This beam is steered using a pair of crossed AODs, which are driven by RF waveforms generated by custom FPGA hardware. In order to rearrange atoms into a desired target pattern, an image is first taken which establishes the locations of initially occupied sites.

This image is used to calculate a set of moves to fill target sites from the initially occupied sites according to the compression algorithm Moves are then performed in three steps: 1 ramp up the intensity of the rearrangement beam, 2 translate the rearrangement beam from the initial site to the target site using linear frequency chirps on the AODs, and 3 ramp down the intensity of the rearrangement beam.

Population in this manifold experiences Raman scattering due to nm trapping light, and ultimately decays into the ground state by way of the 5s5p 3 P 1 manifold In this approach, the POVM M ideal for an ideal single-qubit projective measurement in the computational basis is.

From this, one finds the intuitive result that the non-ideal POVM is given as. The measurement correction matrix is then. such that the measured vector of probabilities P exp i.

Additionally, error bars for a particular measurement are corrected by using this equation to propagate the uncertainties in m exp and q. Typically, one would run dedicated experiments to measure the probabilities p and q and construct the POVM. In fact, our measurement of q is updated from one point to the next during an experimental parameter scan, since the undriven atoms are always read out.

To calculate q for a set of experimental shots, we start by summing the bright counts from all the undriven atoms, with each count conditioned on the corresponding atom remaining trapped throughout the measurement. This sum is then normalized by the total counts from all the undriven atoms, conditioned in the same way as before.

In summary, our procedure amounts to using atoms outside the computational array to find an average value of q for each condition of a parameter sweep and then applying that value to atoms within the computational array in post-processing. Since these corrections have been applied to the measurements shown in the main text, in Fig.

Uncorrected measurements of a the nuclear-spin qubit resonance originally shown in Fig. Solid lines represent fits that use the same underlying models as in the main text to fit these uncorrected data points. Information regarding error bars and counts-per-point are provided in the main text.

Raman scattering from 3 P 0 can be reduced by minimizing the amount of time atoms spend in the clock state before imaging. One strategy for achieving this, recently implemented in 88 Sr 40 , is to remove the ground state population via a pulse of resonant nm light immediately after the clock pulse is performed.

This strategy was used to create the data presented in Fig. Future measurements can push non-POVM-corrected fidelity higher and atom loss lower by collecting photons more efficiently, e. Another approach involves using the narrow 3 P 1 intercombination line to sequentially image atoms in each qubit level eliminating the need for shelving in the clock state altogether , although the smaller scattering rate in this case would lower the readout speed Finally, this error is only a limitation when single-shot measurements are required e.

For all fitted data presented, we perform a weighted least-squares optimization with the indicated functional form. Any fixed parameters for the fits are indicated in the text and are set with independent measurements e.

All fits reported in the main text are performed after applying the POVM correction to the data based on the shelving probability of the atoms outside the computational array including the propagation of errors through the POVM correction , as discussed above.

The reported error bars on fit parameters are the standard error from the weighted least squares optimization fitting routine. As we are driving each qubit individually, it is important to consider the cross-talk of the drive lasers from one site driving rotations of its neighboring atoms.

While further characterization of this cross-talk with dedicated experiments will be required for demonstrating high-fidelity operations, we can use the data presented in Fig.

Specifically, we compare the population of the qubits in the computational array that are undriven and thus neighboring a driven qubit, depicted as red boxes in Fig.

The color of each box represents indicates qubits that are driven blue or undriven red within the computational array for the data presented in Fig. Additionally, the shading of the sites around the perimeter of the computational array indicates whether that site neighbored a driven qubit or an undriven qubit.

All qubits more than one site away from the computational array are categorized as background atoms and are assumed to be undriven by the gate beams. We do not include signal from trap sites immediately neighboring the array in this analysis because the statistics are quite low those sites will be rearranged into the computational array first.

This 1. If the beam were a perfect gaussian, this would be consistent with a larger-than-expected waist of ~2. However, we know the beams are apertured into the objective, which leads to the actual profile including rings around the central spot.

Combining this effect with imperfections in the beam shape due to, e. Future work will aim to fully characterize the cross-talk between neighboring qubits, as well as to modify the beam shaping optics to minimize the cross-talk between neighboring qubits, a requirement for realizing high-fidelity local qubit manipulations.

While the rearrangement process should not couple the nuclear spin states, the process can lead to heating of the atoms, which would degrade the shelving pulse fidelity, resulting in the increased signal Further studies will aim to determine how much of this population imbalance is due to cross-talk of the manipulation beams compared to different state preparation and shelving performance in the computational array.

The processed data used to create all figures in this article are included in Supplementary Data files. The raw data i. No custom code was used that is central to the conclusions of the manuscript.

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The authors would like to thank Sabrina Hong, Alexander Papageorge, Maxwell Parsons, Colm Ryan, and Prasahnt Sivarajah for their contributions during the initial design and buildout of the optical systems, control hardware, and software infrastructure used in this work.

We would also like to thank Jun Ye and Alexey Gorshkov for multiple discussions during the planning stages of this work. This work was partially supported under NSF SBIR Grant Katrina Barnes, Peter Battaglino, Benjamin J.

Bloom, Kayleigh Cassella, Robin Coxe, Nicole Crisosto, Jonathan P. King, Stanimir S. Kondov, Krish Kotru, Stuart C. Larsen, Joseph Lauigan, Brian J. Lester, Mickey McDonald, Eli Megidish, Sandeep Narayanaswami, Ciro Nishiguchi, Remy Notermans, Lucas S. You can also search for this author in PubMed Google Scholar.

performed the foundational design of the Phoenix system. contributed to the design, construction, and operation of Phoenix, as well as making measurements. built custom RF hardware for rearrangement and clock manipulations.

created the gate language and software infrastructure for Phoenix. wrote and assembled the manuscript, M. created diagrams and figures, and K. K performed data analysis. all reviewed the manuscript. Correspondence to Benjamin J. Bloom , Krish Kotru or Mickey McDonald. and J. are co-founders of, and equity shareholders in, Atom Computing, Inc.

All other authors are employees of, and equity shareholders in, Atom Computing, Inc. Nature Communications thanks the other anonymous reviewer s for their contribution to the peer review of this work. Peer reviewer reports are available.

Open Access This article is licensed under a Creative Commons Attribution 4. Reprints and permissions. Barnes, K. Assembly and coherent control of a register of nuclear spin qubits. Nat Commun 13 , Download citation. Received : 14 February Accepted : 08 April Published : 19 May Anyone you share the following link with will be able to read this content:.

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The computational power of quantum networks is expected to far exceed that of classical technologies. Among the most promising quantum bits qubits for such networks are the spins of individual particles in solids, such as electrons and nuclei.

Elementary control of such qubits and links within quantum networks have been demonstrated, but the largest entangled quantum states reported to date have contained just three spins.

Larger quantum registers are essential to realizing advanced computational power. However, controlling individual spins within complex and strongly interacting spin systems is a significant challenge.

In this study, we demonstrate a fully controllable ten-qubit register. Working at 3. We show that the system is fully connected by generating entangled states between all 45 possible spin pairs, and we prepare genuine seven-spin entanglement.

The spins that we study are excellent quantum memories that can store quantum states for up to one minute, the longest coherence time reported for solid-state spin qubits. We expect that our methods can also be applied to other spin platforms in diamond, silicon, and silicon carbide.

Our findings pave the way for advanced quantum algorithms and large multiqubit quantum networks based on tens of solid-state spin qubits.

Illustration of the ten-qubit register developed in this work. The electron spin of a single NV center in diamond acts as a central qubit and is connected by two-qubit gates to the intrinsic N 14 nuclear spin and a further eight C 13 nuclear spins surrounding the NV center.

a Illustration of the pulse sequence employed to realize a DDrf gate. Dynamical decoupling pulses on the electron spin purple are interleaved with rf pulses yellow , which selectively drive a single nuclear spin. b Illustration showing that the initial state of the electron spin determines which rf pulses are resonant with the nuclear spin.

The phase of each rf pulse is adapted to create the desired nuclear spin evolution, accounting for periods of free precession according to Eq. The final state vectors are antiparallel along the equator; therefore, the gate is a maximally entangling two-qubit gate.

d Top-down view of c. a Nuclear spin spectroscopy. The electron spin is then measured along a basis in the equatorial plane defined by angle φ see inset. By fitting the amplitude, we distinguish such deterministic phase shifts from loss of coherence due to entangling interactions.

The signals due to interaction with the eight C 13 spins used in this work are labeled. The dashed gray line indicates the C 13 Larmor frequency ω L.

A detailed analysis of the spectrum is given in the Supplemental Material [ 53 ]. b , c Example phase sweeps for two data points highlighted in red b and orange c in a. Solid lines are fits to f φ.

a Experimental sequence to prepare an electron-nuclear Bell state and determine the expectation value of the two-qubit operator Z X. A series of single- and two-qubit gates are used to initialize the nuclear spin [ 16, 37 ]. A measurement of the electron spin in the Z basis is followed by an X -basis measurement of the nuclear spin through the electron spin.

These measurements are separated by a nuclear spin echo, which is implemented to mitigate dephasing of the nuclear spin. The entire sequence is applied with and without an additional electron π pulse dashed box before the first electron readout in order to reconstruct the electron state while ensuring that the measurement does not disturb the nuclear spin state [ 16, 42 ].

b Density matrix of the electron-nuclear state after applying the sequence shown in a to qubit C1, reconstructed with state tomography. We correct for infidelities in the readout sequence characterized in separate measurements [ 53 ].

We use error function pulse envelopes with a 7. a Experimental sequence for the preparation of a nuclear-nuclear Bell state and measurement of the two-qubit operator Z Z. Measurement of the two-qubit correlations between the nuclear spins is then performed through the electron spin.

Spin echoes dashed boxes built into the measurement sequence protect the nuclear spins from dephasing errors. Blue purple bars show the experimental ideal expectation values for each operator.

The nuclear-nuclear correlations are well preserved after a nondestructive measurement of the electron spin in the X basis. Measured Bell state fidelities for all pairs of qubits in the ten-qubit register. Genuine entanglement is confirmed in all cases, as witnessed by a fidelity exceeding 0.

Qubits C1, C7, C8, and N 14 are controlled using DDrf gates Sec. Qubits C2, C3, C4, C5, and C6 are controlled using the methods described in Taminiau et al. The measurement sequence is broken down into basis rotations BR 1,2 , an electron readout RO , nuclear spin echoes echo 1,2 , and a multiqubit readout of the nuclear spins.

All operations are applied sequentially in the same way as shown in Fig. b , c Bar plots showing the measured expectation values nonzero terms of the ideal state only after preparing the five-spin b and seven-spin c GHZ states. The colors indicate the number of qubits involved, i. Gray bars show the ideal expectation values.

See the Supplemental Material [ 53 ] for the operator corresponding to each bar. The fidelity with the target state is 0. d Plot of GHZ state fidelity against the number of constituent qubits. A value above 0. The blue points are the measured data, while the green points are theoretical predictions assuming a simple depolarizing noise model whose parameters are extracted from single- and two-qubit experiments.

Numerical values are given in the Supplemental Material [ 53 ]. a Dynamical decoupling for spin C5. B , T , and n are fit parameters which account for the decay of the fidelity due to interactions with the nuclear spin bath, external noise, and pulse errors.

b Dynamical decoupling of the N 14 spin. Solid lines are fits to f t , but with A as a free parameter to account for the observed decrease in the Z Z correlations at large pulse numbers, likely due to pulse errors. With decoupling pulses, genuine two-qubit entanglement is witnessed at times up to In addition, interpolation of the fit yields For pair 1, the fitted decay times T are 0.

For pair 2, the equivalent values are 0. It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author s and the published article's title, journal citation, and DOI are maintained.

Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Our experiments demonstrate a fully functional hybrid spin register. We have combined optimal-control-based error avoidance with error Detailed product information can be found using SPIN, Partial Product/Trustee Name. Click on the results to see more information about the specific product The generation of a register of highly coherent, but independent, qubits is a prerequisite to performing universal quantum computation

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It is your responsibility to obtain the proper permission from the rights holder directly for these figures. Physical Review X Highlights Recent Subjects Accepted Collections Authors Referees Search Press About Editorial Team. Featured in Physics Open Access. A Ten-Qubit Solid-State Spin Register with Quantum Memory up to One Minute C.

Bradley, J. Randall, M. Abobeih, R. Berrevoets, M. Degen, M. Bakker, M. Markham, D. Twitchen, and T. Taminiau Phys. X 9 , — Published 11 September See Synopsis: Diamond Qubits Take the Stage. Article References Citing Articles Supplemental Material Article References Citing Articles Supplemental Material PDF HTML Export Citation.

Abstract Spins associated with single defects in solids provide promising qubits for quantum-information processing and quantum networks. Research Areas. Quantum control Quantum entanglement Quantum gates Quantum memories. Diamond Qubits Take the Stage Published 11 September A ten-qubit system based on spins in impure diamond achieves coherence times of over a minute.

See more in Physics. Taminiau TUDelft. Issue Vol. Authorization Required. Log In. Other Options Buy Article » Find an Institution with the Article ». Figure 1 Illustration of the ten-qubit register developed in this work. Figure 2 a Illustration of the pulse sequence employed to realize a DDrf gate.

Figure 3 a Nuclear spin spectroscopy. Figure 4 a Experimental sequence to prepare an electron-nuclear Bell state and determine the expectation value of the two-qubit operator Z X.

Figure 5 a Experimental sequence for the preparation of a nuclear-nuclear Bell state and measurement of the two-qubit operator Z Z. Figure 6 Measured Bell state fidelities for all pairs of qubits in the ten-qubit register.

Figure 8 a Dynamical decoupling for spin C5. Sign up to receive regular email alerts from Physical Review X Sign up. Create an account ×. Journal: Phys. X PRX Energy PRX Life PRX Quantum Rev. A Phys. B Phys. C Phys. D Phys. E Phys. Research Phys. Beams Phys. Berrevoets , M. Degen , M.

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