Quantum computation requires qubits that can be coupled and realized in a scalable manner, together with universal and high-fidelity one-and two-qubit logic gates [1, 2]. Strong effort across several fields have led to an impressive array of qubit realizations, including trapped ions [4], superconducting circuits [5], single photons [3], single defects or atoms in diamond [6,7] and silicon [8], and semiconductor quantum dots [4], all with single qubit fidelities exceeding the stringent thresholds required for fault-tolerant quantum computing [10]. Despite this, high-fidelity two-qubit gates in the solid-state that can be manufactured using standard lithographic techniques have so far been limited to superconducting qubits [5], as semiconductor systems have suffered from difficulties in coupling qubits and dephasing [11][12][13]. Here, we show that these issues can be eliminated altogether using single spins in isotopically enriched silicon [14] by demonstrating single-and two-qubit operations in a quantum dot system using the exchange interaction, as envisaged in the original Loss-DiVincenzo proposal [2]. We realize CNOT gates via either controlled rotation (CROT) or controlled phase (CZ) operations combined with single-qubit operations. Direct gate-voltage control provides single-qubit addressability, together with a switchable exchange interaction that is employed in the two-qubit CZ gate. The speed of the two-qubit CZ operations is controlled electrically via the detuning energy and we find that over 100 two-qubit gates can be performed within a two-qubit coherence time of 8 µs, thereby satisfying the criteria required for scalable quantum computation.Quantum dots have high potential as a qubit platform [2]. Large arrays can be conveniently realized using conventional lithographic approaches, while reading, initializing, controlling and coupling can be done purely by electrical means. Early research focussed mainly on III-V semiconductor compounds such as GaAs, resulting in single spin qubits [15], singlet-triplet qubits [16] and exchange only qubits [17], which can be coupled capacitively [11] or via the exchange interaction [12,13]. While these approaches demonstrate the potential of quantum dot qubits, strong dephasing due to the nuclear spin background have limited the quality of the quantum operations. A strong improvement in coherence times has been observed by defining the quantum dots in silicon [18,19], which can be isotopically purified [14], such that quantum dots with single spin fidelities above the threshold of surface codes [10] can be realized [4].A scalable approach towards quantum computation ideally requires that the coupling between qubits can be turned on and off [1], so that single and two-qubit operations can be selectively chosen. Here, we demonstrate this by realizing a CZ gate, which is commonly used in superconducting qubits [5] and has been theoretically discussed for quantum dot systems [20]. This two-qubit gate, together with single-qubit gates provides all of the necessary opera...

The spin of an electron or a nucleus in a semiconductor [1] naturally implements the unit of quantum information -the qubit -while providing a technological link to the established electronics industry [2]. The solid-state environment, however, may provide deleterious interactions between the qubit and the nuclear spins of surrounding atoms [3], or charge and spin fluctuators in defects, oxides and interfaces [4]. For group IV materials such as silicon, enrichment of the spinzero 28 Si isotope drastically reduces spin-bath decoherence [5]. Experiments on bulk spin ensembles in 28 Si crystals have indeed demonstrated extraordinary coherence times [6][7][8]. However, it remained unclear whether these would persist at the single-spin level, in gated nanostructures near amorphous interfaces. Here we present the coherent operation of individual 31 P electron and nuclear spin qubits in a top-gated nanostructure, fabricated on an isotopically engineered 28 Si substrate. We report new benchmarks for coherence time (> 30 seconds) and control fidelity (> 99.99%) of any single qubit in solid state, and perform a detailed noise spectroscopy [9] to demonstrate that -contrary to widespread belief -the coherence is not limited by the proximity to an interface. Our results represent a fundamental advance in control and understanding of spin qubits in nanostructures.It is well known that the Si/SiO 2 interface hosts a variety of defects that act as charge and spin fluctuators. Spin resonance experiments have documented the deleterious effects of the Si/SiO 2 interface on the coherence of donors in 28 Si, implanted at different depths [10]. Theoretical models suggest that magnetic fluctuation from paramagnetic spins at the interface cause the decohering noise [4], and recent work advocates the use of 'clock transitions' in 209 Bi donors [11] to obtain a spin qubit that is to first-order insensitive to magnetic noise. Fluctuations of interface charges or gate voltages can also cause decoherence, if there is a physical mechanism for electric fields to couple to the spin qubit states. Evidence of such effects was found for instance in carbon nanotube valley-spin qubits [12]. For donors in silicon, fluctuating electric fields can couple to the spin states by modulating the hyperfine coupling [13, 14] or the g-factor [15]. Here we operate single-atom spin qubits in isotopically purified 28 Si, with a residual 29 Si concentration of 800 ppm. Minimizing the effect 29 Si nuclear spin fluctuations allowed us not only to set new benchmarks for qubit performance in solid state, but also to uncover the microscopic origin of residual decoherence mechanisms, specific to a gated nanostructure.A substitutional P atom in Si behaves to a good approximation like hydrogen in vacuum, with energy levels renormalized by the effective mass and the dielectric constant of the host material [16]. Both the bound electron (e − ) and the nucleus ( 31 P) possess a spin 1/2 and constitute natural qubits with simple spin up/down eigenstates, which we denote ...

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...