基于纠缠原子阵列相干运输的量子处理器

　　我们的实验利用了参考文献中先前描述的相同设备。25 。在我们的真空电池内，将87RB原子从磁光陷阱加载到SLM57产生的可编程光学镊子的骨架阵列中
。原子与从交叉2D AOD产生的其他光学镊子并行重新排列为无缺陷的目标位置。按照重排过程 ，我们将选定的原子从静态SLM陷阱转移回移动AOD陷阱
，然后将这些移动原子移至量子电路中的起始位置 。在整个过程中，原子通过极化梯度冷却冷却
。在运行量子电路之前 ，我们在其初始启动位置拍摄原子的相机图像
，然后遵循电路，我们将最终的摄像头图像检测量子态| 0（原子存在）和| 1（原子损失 ，谐振下降后）。我们将所有数据发布有关在运行电路之前查找AOD和SLM原子的完美重排的所有数据 。在此处的所有实验中
，每个原子在整个量子电路的持续时间内仍处于单个静态或单个移动陷阱中20,58,59
。 　　交叉的AOD系统由两个独立控制的AOD（AA Opto电子DTSX-400）组成，用于X和Y的光束位置。这两种AOD均由独立的任意波形驱动 ，这些波形由双通道任意波形发生器（M4I.6631-X8通过Spectrum Instrumentation）生成，然后通过独立的MW放大器（Minicircuits ZHL-5W-W-1）放大 。时间域任意波形由对应于列和行的x和y位置的多个频率调子组成
，这些音调是在动态围绕AOD捕获的原子转向的时间的函数而独立更改的；完整的X和Y波形是通过将每个组件的给定幅度和相位的所有频率组件的时域曲线添加在一起来计算的。对于运行量子电路，我们对每个门位置的AOD原子的位置进行编程 ，然后平滑地插入（带有立方轮廓）AOD频率作为栅极位置之间的时间的函数
。与我们以恒定速度移动（线性轮廓）相比
，立方轮廓构成了原子上的恒定混蛋，这使我们能够更快地移动五到十倍的时间（无加热和损失）（线性轮廓）。在我们的运动协议中 ，我们仅进行AOD陷阱阵列的拉伸
，压缩和翻译：也就是说，AOD行和列永远不会彼此交叉 ，以避免与两个频率分量相互交叉相关的原子损失和加热 。 　　我们将整个原子轨迹的AOD镊子强度均匀
，以最大程度地减少因差异光移的时间变化而引起的
。为此，我们使用图像平面中的参考摄像头来评估每个门位置在每个栅极位置的强度 ，并通过改变每个频率分量的振幅来匀浆；在两个位置之间的运动过程中
，我们插入了每个单个频率分量的幅度。 　　SLM Tweezer Light（830 nm）和AOD Tweezer Light（828 nm）是由两个独立的自由运行的钛产生的：蓝宝石激光器（M Squared，18-W泵） 。SLM Tweezer通过0.5个数值孔径目标投影 ，腰围约为900 nm（AODS大约为1,000 nm）
。当加载原子时，陷阱深度约为2π×16 MHz
，径向陷阱频率约为2π×80 kHz，并且当运行量子循环时 ，陷阱深度约为2π×4 MHz
，径向陷阱频率约为2π×40 kHz。 　　快速，高保真的单量操纵是这项工作中所示的量子电路的关键要素 。为此 ，我们使用高功率795 nm拉曼激光系统来驱动磁性sublevel MF = 0时钟状态之间的全局单量旋转
。该拉曼激光系统基于参考文献中开发和描述的色散光学元件。26. 795 nm的光（Toptica TA Pro
，1.8 W）由电磁调制器（Qubig）进行相位调节，该电气调制器（Qubig）由3.4 GHz的微波驱动（Stanford Research Systems SRS SG384）驱动 ，后者倍增至6.8 GHz
，并驱动为6.8 GHz并放大 。激光相调制转换为振幅调制，用于通过使用Chired Bragg光栅（Optigrate）26驱动拉曼过渡
。SG384的智商（同相和正交）的控制用于微波的频率和相位控制 ，这些频率和相位控制在激光幅度调制到激光振幅调制上
，因此使我们对超细量子驱动器进行了直接频率和相位控制。 　　拉曼激光器以圆形椭圆形光束从侧面从侧面照亮原子平面，腰部和高轴分别为40μm和560μm ，在原子上的总平均光功率为150 mW 。大垂直范围可确保 <1% inhomogeneity across the atoms, and shot-to-shot fluctuations in the laser intensity are also <1%. For Figs. 1–3, we operate our Raman laser at a blue-detuned intermediate-state detuning of 180 GHz, resulting in two-photon Rabi frequencies of 1 MHz and an estimated scattering error per π pulse of 7 × 10−5 (that is, 1 scattering event per 15,000 π pulses)26. For Fig. 4, to shorten the duration of the coherent mapping pulse sequence, we increase the Raman laser power and operate at a smaller blue-detuned intermediate-state detuning of 63 GHz, with a corresponding two-photon Rabi frequency of 3.2 MHz and an estimated scattering error per π pulse of 2 × 10−4. 　　For almost all single-qubit rotations in this work (other than XY8 and XY16 self-correcting sequences), we implement robust single-qubit rotations in the form of composite pulse sequences. These composite pulse sequences are well known in the NMR community27,60 and can be highly insensitive to pulse errors such as amplitude or detuning miscalibrations. Our dominant source of coherent single-qubit errors arise from 1% amplitude drifts and inhomogeneity across the array; as such, we primarily use the ‘BB1’ (broadband 1) pulse sequence, which is a sequence of four pulses that implements an arbitrary rotation on the Bloch sphere while being insensitive to amplitude errors to sixth order27,60. We benchmark the performance of these robust pulses in Extended Data Fig. 3a. Furthermore, by applying a train of BB1 pulses, we find an accumulated error consistent with the estimated scattering limit (not plotted here), suggesting that the scattering limit roughly represents our single-qubit rotation infidelities (about 3 × 10−4 error per BB1 pulse owing to the increased length of the composite pulse sequence). Randomized benchmarking61 can be applied in future studies to further study single-qubit rotation fidelity. 　　In our 830-nm traps, hyperfine qubit coherence is characterized by inhomogeneous dephasing time  = 4 ms (not plotted here), T2 = 1.5 s (XY16 with 128 total π pulses) and relaxation time T1 = 4 s (including atom loss) (Extended Data Fig. 3b, c). All of our experiments in this work are performed in a d.c. magnetic field of 8.5 G. Coherence can be further improved by using further-detuned optical tweezers (with trap depth held constant, the tweezer differential lightshifts decrease as 1/Δ and 1/T1 decreases as 1/Δ3 (ref. 62), where Δ is the detuning of the trap wavelength) and shielding against magnetic field fluctuations. For practical QEC operation, atom loss can be detected in a hardware-efficient manner46 and the atom then replaced from a reservoir, which could in principle be continuously reloaded by a magneto-optical trap for reaching arbitrarily deep circuits. 　　All of our transport sequences20,58,59 are accompanied by dynamical decoupling sequences. The number of pulses we use is a trade-off between preserving qubit coherence while minimizing pulse errors. We interchange between two types of dynamical decoupling sequence: XY8 and XY16 sequences, composed of phase-alternated individual π pulses that are self-correcting for amplitude and detuning errors28,63, and Carr–Purcell–Meiboom–Gill (CPMG)-type dynamical decoupling sequences composed of robust BB1 pulses. The CPMG-BB1 sequence is more robust to amplitude errors but incurs more scattering error. We empirically optimize for any given experiment by choosing between these different sequences and a variable number of decoupling π pulses, optimizing on either single-qubit coherence (including the movement) or the final signal. Typically, our decoupling sequences are composed of a total 12–18 π pulses. 　　We study here the effects of movement on atom loss and heating in the harmonic oscillator potential given by the tweezer trap. Motion of the trap potential is equivalent to the non-inertial frame of reference where the harmonic oscillator potential is stationary but the atom experiences a fictitious force given by F(t) = −ma(t), where m is the mass of the particle and a(t) is the acceleration of the trap as a function of time64,65. By following ref. 66 (equation 5.4), we find the average vibrational quantum number increase ΔN is given by 　　where is the Fourier transform of a(t) evaluated at the trap frequency ω0, and the zero-point size of the particle , where is the reduced Planck constant. ΔN is the same for all initial levels of the oscillator66. Experimentally, we apply an acceleration profile a(t) = jt to the atom, from time −T/2 to +T/2 to move a distance D with constant jerk j. We calculate , simplify using ω0T  1, and assume a small range of trap frequencies to average the oscillatory terms, resulting in 　　Several relevant insights can be gleaned from this formula. First, this expression indicates our ability to move large distances D with comparably small increases in time T. Furthermore, to maintain a constant ΔN, the movement time . Moreover, to perform a large number of moves k for a deep circuit, we can estimate ΔN  k/T4, suggesting that we can increase our number of moves from, for example, 5 to 80 by slowing each move from 200 μs to 400 μs. Move speed could be further improved with different a(t) profiles, but inevitably with finite resources such as trap depth, quantum speed limits will eventually prevent arbitrarily fast motion of qubits across the array30. 　　We now compare equation (2) with our experimental observations. In Fig. 1d we start to observe atom loss when we move 55 μm in 200 μs under a constant negative jerk. This speed limit is consistent with our above estimates: using ω0 = 2π × 40 kHz and xzpf = 38 nm, we predict ΔN ≈ 6 for this move, corresponding to the onset of tangible heating at this move speed. More quantitatively, we assume a Poisson distribution with mean N and variance N and integrate the population above some critical Nmax upon which the atom will leave the trap. From this analysis we find atom retention is given by . 　　Extended Data Fig. 2a, b measures the atom retention as a function of move time T and trap frequency ω0/2π. Using the functional form above, for both sets of measurements, we extract an Nmax of about 30, corresponding to adding about 30 excitations before exciting the atom out of the trap. Such a limit is physically reasonable as the absolute trap depth of 4 MHz implies only about 100 levels, the atom starts at finite temperature, and moreover the effective trap frequency reduces once the anharmonicity of the trap starts to play a role. We note that these estimates are only approximate (we roughly estimate ω0 for the trap depths used during the motion), but nonetheless suggests our motion limit is consistent with physical limits for our chosen a(t). Our analysis here also neglects the acoustic lensing effects associated with ramping the AOD frequency, which causes astigmatism by focusing one axis to a different plane and thus deforms the trap and reduces the peak trap intensity (and ω0) as given by the Strehl ratio. 　　Additional heating and loss during the circuit can also be caused by repeated short drops for performing two-qubit gates, where the tweezers are briefly turned off to avoid anti-trapping of the Rydberg state and light shifts of the ground–Rydberg transition. However, drop–recapture measurements in Extended Data Fig. 2c suggest that the 500-ns drops we use experimentally have a negligible effect until hundreds of drops per atom (corresponding to hundreds of CZ gates). We find that atom loss and heating as a function of number of drops are well described by a diffusion model, which would then predict that reducing atom temperature by a factor of 2× (reducing thermal velocity by ) and reducing the drop time tdrop by 2×, together would increase the number of possible CZ gates per atom to thousands. 　　We implement our two-qubit gates and calibrations following ref. 5. Specifically, the two-qubit CZ gate is implemented by two global Rydberg pulses, with each pulse at detuning Δ and length τ, and with a phase jump ξ between the two pulses. The pulse parameters are chosen such that qubit pairs, adjacent and under the Rydberg blockade constraint, will return from the Rydberg state back to the hyperfine qubit manifold with a phase depending on the state of the other qubit. The numerical values for these pulse parameters are: 　　For our experiments in Figs. 1–3, we operate with a two-photon Rydberg Rabi frequency of Ω/2π = 3.6 MHz, giving a theoretical τ = 190 ns and a theoretical Δ/(2π) = −1.36 MHz. We choose the negative detuning sign to help minimize excitation into the mj = +1/2 Rydberg state (mj denotes magnetic sublevel of the 70S1/2 Rydberg state), which is detuned by about 24 MHz under the field of 8.5 G (and experiences a three-times lower coupling to the Rydberg laser than the desired mj = −1/2 state owing to reduced Clebsch–Gordan coefficients). In this work, we operate with strong blockade between adjacent qubits, with Rydberg–Rydberg interactions V0/2π ranging from 200 MHz to 1 GHz. In Fig. 4, we operate with Ω/2π = 4.45 MHz for the two-qubit gates. 　　The two-qubit gate from ref. 5 induces both an intrinsic single-qubit phase, as well as spurious phases that are primarily induced by the differential light shift from the 420-nm laser. Under certain configurations, the 420-nm-induced differential light shift on the hyperfine qubit can be exceedingly large (>8 MHz），在约6π的超精细量子量子量表上产生相位的积累。因此
，420 nm强度的小百分比变化会导致显着的Qubit脱位
。 　　参考5通过执行回声序列来解决这一420引起的相关问题：在CZ门之后，关闭了1,013 nm Rydberg Laser ，施加了Ramanπ脉冲
，然后再次对420 nm激光脉冲，以在CZ Gate期间再次脉冲420光。该方法回应了420引起的相位 ，但成本为420诱导的散射误差的成本增加了2倍
，这是我们两Q量CZ门中的主要误差来源 。 　　为了解决这些各种问题，在这里 ，我们在每个CZ门之间执行一个拉曼π脉冲
，以回荡超精细量子量子的伪门引起的相位（扩展数据图1）
。这种方法具有几个优势。现在，420引起的相位通过成对的CZ门取消 ，而无需明确施加其他420 nm脉冲以回声每个单独的CZ门
，从而在这项工作中减少了CZ Gate的散射误差，约为两个 。我们估计 ，这种回声技术减少了每个门口中产生的散射误差，大致补偿了通过在2D中传播我们的光学功率来增加的散射速率
，从而使我们可比较的栅极菲德利特斯（Gate Fidelites）与参考文献中报道的两倍CZ Gate Fidelities≥97.4（2）的散射率
。5。此外，CZ门之间的回声还取消了CZ门的内在单Qubit阶段 ，消除了该参数校准中的错误
，并取消了任何其他闸门引起的单个单位Qubit阶段，例如大致诱导的0.01-RAD相位通过脉动捕获的磁带 ，以示为500 ns的捕获量（以下图1） 。在我们应用的CZ门数为奇数的情况下
，我们对最终CZ门进行回声
。 　　为了进一步抑制420引起的伪造的效果，我们操作420 nm激光器以从6p3/2转变中进行红色驱动（由2 GHz）。对于红色的引导 ，| 0状态和| 1状态的光移具有相同的符号
，使差异偏移最小 <6.8 GHz, the light shift on the |0 state and the |1 state have opposite signs and amplify the differential light shift. 　　In typical Rydberg excitation timescales with optical tweezers, the axial trap oscillation frequencies of several kilohertz are inconsequential. Here with our circuits running as long as 1.2 ms, with Rydberg pulses throughout, we find that the axial trap oscillations can have important effects. In particular, the axial oscillations cause the atoms to make oscillations in and out of the Rydberg beams: at our estimated axial temperature of about 25 μK and axial oscillation frequency of 6 kHz, we estimate an axial spread . For our 20-μm-waist beams, the effect of this positional spread is relatively small on the pulse parameters of the CZ gate, but can be significant on the sensitive 420-induced phase we seek to cancel by echoing out the phase induced by CZ gates separated by about 200 μs (see previous section). When using 20-μm-waist beams, and a 2.5-GHz blue detuning of our 420-nm laser, we find that the dephasing due to the axial trap oscillations is significant (Extended Data Fig. 4). To remedy this deleterious effect, we increase the beam waist of our 420-nm laser to 35 μm (while maintaining constant intensity) and change the laser frequency to be 2-GHz red-detuned, together resulting in a significant reduction in the dephasing associated with improper echoing of the 420-nm pulse. 　　In Fig. 1, we prepare the |Φ+ Bell state in the same way that is done in ref. 5. After initializing a pair of qubits in |00, we apply X(π/2) pulse–CZ gate–X(π/4) pulse. We calculate and plot the raw resulting fidelity of this |Φ+ Bell state as the sum of populations in |00 and |11, averaged with the fitted amplitude of parity oscillations (example in Fig. 1c), which measures the off-diagonal coherences. In Fig. 1d, upon significant loss from movement, this fidelity estimate becomes skewed because we begin measuring an artificially large population in |11 (as state |1 is detected as loss); accordingly, we estimate the |Φ+ population as two times the population of |00 once the population difference between |11 and |00 becomes greater than 0.1 (an arbitrary cut-off where the effects of loss start to become significant). In Fig. 1d, for moves slower than 300 μs, we achieve an average raw Bell-state fidelity after the moving of 94.8(2)%. If we do not move or attempt to preserve coherence for 500 μs (that is, if we measure immediately after preparing the Bell state), then we measure a raw Bell-state fidelity of 95.2(1)% (not plotted here), consistent with the results in ref. 5. 　　We detail here some of our measured and estimated sources of error for an entire sequence (toric code preparation in particular, our deepest circuit). We find the total single-qubit fidelity after performing the entire sequence is roughly 96.5% for the toric code circuit, which we measure by embedding the entire experiment in a Ramsey sequence: that is, we perform a Raman π/2 pulse, do all motion and decoupling, and then do a final π/2 pulse with variable phase to measure total contrast. We are able to account for our single-qubit fidelity quantitatively as being composed of our known single-qubit errors in Extended Data Fig. 6c. 　　Estimated contributions to two-qubit gate error are summarized in Extended Data Fig. 6c. These estimates come from numerical simulations in QuTiP (version 4.5.0) with experimental parameters. The effects of intermediate state scattering and Rydberg decay are included via collapse operators in the Lindblad master equation solver. Other error contributions include finite-temperature random Doppler shifts and position fluctuations, as well as laser pulse-to-pulse fluctuations, all of which are simulated using classical Monte Carlo sampling of experiment parameters. Experimental parameters used for the simulations are as follows: blue and red Rabi frequencies (Ωb, Ωr) = 2π × (160, 90) MHz, 6P3/2 intermediate state detuning of 2 GHz, intermediate state lifetime of 110 ns, 70S1/2 Rydberg state lifetime of 150 μs, Rydberg blockade energy of 500 MHz, splitting to second Rydberg state of 24 MHz, radial and axial trap frequencies (ωr, ωz) = 2π × (40, 6) kHz, and temperature T = 20 μK. We can also use this modelling to project for future performance; by assuming a 10 times increase in available 1,013-nm intensity and that atoms are cooled to a temperature of 2 uK, we project a possible CZ gate fidelity of 99.7%, beyond the surface code threshold38,67. Alkaline-earth atoms could also offer other routes to high-fidelity operations for QEC68,69,70. 　　To understand how our various single-qubit and two-qubit errors contribute to our graph-state fidelities, we perform a stochastic simulation of the quantum circuit used for graph-state preparation (Extended Data Fig. 6a, b). We utilize the Clifford properties of our circuit, allowing for efficient numerical evaluation and random sampling of many possible error realizations. The simulation is performed under a realistic error model, where the rates of ambient depolarizing noise and atom loss are measured in the experiment (Extended Data Fig. 6c). The resulting stabilizer and logical qubit expectation values agree well with those measured experimentally. 　　We shape our Rydberg beams into tophats of variable size through wavefront control using the phase profile on an SLM25. This ability allows us to match the height of our beam profile to the experiment zone size of any given experiment, thereby maximizing our 1,013-nm light intensity and CZ gate fidelities. We optimize our Rydberg beam homogeneity until peak-to-peak inhomogenities are below <1%. To this end, we correct all aberrations up to the window of our vacuum chamber, as done in ref. 25, which yields an inhomogeneity on the atoms of several per cent that we attribute to imperfections of the final window. To further optimize the homogeneity, we empirically tune aberration corrections on the tophat through Zernike polynomial corrections to the phase profile in the SLM plane (Fourier plane). With this procedure, we reduce peak-to-peak inhomogeneities to <1% over a range of 40–50 μm in the atom plane. 　　We outline here a description of how we optimize our graph layouts for the cluster state, Steane code, surface code and toric code preparation. Our optimization in this work is heuristic, and future work can develop appropriate algorithms for designing optimal circuits through atom spatial arrangement and AOD trajectories. Extended Data Fig. 5 shows all of the graphs we create and the process for creating them. There are several parameters we optimize for. (1) Minimize the number of parallel two-qubit gate layers. (2) Minimize the total move distance for the moving atoms. (3) Have all moving atoms in one sublattice (all graphs realized here are bipartite) to facilitate the final local rotation of one sublattice. (4) Minimize the vertical extent of the array and the number of distinct rows (to maximize 1,013-nm light intensity and minimize sensitivity to beam inhomogeneity between the rows). (5) When ordering gates, apply two-qubit gates as early as possible in the circuit. If a gate layer induces a bit-flip (X error) then that error can propagate during subsequent gates (becoming a Z error on the other qubit), so gates should be in the earliest layer possible. 　　We perform local rotations in the hyperfine basis by use of our horizontally propagating 420-nm beam, which imposes a differential light of several megahertz on the hyperfine qubit and can thus be used for realizing a fast Z rotation. To realize the local Y(π/2) rotation used throughout this work, we move one sublattice of atoms out of the 420-nm beam, then apply [global Y(π/4)]–[local Z(π)]–[global Y(π/4)]. This realizes a Y(π/2) rotation on one sublattice and a Z(π) rotation on the other sublattice (which is inconsequential as it then commutes with the immediately following measurement in the Z basis). To apply a Y(π/2) on the other sublattice of atoms, we add an additional global Z(π) (implemented by jumping the Raman laser phase) between the two Y(π/4) pulses. Future experiments will benefit from an additional set of locally focused beams for performing local Raman control of hyperfine qubit states, but we find that moving atoms works so efficiently (even for moving >50μm从420 nm梁中移出），这种方法非常适合在大约一半的Qubits上产生高保真性 ，同质旋转 。 　　我们执行局部rydberg控制
，以初始化| 2 = | rgrg ... = | r1r1 ...用于研究多体疤痕动力学的状态
。我们通过使用由SLM生成的810 nm镊子在所需的位点子集上应用| 1和| R之间的大约50 MHz光移，然后应用一个全局的Rydbergπ脉冲 ，从而激发非光移原子。我们在这里使用这种方法将每个链中的其他所有原子都准备成| r，但强调
，由于SLM镊子的位置是完全可编程的，因此可以使用此技术来准备任何初始的封闭式 - 满足原子在| 1 and | r中的原子 。 　　50 MHz的偏置光转移明显大于Rydberg Rabi频率ω/2π= 4.45 MHz ，导致Rydberg人口在不期望的地点上 <1%. The t = 0 time point of Extended Data Fig. 10b shows the high-fidelity preparation of the |2 state using this approach. We note that with 810-nm light, even though the achieved biasing light shift is significant, the Raman-scattering-induced T1 (of the hyperfine qubit) is still about 50 ms and thus leads to a scattering error 4 × 10−6 during the 200-ns pulse of the light-shifting tweezers. There can also be a motional effect from the biasing tweezers, with an estimated radial trapping frequency of 150 kHz, which we also deem to be negligible during the 200-ns pulse. 　　In Fig. 4, we study dynamics under the many-body Rydberg Hamiltonian 　　where is the reduced Planck constant, Ω is the Rabi frequency, Δ is the laser frequency detuning, ni = |riri| is the projector onto the Rydberg state at site i and flips the atomic state. For the entanglement entropy measurements in this work, we choose lattice spacings where the nearest-neighbour interaction V0 >Ω导致Rydberg封锁
，防止相邻原子同时占据|R。特别是，多体实验是在八个原子链上进行的 ，并淬灭了v0/2π= 20 MHz
，ω/2π= 3.1 MHz和δ/2π= 0.3 MHz的时间独立的HRYD
。淬火至小的，正δ= 0.0173V0部分抑制了始终阳性的长距离相互作用 ，因此对于疤痕寿命
，如在参考文献中得出和实验所示。71 。 　　如文本中所述，我们实现了一个连贯的映射协议 ，以{| 1
，| r}基础将通用多体状态传输到长期且非相互作用{| 0，| 1}基础上
。为了实现此映射 ，在Rydberg动力学之后，我们将拉曼π脉冲应用于映射| 1→| 0
，然后将随后的rydbergπ脉冲映射到映射| r→| 1（参考72）。 　　即使是为了完美的拉曼和rydbergπ脉冲（在孤立的原子上），与此映射过程相关的三个关键不忠源 。（1）在最终的rydbergπ脉冲中 ，封锁状态中的任何种群（即| r中的两个相邻原子都在| r中）都将发生强烈转移
。因此
，这个原子量将留在瑞德伯格州并丢失。（2）例如，从下一步的邻居中进行远距离相互作用 ，将使最终的rydbergπ脉冲从共振中捕捉
，从而减少脉搏保真度 。由于所有多体微晶格的远距离相互作用都不相同，因此无法通过简单的失谐偏移来减轻这种效果
。（3）状态的去态发生在拉曼π脉冲的整个持续时间内 ，主要来自基态之间的多普勒在| 0和| 1之间以及rydberg state | r之间移动。尽管在多体动力学中也存在这些随机的现场失调
，但转动Rydberg驱动器ωoff使系统可以自由积累相位，并使我们对DEPHAS的错误特别敏感 。 　　现在 ，我们详细介绍了对上述错误机制的缓解
。为了最大程度地减少（1）中的错误
，我们使用多体动态。这样可以最大程度地减少原子违反封锁的可能性为1％ 。为了帮助最大程度地减少（2）中的错误，我们将最终π脉冲的420-nm激光器的振幅增加了2倍 ，使得（vnnn/ω）2 = 0.005（其中vnnn是与下一个最早的邻居的相互作用），从而减少了从远距离互动到长期阶段脉冲误差
，从而减少了1％的脉冲误差。最后，为了减少（3）的错误 ，我们执行一个快速的拉曼π脉冲
，在结束多体rydberg动力学和开始rydbergπ脉冲之间仅留下150 ns
。相对于≈3–4μs的{| g，| r}的基础 ，150-ns间隙相当短
，导致每个粒子的随机相累积约为0.02×2πrad，但通过在一个副本中串起n个粒子的n粒子的纠缠状态与一个随机相对于n个粒子的n粒子中的n粒子中的n粒子纠缠在一起 ，从而进一步复杂化。我们在扩展数据中研究了这些各种效果图9c 。 　　最后
，我们注意到，在拉曼π脉冲期间 ，全局拉曼束在| 0和| 1相对于| r诱导了大约π的轻相诱导的相移
。同样
，全局的420 nm激光也诱导了在rydbergπ脉冲期间在| 0和| 1之间的轻移相移。尽管我们在此处执行的测量值是干涉测量值（换句话说，我们测量的单线状态在全球旋转下是不变的） ，因此不受这些全球相移的影响，但在将来的工作中
，可以测量并考虑相关的位置 。 　　二阶Renyi纠缠熵由子系统A上降低密度矩阵ρA的状态纯度给出
。可以通过注意到多体交换操作员的期望值来测量纯度（参考文献10,11）。多体交换操作员由每个双胞胎对上的单个交换操作员组成，即（使用ia） 。衡量这种期望值等于单点状态的探测（在所有其他本征态都具有特征值+1
。单元状态在每个双胞胎对中的发生 ，即贝尔状态|ψ-的发生
，也可以通过铃声|（可以用其他本地Z（π）提取，以下是| | | | | | | | | |在计算基础上进行测量。系统的其余部分 。 　　可以将贝尔测量电路分解为在双对的一个原子上施加X（π/2）旋转 ，然后施加CZ栅极
，然后施加一个全局X（π/2）旋转
。在其他测量值中，我们通过进行全局X（π/4）旋转 ，然后将局部Z（π）旋转
，然后将全局X（π/4）实现局部X（π/2）。但是，我们注意到 ，对于此单元测量电路
，第一个X（π/4）是冗余的，因为单元状态在全局旋转下是不变的 ，因此对于局部X（π/2），我们仅应用局部Z（π）
，然后应用第二个全局x（π/4） 。这有效地实现了一个Qubit上的x（π/2），在另一个量子位上最多达到z（π）（图4中的电路图中未显示）。在此简化下 ，可以将钟的测量电路大致理解为参考文献中钟形准备电路的反面
。5
，这正是我们如何校准铃铛测量的参数。 　　为了验证干涉测量值（并检查正确的校准），我们将其与多体动力学和相干映射协议分开基准 。我们通过在相同的 ，可变的单量子叠加（通过可变时间的全局拉曼脉冲）中制备独立的Qubit来执行此基准测试
，并确保干涉法很少会导致所有可变初始产物状态的| 00（扩展数据图8A）
。我们发现这是一个重要的基准测试步骤，因为我们发现对贝尔测量的微小错误校准会导致不同初始产品状态的忠诚度（即较高的熵） ，从而导致纠缠熵测量中的其他虚假信号。我们注意到
，在最终X（π/2）脉冲之前（由CZ Gate诱导并由全局Z（θ）脉冲取消），此测量对单量相特别敏感 。 　　为了基准我们在多体系统中测量纠缠熵的方法 ，在扩展数据中
，我们研究了在| 1中初始化两个近端原子后的纠缠动态，并以可变的时间t对Rydberg State令人兴奋
。在Rydberg封锁的条件下 ，这种激发会导致| 11和纠缠状态之间的两粒子狂欢振荡（扩展数据的顶部面板图8b）3,13,72。该两粒子系统的状态纯度是通过对两个相同副本对原子对进行铃铛测量来测量的 。在局部，当系统进入最大纠结| W状态时
，一粒子子系统的测得的纯度降低至约0.5，此时 ，每个个体原子的降低密度矩阵最大混合
。相反
，全球两粒子状态的纯度保持较高。关于全球状态纯度高于局部毕业的纯度的观察结果是量子纠缠的独特特征 。11,12
。 　　对于图4c，e中所示的数据 ，我们像参考文献中所做的那样
，通过广泛的经典熵减去数据。12 。这个固定的，无关的偏移由每个粒子的熵给出 ，即（淬灭时间t = 0）×（子系统大小）/（全局系统大小）。在扩展数据图9a中
，我们显示了与数字旁边的原始纠缠熵测量值，以指示广泛的经典熵贡献的大小
。在绘图中 ，我们还将理论曲线延迟了10 ns
，以说明拉曼π脉冲切断了Rydberg Evolution的最后10 ns，这是为了使相干映射间隙尽可能短并最小化多普勒dephasing。此外 ，在扩展数据中，我们绘制了测得的全局纯度
，并将其与包含实验误差的数值模拟进行比较（扩展数据图9C） 。 　　在扩展数据图10中，我们在八原子链系统上显示了其他多体数据 ，其参数与主文本中使用的参数相同
。我们显示了八原子链中每个位点的测得的单位熵
，用于扩展数据中的| 2淬灭图10a。此外，在扩展数据图10b中 ，我们绘制了全局rydberg总体
，在{| 1，| r}基础和{| 0 ，| 1}基础上都测量 。