The predominant material in modern classical computers, silicon, is also a strong contender for the practical implementation of quantum processors3,6,7,8. To unlock the promised computational benefits of quantum computing, the qubit count needs to scale while maintaining high operation fidelity and connectivity. In terms of qubit numbers, the lead is at present held by superconducting9,10, ion-trap11 and neutral-atom12 processors, which approach hundreds of interconnected qubits. Further scale-up faces platform-specific challenges related to manufacturing, control-systems miniaturization and materials engineering. In this context, silicon quantum processors are emerging as a promising platform owing to their small footprint and materials compatibility with industrial manufacturing8,13,14.
In semiconductor devices, the number of individual qubits is increasing, with gate-defined arrays hosting up to 16 quantum dots14,15. So far, however, no more than four interconnected spin qubits were used in the execution of quantum circuits owing to challenges associated with multi-qubit control16,17,18,19. In this context, quantum computing with precision-placed phosphorus atoms in silicon, which we refer to as the 14|15 platform (according to the respective positions in the periodic table), is attracting growing interest driven by industry-leading physical-level metrics3 with exceptional, second-long coherence times2,20. The 14|15 platform uses precision manufacturing21 to place individual phosphorus atoms in close proximity (≲3 nm) to each other, in which a single loaded electron exhibits a hyperfine interaction with several nuclei. Such spin registers provide a unique set of advantages: the shared electron naturally acts as an ancilla qubit enabling quantum non-demolition (QND) readout of the nuclear spins and native multi-qubit (Toffoli) gates4,5. Combined with recent advances in silicon purification with sub-200 ppm of 29Si (ref. 22), these features enabled nuclear–nuclear CZ operations with fidelities exceeding 99% and the execution of three-qubit algorithms on a single multi-spin register5.
To enable the scaling of the 14|15 platform, it is essential to develop fast interconnects between quantum processing nodes without compromising performance23. The coupling of spin qubits is achievable by various mechanisms, such as dipolar interaction24 or spin–photon conversion in superconducting cavities25. The fastest coupling mechanism is provided by exchange interaction, as demonstrated with a 0.8-ns \(\sqrt{{\rm{SWAP}}}\) gate between atomic qubits in natural silicon26. Exchange gates on electron spins have also been implemented with gate-defined quantum dots in isotopically pure silicon with fidelities greater than 99% (refs. 27,28,29,30). Successful implementation of exchange gates in atom qubits have already been achieved in purified silicon-28 (ref. 31), yet the limited two-qubit gate fidelity challenges the applicability of quantum-error-correction protocols32,33.
Here we report a precision-placed 11-qubit atom processor in isotopically purified silicon-28 that runs on a fast and efficient exchange-based link. Compared with the previous atom-based implementations with nuclear spin qubits4,5,22, we triple the number of coupled data qubits while maintaining the performance of single-qubit and two-qubit gates well above 99% fidelity. This achievement is enabled by systematic investigations of qubit stability, contextual errors and crosstalk, which informed the development of scalable calibration and control protocols. After outlining the basic set-up of the 11-qubit atom processor, we report the key metrics of single-qubit and two-qubit gates, assess pairwise entanglement for all combinations of nuclear spins and benchmark all-to-all connectivity through multi-qubit entanglement.
The connectivity of the nuclei and electrons both within each register and across registers is central to the operation of the 11-qubit atom processor (Fig. 1a). Each spin register contains nuclei (n 1 –n 4 and n 5 –n 9 ) that are hyperfine-coupled to a common electron (e 1 and e 2 ). Notably, these electrons are also exchange-coupled to each other, enabling non-local connectivity across the registers (Fig. 1b). The strength of electron exchange coupling J is tunable by the voltage detuning ε across in-plane control gates (Fig. 1c and Supplementary Information Section I). The Hamiltonian of the system is described in Supplementary Information Section II. Here we operate in a weak exchange-coupled regime with J ≈ 1.55 MHz (Fig. 1c). In this regime, the controlled rotations (CROT) on the electron are less susceptible to charge noise and not conditional on the nuclear spins in the other register26,34,35,36. We note that the CROT operation on the electron spin has the advantage of implementing a native multi-qubit Toffoli gate that is conditional on the nuclear spins.
Fig. 1: Single-qubit characteristics of the 11-qubit atom processor. a, Connectivity of nuclear spins (n 1 –n 9 ) and electron spins (e 1 and e 2 ) through hyperfine and exchange coupling with energies in MHz. b, Scanning tunnelling micrograph of the processor core after hydrogen lithography showing the 4P register hosting n 1 –n 4 and e 1 (square) and the 5P register hosting n 5 –n 9 and e 2 (pentagon). The distance 13(1) nm (centre to centre) between the nuclear spin registers is atomically engineered to enable exchange coupling26,54. Scale bar, 10 nm. c, Exchange-coupled ESR spectrum of e 2 as a function of voltage detuning ε with indications on the resonance frequencies corresponding to CROT and zCROT. d, Rabi oscillations along one period T Rabi for all spins of the processor. We measure the spin-up probability of the nucleus P ⇑ (electron P ↑ ) as a function of the coherent NMR (ESR) drive duration. e, Phase coherence times measured for each spin through Ramsey (open symbols) and Hahn-echo (filled symbols) measurements. f, 1Q-RB results for each qubit showing average physical gate fidelities. SET, single-electron transistor. Full size image
The initial calibration of the 11-qubit atom processor requires the characterization of 24 + 25 = 48 electron spin resonances (ESRs), which is doubled to 96 in the presence of electron exchange interaction. Analysing the stability of the ESR peaks (Supplementary Information Section III), we find that the frequencies within each register shift collectively. Accordingly, we can implement an efficient recalibration protocol that scales linearly with the number of coupled spin registers. By characterizing the ESR frequency for a single reference configuration of the nuclear spins, we infer the exact positions of all other ESR transitions of the register from the frequency offsets of the initial calibration. As a result, recalibrating all 96 ESR frequencies requires only two measurements, that is, one per register.
The state of the individual nuclear spins is controlled using nuclear magnetic resonance (NMR), similar to molecules in solution37 and nitrogen-vacancy centres in diamond38,39. The readout of an individual nuclear spin is performed through QND readout using the ancillary electron (Supplementary Information Section IV). For nuclear spin initialization, we combine this ESR-based approach with conditional NMR π pulses (Supplementary Information Section V). To maximize the fidelity of the initialized state, we perform QND readout of the nuclear spin configuration of each register before each experiment and apply post-selection on the desired nuclear spin configuration (Supplementary Information Section VI). For all experiments, unless stated otherwise, spectator qubits—that is, spins not actively involved in a given gate or quantum circuit—are initialized in the ⇓ state, and spin manipulations are performed conditional on these initialized states. The large contrast observed in Rabi oscillations (Fig. 1d) across all data qubits shows the performance of the nuclear-spin readout and initialization procedure.
The coherence times for both nuclear and electron spins are characterized by means of Ramsey and Hahn-echo measurements (Fig. 1e). For the nuclear spins, the phase coherence time extracted from Ramsey measurements, \({T}_{2}^{\star }\), ranges from 1 to 46 ms. Refocusing with Hahn echo greatly extends such a phase coherence, \({T}_{2}^{{\rm{Hahn}}}\), to values between 3 and 660 ms. We observe that the phase coherence of the data qubits is related to its hyperfine Stark coefficient (Supplementary Information Section VII). Accordingly, we note that deterministic atom placement will provide a way to improve coherence by tailoring the spin registers for smaller susceptibility to electric field fluctuations. For the electrons e 1 and e 2 , we measure similar phase coherence times of \({T}_{2}^{\star }\approx 20\,{\rm{\mu }}{\rm{s}}\) and \({T}_{2}^{{\rm{Hahn}}}\approx 350\,{\rm{\mu }}{\rm{s}}\). Overall, our investigations affirm the potential of refocusing techniques to substantially improve the performance of our 11-qubit atom processor.
Single-qubit randomized benchmarking (1Q-RB) reveals that all qubits except n 4 operate with gate fidelities greater than 99.90% and as high as 99.99% for n 5 (see Supplementary Information Section VIII for optimization details). We attribute this excellent performance to long coherence times and minimal frequency drifts in both ESR and NMR (Supplementary Information Sections III and VII). These single-qubit metrics are on par with our recent results using a single spin register5, indicating consistency in atomic-scale fabrication.
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