High-fidelity initialization and control of electron and nuclear spins in a four-qubit register
J. Reiner, Yousun Chung, S. H. Misha, Christian A. Lehner, Christian M. Moehle, D. Poulos, Serajum Monir, Keshavi Charde, P. Macha, Ludwik Kranz, Ian Thorvaldson, Brandur Thorgrimsson, Daniel Keith, Yu‐Ling Hsueh, Rajib Rahman, S. K. Gorman, J. G. Keizer, M. Y. Simmons
Abstract
Abstract Single electron spins bound to multi-phosphorus nuclear spin registers in silicon have demonstrated fast (0.8 ns) two-qubit $$\sqrt{\mathrm{SWAP}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mrow> <mml:mi>SWAP</mml:mi> </mml:mrow> </mml:msqrt> </mml:math> gates and long spin relaxation times (~30 s). In these spin registers, when the donors are ionized, the nuclear spins remain weakly coupled to their environment, allowing exceptionally long coherence times. When the electron is present, the hyperfine interaction allows coupling of the spin and charge degrees of freedom for fast qubit operation and control. Here we demonstrate the use of the hyperfine interaction to enact electric dipole spin resonance to realize high-fidelity ( $$F=10{0}_{-6}^{+0}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo>=</mml:mo> <mml:mn>10</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> %) initialization of all the nuclear spins within a four-qubit nuclear spin register. By controllably initializing the nuclear spins to $$\left\vert \Downarrow \Downarrow \Downarrow \right\rangle$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mrow> <mml:mi>⇓</mml:mi> <mml:mi>⇓</mml:mi> <mml:mi>⇓</mml:mi> </mml:mrow> </mml:mfenced> </mml:math> , we achieve single-electron qubit gate fidelities of F = 99.78 ± 0.07% (Clifford gate fidelities of 99.58 ± 0.14%), above the fault-tolerant threshold for the surface code with a coherence time of $${T}_{2}^{\,* }=12\,\upmu {{{\rm{s}}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mspace/> <mml:mo>*</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>12</mml:mn> <mml:mspace/> <mml:mi>μ</mml:mi> <mml:mi>s</mml:mi> </mml:mrow> </mml:math> .