Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1312.2197 · Physical Review X

Robust Two-Qubit Gates for Donors in Silicon Controlled by Hyperfine Interactions

Rachpon Kalra, Arne Laucht, Charles D. Hill, Andrea Morello

Published Jun 6, 2014• 67 citations
arXivHTMLPDF

Abstract

Recent breakthrough demonstrations of the measurement and control of a single atom's electrons and nuclear spins in silicon have added momentum to the pursuit of quantum computing. New results show that two-qubit quantum logic gates can perform with high fidelity, without the need for placing atoms with subnanometer precision.
DOI
10.1103/physrevx.4.021044

Related papers

Fast noise-resistant control of donor nuclear spin qubits in silicon

James Simon, F. A. Calderon-Vargas, Edwin Barnes +1 more

A high degree of controllability and long coherence time make the nuclear spin of a phosphorus donor in isotopically purified silicon a promising candidate for a quantum bit. However, long-distance two-qubit coupling and fast, robust gates remain outstanding challenges for these systems. Here, following recent proposals for long-distance coupling via dipole-dipole interactions, we present a simple method to implement fast, high-fidelity arbitrary single- and two-qubit gates in the absence of charge noise. Moreover, we provide a method to make the single-qubit gates robust to moderate levels of charge noise to well within an error bound of ${10}^{\ensuremath{-}3}$.

arXiv:2001.10029•Physical review. B./Physical review. B•May 18, 2020•6 citations

Fast high-fidelity single-qubit gates for flip-flop qubits in silicon

F. A. Calderon-Vargas, Edwin Barnes, Sophia E. Economou

Flip-flop qubits, encoded in the antiparallel spin states of electron and nuclear spins in phosphorus donors in silicon, are promising for quantum processors due to their long coherence times, long-range two-qubit coupling, and CMOS compatibility. However, the large Hilbert space complicates understanding and controlling the dynamics. In this work, the authors use sophisticated techniques to derive effective flip-flop qubit Hamiltonians and design optimal control pulses that implement high-fidelity single-qubit gates that are much faster and more robust than previous proposals.

arXiv:2101.11592•Physical review. B./Physical review. B•Oct 10, 2022•10 citations

Scalable entanglement of nuclear spins mediated by electron exchange

Holly G. Stemp, Mark R. van Blankenstein, Serwan Asaad +11 more

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.

arXiv:2503.06872•Science•Sep 18, 2025•11 citations

Single atom spin qubits in silicon

Jarryd J. Pla

Spin is a quantum mechanical property that describes the magnetic orientation of elementary and composite particles such as electrons and nuclei. For spin-half particles placed in a magnetic field, two states with differing energies are defined. Proposals exist for developing a revolutionary kind of computer that encodes bits of information on the states of a simple quantum two-level system - like those of a spin in a magnetic field. These quantum computers exploit the fundamental principles of quantum mechanics in order to perform certain calculations exponentially faster than their classical counterparts. Key to the development of such a device is the identification of potential systems that are suitable for employment as a quantum bit (qubit). This thesis explores quantum bits constructed from the spin states of single atoms hosted in silicon semiconductor devices. Silicon is an exceptional platform for spin-based quantum computing - in addition to being the dominant material in the microelectronic industry, it is also predominantly composed of nuclear spin-zero isotopes, providing very little background magnetic disturbance. The donor-atom phosphorus (31P) is investigated here. It possesses a nucleus that binds an additional electron to its positive charge, providing two distinct spin qubits. Here, several world-first experimental milestones in spin-based quantum information processing are reported. First, the readout of the electron spin is demonstrated in single-shot, using a silicon device which combines implanted phosphorus donors with a sensitive nanoscale electrometer. Then, the electron spin is coherently operated as a qubit by delivering on-chip microwave excitations. Combining the electron spin detection and control capabilities enables a quantum non-demolition measurement of the single 31P nuclear spin. Experiments yield exceptional nuclear readout fidelities - the highest for any solid-state qubit. Through an application of nuclear magnetic resonance, high-fidelity quantum control of the nuclear spin qubit is demonstrated. Finally, a single spin-bearing silicon nucleus (29Si) coupled to the electron spin is detected in single-shot and operated as a qubit. These results, along with the clear pathways identified for improving device performance, illustrate that single-atom electron and nuclear spin qubits in silicon constitute an excellent basis on which to construct a quantum computer.

Science Education News•Mar 21, 2022•0 citations

Silicon quantum processor with robust long-distance qubit couplings

G. Tosi, Fahd A. Mohiyaddin, Vivien Schmitt +4 more

Practical quantum computers require a large network of highly coherent qubits, interconnected in a design robust against errors. Donor spins in silicon provide state-of-the-art coherence and quantum gate fidelities, in a platform adapted from industrial semiconductor processing. Here we present a scalable design for a silicon quantum processor that does not require precise donor placement and leaves ample space for the routing of interconnects and readout devices. We introduce the flip-flop qubit, a combination of the electron-nuclear spin states of a phosphorus donor that can be controlled by microwave electric fields. Two-qubit gates exploit a second-order electric dipole-dipole interaction, allowing selective coupling beyond the nearest-neighbor, at separations of hundreds of nanometers, while microwave resonators can extend the entanglement to macroscopic distances. We predict gate fidelities within fault-tolerance thresholds using realistic noise models. This design provides a realizable blueprint for scalable spin-based quantum computers in silicon.Quantum computers will require a large network of coherent qubits, connected in a noise-resilient way. Tosi et al. present a design for a quantum processor based on electron-nuclear spins in silicon, with electrical control and coupling schemes that simplify qubit fabrication and operation.

arXiv:1509.08538•Nature Communications•Aug 31, 2017•170 citations

Hydrogenic Spin Quantum Computing in Silicon: A Digital Approach

A Skinner, Michael Davenport, Bruce E. Kane

We suggest an architecture for quantum computing with spin-pair encoded qubits in silicon. Electron-nuclear spin-pairs are controlled by a dc magnetic field and electrode-switched on and off hyperfine interaction. This digital processing is insensitive to tuning errors and easy to model. Electron shuttling between donors enables multiqubit logic. These hydrogenic spin qubits are transferable to nuclear spin-pairs, which have long coherence times, and electron spin-pairs, which are ideally suited for measurement and initialization. The architecture is scalable to a highly parallel operation.

arXiv:quant-ph/0206159•Physical Review Letters•Feb 25, 2003•183 citations
A high degree of controllability and long coherence time make the nuclear spin of a phosphorus donor in isotopically purified silicon a promising candidate for a quantum bit. However, long-distance two-qubit coupling and fast, robust gates remain outstanding challenges for these systems. Here, following recent proposals for long-distance coupling via dipole-dipole interactions, we present a simple method to implement fast, high-fidelity arbitrary single- and two-qubit gates in the absence of charge noise. Moreover, we provide a method to make the single-qubit gates robust to moderate levels of charge noise to well within an error bound of ${10}^{\ensuremath{-}3}$.
Flip-flop qubits, encoded in the antiparallel spin states of electron and nuclear spins in phosphorus donors in silicon, are promising for quantum processors due to their long coherence times, long-range two-qubit coupling, and CMOS compatibility. However, the large Hilbert space complicates understanding and controlling the dynamics. In this work, the authors use sophisticated techniques to derive effective flip-flop qubit Hamiltonians and design optimal control pulses that implement high-fidelity single-qubit gates that are much faster and more robust than previous proposals.
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.
Spin is a quantum mechanical property that describes the magnetic orientation of elementary and composite particles such as electrons and nuclei. For spin-half particles placed in a magnetic field, two states with differing energies are defined. Proposals exist for developing a revolutionary kind of computer that encodes bits of information on the states of a simple quantum two-level system - like those of a spin in a magnetic field. These quantum computers exploit the fundamental principles of quantum mechanics in order to perform certain calculations exponentially faster than their classical counterparts. Key to the development of such a device is the identification of potential systems that are suitable for employment as a quantum bit (qubit). This thesis explores quantum bits constructed from the spin states of single atoms hosted in silicon semiconductor devices. Silicon is an exceptional platform for spin-based quantum computing - in addition to being the dominant material in the microelectronic industry, it is also predominantly composed of nuclear spin-zero isotopes, providing very little background magnetic disturbance. The donor-atom phosphorus (31P) is investigated here. It possesses a nucleus that binds an additional electron to its positive charge, providing two distinct spin qubits. Here, several world-first experimental milestones in spin-based quantum information processing are reported. First, the readout of the electron spin is demonstrated in single-shot, using a silicon device which combines implanted phosphorus donors with a sensitive nanoscale electrometer. Then, the electron spin is coherently operated as a qubit by delivering on-chip microwave excitations. Combining the electron spin detection and control capabilities enables a quantum non-demolition measurement of the single 31P nuclear spin. Experiments yield exceptional nuclear readout fidelities - the highest for any solid-state qubit. Through an application of nuclear magnetic resonance, high-fidelity quantum control of the nuclear spin qubit is demonstrated. Finally, a single spin-bearing silicon nucleus (29Si) coupled to the electron spin is detected in single-shot and operated as a qubit. These results, along with the clear pathways identified for improving device performance, illustrate that single-atom electron and nuclear spin qubits in silicon constitute an excellent basis on which to construct a quantum computer.
Practical quantum computers require a large network of highly coherent qubits, interconnected in a design robust against errors. Donor spins in silicon provide state-of-the-art coherence and quantum gate fidelities, in a platform adapted from industrial semiconductor processing. Here we present a scalable design for a silicon quantum processor that does not require precise donor placement and leaves ample space for the routing of interconnects and readout devices. We introduce the flip-flop qubit, a combination of the electron-nuclear spin states of a phosphorus donor that can be controlled by microwave electric fields. Two-qubit gates exploit a second-order electric dipole-dipole interaction, allowing selective coupling beyond the nearest-neighbor, at separations of hundreds of nanometers, while microwave resonators can extend the entanglement to macroscopic distances. We predict gate fidelities within fault-tolerance thresholds using realistic noise models. This design provides a realizable blueprint for scalable spin-based quantum computers in silicon.Quantum computers will require a large network of coherent qubits, connected in a noise-resilient way. Tosi et al. present a design for a quantum processor based on electron-nuclear spins in silicon, with electrical control and coupling schemes that simplify qubit fabrication and operation.
We suggest an architecture for quantum computing with spin-pair encoded qubits in silicon. Electron-nuclear spin-pairs are controlled by a dc magnetic field and electrode-switched on and off hyperfine interaction. This digital processing is insensitive to tuning errors and easy to model. Electron shuttling between donors enables multiqubit logic. These hydrogenic spin qubits are transferable to nuclear spin-pairs, which have long coherence times, and electron spin-pairs, which are ideally suited for measurement and initialization. The architecture is scalable to a highly parallel operation.