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

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.

Scalable Atomic Arrays for Spin-Based Quantum Computers in Silicon.

Semiconductor spin qubits combine excellent quantum performance with the prospect of manufacturing quantum devices using industry-standard metal-oxide-semiconductor (MOS) processes. This applies also to ion-implanted donor spins, which further afford exceptional coherence times and large Hilbert space dimension in their nuclear spin. Here multiple strategies are demonstrated and integrated to manufacture scale-up donor-based quantum computers. 31PF2 molecule implants are used to triple the placement certainty compared to 31P ions, while attaining 99.99% confidence in detecting the implant. Similar confidence is retained by implanting heavier atoms such as 123Sb and 209Bi, which represent high-dimensional qudits for quantum information processing, while Sb2 molecules enable deterministic formation of closely-spaced qudits. The deterministic formation of regular arrays of donor atoms with 300 nm spacing is demonstrated, using step-and-repeat implantation through a nano aperture. These methods cover the full gamut of technological requirements for the construction of donor-based quantum computers in silicon.

Navigating the 16-dimensional Hilbert space of a high-spin donor qudit with electric and magnetic fields.

Efficient scaling and flexible control are key aspects of useful quantum computing hardware. Spins in semiconductors combine quantum information processing with electrons, holes or nuclei, control with electric or magnetic fields, and scalable coupling via exchange or dipole interaction. However, accessing large Hilbert space dimensions has remained challenging, due to the short-distance nature of the interactions. Here, we present an atom-based semiconductor platform where a 16-dimensional Hilbert space is built by the combined electron-nuclear states of a single antimony donor in silicon. We demonstrate the ability to navigate this large Hilbert space using both electric and magnetic fields, with gate fidelity exceeding 99.8% on the nuclear spin, and unveil fine details of the system Hamiltonian and its susceptibility to control and noise fields. These results establish high-spin donors as a rich platform for practical quantum information and to explore quantum foundations.

An electrically driven single-atom "flip-flop" qubit.

The spins of atoms and atom-like systems are among the most coherent objects in which to store quantum information. However, the need to address them using oscillating magnetic fields hinders their integration with quantum electronic devices. Here, we circumvent this hurdle by operating a single-atom "flip-flop" qubit in silicon, where quantum information is encoded in the electron-nuclear states of a phosphorus donor. The qubit is controlled using local electric fields at microwave frequencies, produced within a metal-oxide-semiconductor device. The electrical drive is mediated by the modulation of the electron-nuclear hyperfine coupling, a method that can be extended to many other atomic and molecular systems and to the hyperpolarization of nuclear spin ensembles. These results pave the way to the construction of solid-state quantum processors where dense arrays of atoms can be controlled using only local electric fields.

Precision tomography of a three-qubit donor quantum processor in silicon.

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.

Deterministic Shallow Dopant Implantation in Silicon with Detection Confidence Upper-Bound to 99.85% by Ion-Solid Interactions.

Silicon chips containing arrays of single dopant atoms can be the material of choice for classical and quantum devices that exploit single donor spins. For example, group-V donors implanted in isotopically purified 28 Si crystals are attractive for large-scale quantum computers. Useful attributes include long nuclear and electron spin lifetimes of 31 P, hyperfine clock transitions in 209 Bi or electrically controllable 123 Sb nuclear spins. Promising architectures require the ability to fabricate arrays of individual near-surface dopant atoms with high yield. Here, an on-chip detector electrode system with 70 eV root-mean-square noise (≈20 electrons) is employed to demonstrate near-room-temperature implantation of single 14 keV 31 P+ ions. The physics model for the ion-solid interaction shows an unprecedented upper-bound single-ion-detection confidence of 99.85 ± 0.02% for near-surface implants. As a result, the practical controlled silicon doping yield is limited by materials engineering factors including surface gate oxides in which detected ions may stop. For a device with 6 nm gate oxide and 14 keV 31 P+ implants, a yield limit of 98.1% is demonstrated. Thinner gate oxides allow this limit to converge to the upper-bound. Deterministic single-ion implantation can therefore be a viable materials engineering strategy for scalable dopant architectures in silicon devices.

Conditional quantum operation of two exchange-coupled single-donor spin qubits in a MOS-compatible silicon device.

Silicon nanoelectronic devices can host single-qubit quantum logic operations with fidelity better than 99.9%. For the spins of an electron bound to a single-donor atom, introduced in the silicon by ion implantation, the quantum information can be stored for nearly 1 second. However, manufacturing a scalable quantum processor with this method is considered challenging, because of the exponential sensitivity of the exchange interaction that mediates the coupling between the qubits. Here we demonstrate the conditional, coherent control of an electron spin qubit in an exchange-coupled pair of 31P donors implanted in silicon. The coupling strength, J = 32.06 ± 0.06 MHz, is measured spectroscopically with high precision. Since the coupling is weaker than the electron-nuclear hyperfine coupling A ≈ 90 MHz which detunes the two electrons, a native two-qubit controlled-rotation gate can be obtained via a simple electron spin resonance pulse. This scheme is insensitive to the precise value of J, which makes it suitable for the scale-up of donor-based quantum computers in silicon that exploit the metal-oxide-semiconductor fabrication protocols commonly used in the classical electronics industry.

Controllable freezing of the nuclear spin bath in a single-atom spin qubit.

The quantum coherence and gate fidelity of electron spin qubits in semiconductors are often limited by nuclear spin fluctuations. Enrichment of spin-zero isotopes in silicon markedly improves the dephasing time [Formula: see text], which, unexpectedly, can extend two orders of magnitude beyond theoretical expectations. Using a single-atom 31P qubit in enriched 28Si, we show that the abnormally long [Formula: see text] is due to the freezing of the dynamics of the residual 29Si nuclei, caused by the electron-nuclear hyperfine interaction. Inserting a waiting period when the electron is controllably removed unfreezes the nuclear dynamics and restores the ergodic [Formula: see text] value. Our conclusions are supported by a nearly parameter-free modeling of the 29Si nuclear spin dynamics, which reveals the degree of backaction provided by the electron spin. This study clarifies the limits of ergodic assumptions in nuclear bath dynamics and provides previously unidentified strategies for maximizing coherence and gate fidelity of spin qubits in semiconductors.

A dressed spin qubit in silicon.

Coherent dressing of a quantum two-level system provides access to a new quantum system with improved properties-a different and easily tunable level splitting, faster control and longer coherence times. In our work we investigate the properties of the dressed, donor-bound electron spin in silicon, and assess its potential as a quantum bit in scalable architectures. The two dressed spin-polariton levels constitute a quantum bit that can be coherently driven with an oscillating magnetic field, an oscillating electric field, frequency modulation of the driving field or a simple detuning pulse. We measure coherence times of and , one order of magnitude longer than those of the undressed spin. Furthermore, the use of the dressed states enables coherent coupling of the solid-state spins to electric fields and mechanical oscillations.

Bell's inequality violation with spins in silicon.

Bell's theorem proves the existence of entangled quantum states with no classical counterpart. An experimental violation of Bell's inequality demands simultaneously high fidelities in the preparation, manipulation and measurement of multipartite quantum entangled states, and provides a single-number benchmark for the performance of devices that use such states for quantum computing. We demonstrate a Bell/ Clauser-Horne-Shimony-Holt inequality violation with Bell signals up to 2.70(9), using the electron and the nuclear spins of a single phosphorus atom embedded in a silicon nanoelectronic device. Two-qubit state tomography reveals that our prepared states match the target maximally entangled Bell states with >96% fidelity. These experiments demonstrate complete control of the two-qubit Hilbert space of a phosphorus atom and highlight the important function of the nuclear qubit to expand the computational basis and maximize the readout fidelity.