Coherent spin qubit transport in silicon.

A fault-tolerant quantum processor may be configured using stationary qubits interacting only with their nearest neighbours, but at the cost of significant overheads in physical qubits per logical qubit. Such overheads could be reduced by coherently transporting qubits across the chip, allowing connectivity beyond immediate neighbours. Here we demonstrate high-fidelity coherent transport of an electron spin qubit between quantum dots in isotopically-enriched silicon. We observe qubit precession in the inter-site tunnelling regime and assess the impact of qubit transport using Ramsey interferometry and quantum state tomography techniques. We report a polarization transfer fidelity of 99.97% and an average coherent transfer fidelity of 99.4%. Our results provide key elements for high-fidelity, on-chip quantum information distribution, as long envisaged, reinforcing the scaling prospects of silicon-based spin qubits.

Operation of a silicon quantum processor unit cell above one kelvin.

Quantum computers are expected to outperform conventional computers in several important applications, from molecular simulation to search algorithms, once they can be scaled up to large numbers-typically millions-of quantum bits (qubits)1-3. For most solid-state qubit technologies-for example, those using superconducting circuits or semiconductor spins-scaling poses a considerable challenge because every additional qubit increases the heat generated, whereas the cooling power of dilution refrigerators is severely limited at their operating temperature (less than 100 millikelvin)4-6. Here we demonstrate the operation of a scalable silicon quantum processor unit cell comprising two qubits confined to quantum dots at about 1.5 kelvin. We achieve this by isolating the quantum dots from the electron reservoir, and then initializing and reading the qubits solely via tunnelling of electrons between the two quantum dots7-9. We coherently control the qubits using electrically driven spin resonance10,11 in isotopically enriched silicon12 28Si, attaining single-qubit gate fidelities of 98.6 per cent and a coherence time of 2 microseconds during 'hot' operation, comparable to those of spin qubits in natural silicon at millikelvin temperatures13-16. Furthermore, we show that the unit cell can be operated at magnetic fields as low as 0.1 tesla, corresponding to a qubit control frequency of 3.5 gigahertz, where the qubit energy is well below the thermal energy. The unit cell constitutes the core building block of a full-scale silicon quantum computer and satisfies layout constraints required by error-correction architectures8,17. Our work indicates that a spin-based quantum computer could be operated at increased temperatures in a simple pumped 4He system (which provides cooling power orders of magnitude higher than that of dilution refrigerators), thus potentially enabling the integration of classical control electronics with the qubit array18,19.

Coherent spin control of s-, p-, d- and f-electrons in a silicon quantum dot.

Once the periodic properties of elements were unveiled, chemical behaviour could be understood in terms of the valence of atoms. Ideally, this rationale would extend to quantum dots, and quantum computation could be performed by merely controlling the outer-shell electrons of dot-based qubits. Imperfections in semiconductor materials disrupt this analogy, so real devices seldom display a systematic many-electron arrangement. We demonstrate here an electrostatically confined quantum dot that reveals a well defined shell structure. We observe four shells (31 electrons) with multiplicities given by spin and valley degrees of freedom. Various fillings containing a single valence electron-namely 1, 5, 13 and 25 electrons-are found to be potential qubits. An integrated micromagnet allows us to perform electrically-driven spin resonance (EDSR), leading to faster Rabi rotations and higher fidelity single qubit gates at higher shell states. We investigate the impact of orbital excitations on single qubits as a function of the dot deformation and exploit it for faster qubit control.

Single-spin qubits in isotopically enriched silicon at low magnetic field.

Single-electron spin qubits employ magnetic fields on the order of 1 Tesla or above to enable quantum state readout via spin-dependent-tunnelling. This requires demanding microwave engineering for coherent spin resonance control, which limits the prospects for large scale multi-qubit systems. Alternatively, singlet-triplet readout enables high-fidelity spin-state measurements in much lower magnetic fields, without the need for reservoirs. Here, we demonstrate low-field operation of metal-oxide-silicon quantum dot qubits by combining coherent single-spin control with high-fidelity, single-shot, Pauli-spin-blockade-based ST readout. We discover that the qubits decohere faster at low magnetic fields with [Formula: see text] µs and [Formula: see text] µs at 150 mT. Their coherence is limited by spin flips of residual 29Si nuclei in the isotopically enriched 28Si host material, which occur more frequently at lower fields. Our finding indicates that new trade-offs will be required to ensure the frequency stabilization of spin qubits, and highlights the importance of isotopic enrichment of device substrates for the realization of a scalable silicon-based quantum processor.

Fidelity benchmarks for two-qubit gates in silicon.

Universal quantum computation will require qubit technology based on a scalable platform1, together with quantum error correction protocols that place strict limits on the maximum infidelities for one- and two-qubit gate operations2,3. Although various qubit systems have shown high fidelities at the one-qubit level4-10, the only solid-state qubits manufactured using standard lithographic techniques that have demonstrated two-qubit fidelities near the fault-tolerance threshold6 have been in superconductor systems. Silicon-based quantum dot qubits are also amenable to large-scale fabrication and can achieve high single-qubit gate fidelities (exceeding 99.9 per cent) using isotopically enriched silicon11,12. Two-qubit gates have now been demonstrated in a number of systems13-15, but as yet an accurate assessment of their fidelities using Clifford-based randomized benchmarking, which uses sequences of randomly chosen gates to measure the error, has not been achieved. 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 per cent, and two-qubit randomized benchmarking with an average Clifford gate fidelity of 94.7 per cent and an average controlled-rotation fidelity of 98 per cent. These fidelities are found to be limited by the relatively long gate times used here compared with the decoherence times of the qubits. Silicon qubit designs employing fast gate operations with high Rabi frequencies16,17, together with advanced pulsing techniques18, should therefore enable much higher fidelities in the near future.

Integrated silicon qubit platform with single-spin addressability, exchange control and single-shot singlet-triplet readout.

Silicon quantum dot spin qubits provide a promising platform for large-scale quantum computation because of their compatibility with conventional CMOS manufacturing and the long coherence times accessible using 28Si enriched material. A scalable error-corrected quantum processor, however, will require control of many qubits in parallel, while performing error detection across the constituent qubits. Spin resonance techniques are a convenient path to parallel two-axis control, while Pauli spin blockade can be used to realize local parity measurements for error detection. Despite this, silicon qubit implementations have so far focused on either single-spin resonance control, or control and measurement via voltage-pulse detuning in the two-spin singlet-triplet basis, but not both simultaneously. Here, we demonstrate an integrated device platform incorporating a silicon metal-oxide-semiconductor double quantum dot that is capable of single-spin addressing and control via electron spin resonance, combined with high-fidelity spin readout in the singlet-triplet basis.

Spin and orbital structure of the first six holes in a silicon metal-oxide-semiconductor quantum dot.

Valence band holes confined in silicon quantum dots are attracting significant attention for use as spin qubits. However, experimental studies of single-hole spins have been hindered by challenges in fabrication and stability of devices capable of confining a single hole. To fully utilize hole spins as qubits, it is crucial to have a detailed understanding of the spin and orbital states. Here we show a planar silicon metal-oxide-semiconductor-based quantum dot device and demonstrate operation down to the last hole. Magneto-spectroscopy studies show magic number shell filling consistent with the Fock-Darwin states of a circular two-dimensional quantum dot, with the spin filling sequence of the first six holes consistent with Hund's rule. Next, we use pulse-bias spectroscopy to determine that the orbital spectrum is heavily influenced by the strong hole-hole interactions. These results provide a path towards scalable silicon hole-spin qubits.

A two-qubit logic gate in silicon.

Quantum computation requires qubits that can be coupled in a scalable manner, together with universal and high-fidelity one- and two-qubit logic gates. Many physical realizations of qubits exist, including single photons, trapped ions, superconducting circuits, single defects or atoms in diamond and silicon, and semiconductor quantum dots, with single-qubit fidelities that exceed the stringent thresholds required for fault-tolerant quantum computing. 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, owing to the difficulties of coupling qubits and dephasing in semiconductor systems. Here we present a two-qubit logic gate, which uses single spins in isotopically enriched silicon and is realized by performing single- and two-qubit operations in a quantum dot system using the exchange interaction, as envisaged in the Loss-DiVincenzo proposal. We realize CNOT gates via controlled-phase operations combined with single-qubit operations. Direct gate-voltage control provides single-qubit addressability, together with a switchable exchange interaction that is used in the two-qubit controlled-phase gate. By independently reading out both qubits, we measure clear anticorrelations in the two-spin probabilities of the CNOT gate.

Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking.

Building upon the demonstration of coherent control and single-shot readout of the electron and nuclear spins of individual (31)P atoms in silicon, we present here a systematic experimental estimate of quantum gate fidelities using randomized benchmarking of 1-qubit gates in the Clifford group. We apply this analysis to the electron and the ionized (31)P nucleus of a single P donor in isotopically purified (28)Si. We find average gate fidelities of 99.95% for the electron and 99.99% for the nuclear spin. These values are above certain error correction thresholds and demonstrate the potential of donor-based quantum computing in silicon. By studying the influence of the shape and power of the control pulses, we find evidence that the present limitation to the gate fidelity is mostly related to the external hardware and not the intrinsic behaviour of the qubit.

Single atom devices by ion implantation.

To expand the capabilities of semiconductor devices for new functions exploiting the quantum states of single donors or other impurity atoms requires a deterministic fabrication method. Ion implantation is a standard tool of the semiconductor industry and we have developed pathways to deterministic ion implantation to address this challenge. Although ion straggling limits the precision with which atoms can be positioned, for single atom devices it is possible to use post-implantation techniques to locate favourably placed atoms in devices for control and readout. However, large-scale devices will require improved precision. We examine here how the method of ion beam induced charge, already demonstrated for the deterministic ion implantation of 14 keV P donor atoms in silicon, can be used to implant a non-Poisson distribution of ions in silicon. Further, we demonstrate the method can be developed to higher precision by the incorporation of new deterministic ion implantation strategies that employ on-chip detectors with internal charge gain. In a silicon device we show a pulse height spectrum for 14 keV P ion impact that shows an internal gain of 3 that has the potential of allowing deterministic implantation of sub-14 keV P ions with reduced straggling.

An addressable quantum dot qubit with fault-tolerant control-fidelity.

Exciting progress towards spin-based quantum computing has recently been made with qubits realized using nitrogen-vacancy centres in diamond and phosphorus atoms in silicon. For example, long coherence times were made possible by the presence of spin-free isotopes of carbon and silicon. However, despite promising single-atom nanotechnologies, 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 engineered, 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. This qubit has dephasing time T2* = 120 µs and coherence time T2 = 28 ms, both orders of magnitude larger than in other types of semiconductor qubit. By gate-voltage-tuning the electron g*-factor we can Stark shift the electron spin resonance frequency by more than 3,000 times the 2.4 kHz electron spin resonance linewidth, providing a direct route to large-scale arrays of addressable high-fidelity qubits that are compatible with existing manufacturing technologies.

Gate-controlled charge transfer in Si:P double quantum dots.

We present low temperature charge sensing measurements of nanoscale phosphorus-implanted double dots in silicon. The implanted phosphorus forms two 50 nm diameter islands with source and drain leads, which are separated from each other by undoped silicon tunnel barriers. Occupancy of the dots is controlled by surface gates and monitored using an aluminium single-electron transistor which is capacitively coupled to the dots. We observe a charge stability diagram consistent with the designed many-electron double-dot system and this agrees well with capacitance modelling of the structure. We discuss the significance of these results to the realization of smaller devices which may be used as charge or spin qubits.

Microsecond resolution of quasiparticle tunneling in the single-Cooper-pair transistor.

We present radio-frequency measurements on a single-Cooper-pair-transistor in which individual quasiparticle poisoning events were observed with microsecond temporal resolution. Thermal activation of the quasiparticle dynamics is investigated, and consequently, we are able to determine energetics of the poisoning and unpoisoning processes. In particular, we are able to assign an effective quasiparticle temperature to parametrize the poisoning rate.