Hyperfine Spectroscopy and Fast, All-Optical Arbitrary State Initialization and Readout of a Single, Ten-Level

A high-spin nucleus coupled to a color center can act as a long-lived memory qudit in a spin-photon interface. The germanium vacancy (GeV) in diamond has attracted recent attention due to its excellent spectral properties and provides access to the ten-dimensional Hilbert space of the I=9/2 ^{73}Ge nucleus. Here, we observe the ^{73}GeV hyperfine structure, perform nuclear spin readout, and optically initialize the ^{73}Ge spin into any eigenstate on a µs timescale and with a fidelity of up to ∼84%. Our results establish ^{73}GeV as an optically addressable high-spin quantum platform for a high-efficiency spin-photon interface as well as for foundational quantum physics and metrology.

An ultra-stable 1.5 T permanent magnet assembly for qubit experiments at cryogenic temperatures.

Magnetic fields are a standard tool in the toolbox of every physicist and are required for the characterization of materials, as well as the polarization of spins in nuclear magnetic resonance or electron paramagnetic resonance experiments. Quite often, a static magnetic field of sufficiently large, but fixed, magnitude is suitable for these tasks. Here, we present a permanent magnet assembly that can achieve magnetic field strengths of up to 1.5 T over an air gap length of 7 mm. The assembly is based on a Halbach array of neodymium magnets, with the inclusion of the soft magnetic material Supermendur to boost the magnetic field strength inside the air gap. We present the design, simulation, and characterization of the permanent magnet assembly, measuring an outstanding magnetic field stability with a drift rate of |D| < 2.8 ppb/h. Our measurements demonstrate that this assembly can be used for spin qubit experiments inside a dilution refrigerator, successfully replacing the more expensive and bulky superconducting solenoids.

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.

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.

Dephasing of exciton polaritons in photoexcited InGaAs quantum dots in GaAs nanocavities.

We present a combined experimental and theoretical study of the emission spectrum of zero dimensional nanocavity polaritons in electrically tunable single dot nanocavities. Such devices allow us to vary the dot-cavity detuning in situ and probe the emission spectrum under well-controlled conditions of lattice temperature and incoherent excitation level. Our results show that the observation of a double peak in the emission spectrum is not an unequivocal signature of strong coupling. Moreover, by comparing our results with theory, we extract the effective vacuum Rabi splitting, the pure dephasing rate, and their dependence on the incoherent optical pumping power and lattice temperature. Our study highlights how coupling to the lattice and dynamical fluctuations in the solid-state environment influence the coherence properties of quantum dot microcavity polaritons and, sometimes, may mask the occurrence of strong coupling.