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Nature Communications

Tomography of entangling two-qubit logic operations in exchange-coupled donor electron spin qubits

Holly G. Stemp, Serwan Asaad, Mark R. van Blankenstein, Arjen Vaartjes, Mark A. I. Johnson, Mateusz Tomasz Mądzik, Amber Heskes, Hannes R. Firgau, Rocky Y. Su, Chih Hwan Yang, Arne Laucht, Corey Ostrove, Kenneth Rudinger, Kevin C Young, Robin Blume-Kohout, Fay E. Hudson, Andrew S. Dzurak, Kohei M. Itoh, Alexander M. Jakob, Brett C. Johnson, David N. Jamieson, Andrea Morello

Published Sep 28, 2024• 18 citations
Publisher

Abstract

Scalable quantum processors require high-fidelity universal quantum logic operations in a manufacturable physical platform. Donors in silicon provide atomic size, excellent quantum coherence and compatibility with standard semiconductor processing, but no entanglement between donor-bound electron spins has been demonstrated to date. Here we present the experimental demonstration and tomography of universal one- and two-qubit gates in a system of two weakly exchange-coupled electrons, bound to single phosphorus donors introduced in silicon by ion implantation. We observe that the exchange interaction has no effect on the qubit coherence. We quantify the fidelity of the quantum operations using gate set tomography (GST), and we use the universal gate set to create entangled Bell states of the electrons spins, with fidelity 91.3 ± 3.0%, and concurrence 0.87 ± 0.05. These results form the necessary basis for scaling up donor-based quantum computers. Donors spins in silicon are coherent, high-performance qubits, but scale-up has been challenging. Here the authors present the first experimental demonstration of exchange-based, entangling two qubit gates between electrons bound to 31P donors in Si.

DOI
10.1038/s41467-024-52795-4

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Statistical exchange-coupling errors and the practicality of scalable silicon donor qubits

Yang Song, S. Das Sarma

Recent experimental efforts have led to considerable interest in donor-based localized electron spins in Si as viable qubits for a scalable silicon quantum computer. With the use of isotopically purified 28Si and the realization of extremely long spin coherence time in single-donor electrons, the recent experimental focus is on two-coupled donors with the eventual goal of a scaled-up quantum circuit. Motivated by this development, we simulate the statistical distribution of the exchange coupling J between a pair of donors under realistic donor placement straggles, and quantify the errors relative to the intended J value. With J values in a broad range of donor-pair separation (5<|R|<60 nm), we work out various cases systematically, for a target donor separation R0 along the [001], [110] and [111] Si crystallographic directions, with |R0|=10,20 or 30 nm and standard deviation σR=1,2,5 or 10 nm. Our extensive theoretical results demonstrate the great challenge for a prescribed J gate even with just a donor pair, a first step for any scalable Si-donor-based quantum computer.

arXiv:1611.02808•Applied Physics Letters•Dec 19, 2016•12 citations
Scalable quantum processors require high-fidelity universal quantum logic operations in a manufacturable physical platform. Donors in silicon provide atomic size, excellent quantum coherence and compatibility with standard semiconductor processing, but no entanglement between donor-bound electron spins has been demonstrated to date. Here we present the experimental demonstration and tomography of universal one- and two-qubit gates in a system of two weakly exchange-coupled electrons, bound to single phosphorus donors introduced in silicon by ion implantation. We observe that the exchange interaction has no effect on the qubit coherence. We quantify the fidelity of the quantum operations using gate set tomography (GST), and we use the universal gate set to create entangled Bell states of the electrons spins, with fidelity 91.3 ± 3.0%, and concurrence 0.87 ± 0.05. These results form the necessary basis for scaling up donor-based quantum computers. Donors spins in silicon are coherent, high-performance qubits, but scale-up has been challenging. Here the authors present the first experimental demonstration of exchange-based, entangling two qubit gates between electrons bound to 31P donors in Si.
Scalable quantum processors require high-fidelity universal quantum logic operations in a manufacturable physical platform. Donors in silicon provide atomic size, excellent quantum coherence and compatibility with standard semiconductor processing, but no entanglement between donor-bound electron spins has been demonstrated to date. Here we present the experimental demonstration and tomography of universal 1- and 2-qubit gates in a system of two weakly exchange-coupled electrons, bound to single phosphorus donors introduced in silicon by ion implantation. We surprisingly observe that the exchange interaction has no effect on the qubit coherence. We quantify the fidelity of the quantum operations using gate set tomography (GST), and we use the universal gate set to create entangled Bell states of the electrons spins, with fidelity ~ 93%, and concurrence 0.91 +/- 0.08. These results form the necessary basis for scaling up donor-based quantum computers.
Nuclear spins were among the first physical platforms to be considered for quantum information processing1,2, because of their exceptional quantum coherence3 and atomic-scale footprint. However, their full potential for quantum computing has not yet been realized, owing to the lack of methods with which to link nuclear qubits within a scalable device combined with multi-qubit operations with sufficient fidelity to sustain fault-tolerant quantum computation. Here we demonstrate universal quantum logic operations using a pair of ion-implanted 31P donor nuclei in a silicon nanoelectronic device. A nuclear two-qubit controlled-Z gate is obtained by imparting a geometric phase to a shared electron spin4, and used to prepare entangled Bell states with fidelities up to 94.2(2.7)%. The quantum operations are precisely characterized using gate set tomography (GST)5, yielding one-qubit average gate fidelities up to 99.95(2)%, two-qubit average gate fidelity of 99.37(11)% and two-qubit preparation/measurement fidelities of 98.95(4)%. These three metrics indicate that nuclear spins in silicon are approaching the performance demanded in fault-tolerant quantum processors6. We then demonstrate entanglement between the two nuclei and the shared electron by producing a Greenberger-Horne-Zeilinger three-qubit state with 92.5(1.0)% fidelity. Because electron spin qubits in semiconductors can be further coupled to other electrons7-9 or physically shuttled across different locations10,11, these results establish a viable route for scalable quantum information processing using donor nuclear and electron spins.
Nuclear spins were among the first physical platforms to be considered for quantum information processing, because of their exceptional quantum coherence and atomic-scale footprint. However, their full potential for quantum computing has not yet been realized, due to the lack of methods to link nuclear qubits within a scalable device combined with multi-qubit operations with sufficient fidelity to sustain fault-tolerant quantum computation. Here we demonstrate universal quantum logic operations using a pair of ion-implanted 31P nuclei in a silicon nanoelectronic device. A nuclear two-qubit controlled-Z gate is obtained by imparting a geometric phase to a shared electron spin, and used to prepare entangled Bell states with fidelities up to 94.2(2.7)%. The quantum operations are precisely characterised using gate set tomography (GST), yielding one-qubit gate fidelities up to 99.93(3)%, two-qubit gate fidelity of 99.21(14)% and two-qubit preparation/measurement fidelities of 98.95(4)%. These three metrics indicate that nuclear spins in silicon are approaching the performance demanded in fault-tolerant quantum processors. We then demonstrate entanglement between the two nuclei and the shared electron by producing a Greenberger-Horne-Zeilinger three-qubit state with 92.5(1.0)% fidelity. Since electron spin qubits in semiconductors can be further coupled to other electrons or physically shuttled across different locations, these results establish a viable route for scalable quantum information processing using nuclear spins.
Abstract Donor spins in silicon have achieved record values of coherence times and single-qubit gate fidelities. The next stage of development involves demonstrating high-fidelity two-qubit logic gates, where the most natural coupling is the exchange interaction. To aid the efficient design of scalable donor-based quantum processors, we model the two-electron wave function using a full configuration interaction method within a multi-valley effective mass theory. We exploit the high computational efficiency of our code to investigate the exchange interaction, valley population, and electron densities for two phosphorus donors in a wide range of lattice positions, orientations, and as a function of applied electric fields. The outcomes are visualized with interactive images where donor positions can be swept while watching the valley and orbital components evolve accordingly. Our results provide a physically intuitive and quantitatively accurate understanding of the placement and tuning criteria necessary to achieve high-fidelity two-qubit gates with donors in silicon.
The use of nuclear spins for quantum computation is limited by the difficulty in creating genuine quantum entanglement between distant nuclei. Current demonstrations of nuclear entanglement in semiconductors rely on coupling the nuclei to a common electron, which is not a scalable strategy. In this work, we demonstrated a two-qubit controlled-Z logic operation between the nuclei of two phosphorus atoms in a silicon device, separated by up to 20 nanometers. Each atom binds separate electrons, whose exchange interaction mediates the nuclear two-qubit gate. We prepared and measured a nuclear Bell state with a fidelity of [Formula: see text] and a concurrence of [Formula: see text]. With this method, future progress in scaling up semiconductor spin qubits can be extended to the development of nuclear spin-based quantum computers.
Recent experimental efforts have led to considerable interest in donor-based localized electron spins in Si as viable qubits for a scalable silicon quantum computer. With the use of isotopically purified 28Si and the realization of extremely long spin coherence time in single-donor electrons, the recent experimental focus is on two-coupled donors with the eventual goal of a scaled-up quantum circuit. Motivated by this development, we simulate the statistical distribution of the exchange coupling J between a pair of donors under realistic donor placement straggles, and quantify the errors relative to the intended J value. With J values in a broad range of donor-pair separation (5<|R|<60 nm), we work out various cases systematically, for a target donor separation R0 along the [001], [110] and [111] Si crystallographic directions, with |R0|=10,20 or 30 nm and standard deviation σR=1,2,5 or 10 nm. Our extensive theoretical results demonstrate the great challenge for a prescribed J gate even with just a donor pair, a first step for any scalable Si-donor-based quantum computer.