Fidelity benchmarks for two-qubit gates in silicon

Abstract

Universal quantum computation will require qubit technology based on a scalable platform, together with quantum error correction protocols that place strict limits on the maximum infidelities for one-and two-qubit gate operations 1,2 . While a variety of qubit systems have shown high fidelities at the one-qubit level 3-9 , superconductor technologies have been the only solidstate qubits manufactured via standard lithographic techniques which have demonstrated twoqubit fidelities near the fault-tolerant threshold 5 . Silicon-based quantum dot qubits are also amenable to large-scale manufacture and can achieve high single-qubit gate fidelities (exceeding 99.9 %) using isotopically enriched silicon 10-12 . However, while two-qubit gates have been demonstrated in silicon 13-15 , it has not yet been possible to rigorously assess their fidelities using randomized benchmarking, since this requires sequences of significant numbers of qubit operations ( 20) to be completed with non-vanishing fidelity. Here, for qubits encoded on the electron spin states of gate-defined quantum dots, we demonstrate Bell state tomography with fidelities ranging from 80 % to 89 %, and two-qubit randomized benchmarking with an average Clifford gate fidelity of 94.7 % and average Controlled-ROT (CROT) fidelity of 98.0 %. These fidelities are found to be limited by the relatively slow gate times employed here compared with the decoherence times T * 2 of the qubits. Silicon qubit designs employing fast gate operations based on high Rabi frequencies 16-18 , together with advanced pulsing techniques 19 , should therefore enable significantly higher fidelities in the near future.Silicon provides an ideal environment for spin qubits thanks to its compatibility with industrial manufacturing technologies and the near-perfect nuclear-spin vacuum that isotopically enriched 28 Si provides 10,11 . Qubits can be encoded directly on the spins of individual nuclei, donor-bound electrons, or electrons confined in gatedefined quantum dots, or they can be encoded in subspaces provided by two or more spins 12 . Electrostatic gate electrodes allow initialization, readout 23 and, in some cases, manipulation of qubits 24 to be implemented with local electrical pulses. For qubits encoded on single spins, one-qubit gates can be driven using an AC magnetic field to perform electron spin resonance (ESR) directly 8,25 , through an AC electric field produced by a gate electrode combined with the magnetic field gradient from an on-chip micro-magnet 16,17,26 , or with an AC electric field acting on the spin-orbit field 27-29 . In enriched 28 Si devices such one-qubit gates have attained fidelities of 99.9 % or above 18,30,31 .Two-qubit gates, required to complete the universal gate set, are commonly implemented in spin systems as the √ SW AP 24,32 , the C-Phase 13,14 or the CROT 13,15 . While the √ SW AP and the C-Phase gates require fast temporal control of the exchange interaction J, accurately synchronized with spin resonance pulses, the CROT can also be implemented wit...

Adiabatic electron charge transfer between two quantum dots in presence of 1/f noise

“…We focus here on this long-distance electron transfer, since it works also for nonpolar semiconductors, such as silicon. Electron spin localized in a silicon-based structure experiences much less nuclear noise than in GaAs, and creation of coherently controlled silicon-based quantum dot * krzywda@ifpan.edu.pl † lcyw@ifpan.edu.pl spin qubits has recently achieved a high degree of success both in Si/SiO 2 [6,7] and Si/SiGe structures [4,5,27]. The process of electron transfer along a chain of quantum dots [26] naturally decomposes into basic building blocks of charge transfer between pairs of neighboring dots.…”

Tunable Coupling and Isolation of Single Electrons in Silicon Metal-Oxide-Semiconductor Quantum Dots

“…Reaching this level of control in silicon metal-oxide-semiconductor (SiMOS) quantum dots is highly desired as this platform has a high potential for complete integration with classical manufacturing technology [14][15][16]. However, current two-qubit logic with single spins in SiMOS is based on controlling the exchange using the detuning only [17] or is executed at fixed exchange interaction [18].In SiMOS, a first step toward the required control to materialize architectures for large-scale quantum computation [1,[19][20][21][22][23][24] has been the demonstration of tunable coupling in a double quantum dot system operated in the many-electron regime, where gaining control is more accessible owing to the larger electron wave function [25]. More recently, exchange-controlled two-qubit operations have been shown with three-electron quantum dots [26].…”

A sparse spin qubit array with integrated control electronics

“…Semiconductor spin qubits [1,2] are an attractive platform for large-scale quantum computers, due to their potential compatibility with well-established semiconductor manufacturing processes. In the last decade we have witnessed tremendous progress in the development of spin-qubit hardware [3][4][5][6][7][8] and significant interest and contribution of the semiconductor industry into spin-qubit research [9][10][11].…”