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...

Exciting progress towards spin-based quantum computing [1,2] has recently been made with qubits realized using nitrogen-vacancy (N-V) centers in diamond and phosphorus atoms in silicon [3], including the demonstration of long coherence times made possible by the presence of spin-free isotopes of carbon [4] and silicon [5]. However, despite promising single-atom nanotechnologies [6], there remain substantial challenges in coupling such qubits and addressing them individually. Conversely, lithographically defined quantum dots have an exchange coupling that can be precisely engineered1, but strong coupling to noise has severely limited their dephasing times and control fidelities. Here we combine the best aspects of both spin qubit schemes and demonstrate a gate-addressable quantum dot qubit in isotopically engineered silicon with a control fidelity of 99.6%, obtained via Clifford based randomized benchmarking and consistent with that required for fault-tolerant quantum computing [7,8]. This qubit has orders of magnitude improved coherence times compared with other quantum dot qubits, with T * 2 = 120 µs and T2 = 28 ms. By gate-voltage tuning of the electron g * -factor, we can Stark shift the electron spin resonance (ESR) frequency by more than 3000 times the 2.4 kHz ESR linewidth, providing a direct path to large-scale arrays of addressable high-fidelity qubits that are compatible with existing manufacturing technologies.The seminal work by Loss and DiVincenzo[1] to encode quantum information using the spin states of semiconductor quantum dots generated great excitement, as it fulfilled what were then understood to be the key criteria[2] for quantum computation, and has already led to the realization of 2-qubit operations such as the √ SWAP[9, 10] and CPHASE [11]. However, the limited lifetime and the associated fidelity of the quantum state represent a significant hurdle for the semiconductor quantum dot qubits realized thus far. A dephasing time up to T * 2 = 37 ns [12], improved to T * 2 = 94 ns[13] using nuclear spin bath control, has been recorded for quantum dot spin qubits in GaAs/AlGaAs. A longer T * 2 = 360 ns has been achieved using Si/SiGe quantum dots [14]. The main strategy to improve these times has involved applying pulse sequences developed for bulk magnetic resonance, and we can specify a T 2 according to the applied pulse sequence. Using a Hahn echo sequence the coherence time of GaAs-based qubits has been extended to T 28 Si), we remove the dephasing effect of the nuclear spin bath present in these previous studies, and show that all of the above coherence times can be improved by orders of magnitude. These long coherence times, in particular the dephasing time T * 2 , lead to low control error rates and the high fidelities that will be required for large-scale, fault tolerant quantum computing [7,8].In contrast with quantum dots, electron spin qubits localized on atoms or defects have been realized in almost spinfree environments, showing coherence times approaching [4] and even exceeding seco...

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 ...