow. For this reason, in most gating protocols, spin qubits adopt a charge character briefly during gate operations. Successful gate operations generally entail a tradeoff: charge-like for faster gates vs. spin-like for better coherence.Several types of logical qubits have been designed to enable electrically controlled manipulation and measurement of qubits encoded in spin degrees of freedom formed of two or more electrons in two (7, 9, 16) or three (11) coupled dots. These logical qubits share experimental control knobs; however, their spin-charge characteristics vary widely, yielding ...

Quantum information density scaling and qubit operation time constraints of CMOS silicon-based quantum computer architectures

“…Originally, an architecture of this kind was proposed in systems of triple QDs, where the complete control of qubit states is obtained by tuning the inter-dot exchange couplings. 33,42 Later, a more compact version of the exchange-only triple electron spin virtual qubits has been proposed 37,43 and implemented 36 by using only two QDs, one of which is doubly occupied. Both architecture are extensively reviewed in ref.…”

“…The first experimental work demonstrated coherent qubit rotations at GHz frequencies with fidelity of about 90%, 36 albeit much better performances are theoretically predicted with optimized fabrication and pulse sequences. 43,45,48 The final state is read out by means of charge sensing after collapsing the DQD system in either the (2,1) or the (1,2) charge state, corresponding to the 0 j i and the 1 j i logic state, respectively. Two-qubit gates could be performed similarly as in Fig.…”

“…We note that previous theoretical works identified several strategies to obtain gate fidelity approaching 99.999%. 43,70 This may be good enough to enable QEC by means of the Steane code, which could deal with an error threshold in the range 10 −6 -10 −4 depending on the geometry.…”

“…86 The vertical constraint on the silicon thickness (t Si « w Si ) is related to the transverse size w Si and it may contribute to valley splitting so that a controlled valley states filling is obtained 43,60 as preferable for the three spin exchange-only qubit. 47 Notably, such requirement is implicitly granted by ultra-thin body SOI technology to be employed for nodes beyond 14 nm.…”

“…However, an upper bound to operational speed is set by the tunnel coupling being smaller than the single particle level spacing and the S-T energy splitting. 43 In order to identify the time operation window compatible with physical constraints as a function of the technology node, we consider the three following requirements: adiabaticity, coherence, and node-dependent minimum operation time. First, adiabaticity means that tunnel coupling t must be lower than half the S-T splitting t < ΔE ST /2.…”