A Race-Track Trapped-Ion Quantum Processor

We describe and benchmark a new quantum charge-coupled device (QCCD) trapped-ion quantum computer based on a linear trap with periodic boundary conditions, which resembles a race track. The new system successfully incorporates several technologies crucial to future scalability—including electrode broadcasting, multilayer rf routing, and magneto-optical trap (MOT) loading—while maintaining, and in some cases exceeding, the gate fidelities of previous QCCD systems. The system is initially operated with 32 qubits, but future upgrades will allow for more. We benchmark the performance of primitive operations, including an average state preparation and measurement error of $1.6(1)\times {10}^{-3}$, an average single-qubit gate infidelity of $2.5(3)\times {10}^{-5}$, and an average two-qubit gate infidelity of $1.84(5)\times {10}^{-3}$. The system-level performance of the quantum processor is assessed with mirror benchmarking, linear cross-entropy benchmarking, a quantum volume measurement of $\mathrm{QV}=2^{16}$, and the creation of 32-qubit entanglement in a GHZ state. We also tested application benchmarks, including Hamiltonian simulation, QAOA, error correction on a repetition code, and dynamics simulations using qubit reuse. We also discuss future upgrades to the new system aimed at adding more qubits and capabilities.

Popular Summary

Quantum computing is a fast-moving field, with researchers making tremendous progress in the last few years in building hardware. There are many proposed architectures for large-scale quantum computing, each with their own plans for scaling to large systems. Here, we present our progress in scaling a trapped-ion quantum computer to a larger number of qubits in a more complex trap, while maintaining similar or better performance compared to our earlier devices. The new system features several upgrades that will enable us to realistically scale to larger numbers of qubits.

We benchmarked the performance of our system at three progressively higher levels. First, we measured the errors of individual gates and other primitive operations that are the building blocks of our quantum computer. Then, we looked at more complex circuits, where errors can accumulate in nontrivial ways. From these measurements, we can extract effective gate fidelities that are consistent with the individual gate benchmarking. Finally, we ran example algorithms that closely match potential near-term use cases. Our results suggest that increasing circuit depth or time to a nontrivial degree is viable given our gate fidelities.

Our new system is currently operating with 32 qubits, but we plan on continuing to upgrade to more qubits and better performance. Doing so will allow us to enter the quantum advantage regime, where quantum computers will begin to perform computations that cannot be done in a reasonable amount of time on classical computers.

Figure 1

Picture of the H2 surface ion trap microchip. The image has been modified to enhance visibility of the trap features. The trap sits in the isthmus in the center of the trap die. The long axis of the trap is 6.58 mm (from the edge of the dc electrodes on either side), and the isthmus width is 2.02 mm.

Figure 2

Overview of the H2 trap including upgrades in trap design and gating operations. (a) 2D MOT producing a collimated beam of atoms, allowing for higher neutral atom density and faster loading than an effusive oven. (b) The abc tiling of electrodes for conveyor belt transport. (c) rf tunnels to implement inner and outer rf electrodes. Ions are trapped $70\mathrm{\mu }\mathrm{m}$ away from the trap surface. (d) Colored top metal layer of the H2 trap. Green curved zones are conveyor belt regions for ion storage. The bottom blue zones are DG01–DG04 (from left to right), which are used for quantum operations. The top blue zones are UG01–UG04 gate zones (from right to left), which are used for sorting but not quantum operations. Darker gray loops are rf electrodes. Yellow circles represent qubits that are gated while red circles represent qubits sitting in storage during gates (note that ${}^{138}{\mathrm{Ba}}^{+}$ ions are omitted for simplicity). Yellow arrows indicate the Doppler sheet beam direction while blue arrows indicate the Doppler repump sheet beam direction. (e) Ion configuration and beam direction for 2Q gates. Large orange circles represent ${}^{171}{\mathrm{Yb}}^{+}$ while smaller purple circles represent ${}^{138}{\mathrm{Ba}}^{+}$. (f) Ion configuration and beam directions for 1Q gates on the left ${}^{171}{\mathrm{Yb}}^{+}$. (g) Ion configuration and beam directions for state preparation and measurement (SPAM) operations on the left ${}^{171}{\mathrm{Yb}}^{+}$ with micromotion hiding on the right ${}^{171}{\mathrm{Yb}}^{+}$ [31]. (h) Storage ion configuration in the conveyor belt region.

Figure 3

Average infidelity as a function of angle for the parametrized 2Q gate $U_{ZZ}(\theta )$. Each data point is obtained by fitting the decay curves shown in Fig. 21 to an exponential decay function. The infidelity at $\theta =0$ is due to both the wrapper pulses and memory error incurred during the cooling pulses, which are still applied in the absence of an MS gate. The linear best fit to the zone-averaged data is given by $\epsilon (\theta )=(2.9(2)\theta /\pi +0.46(6))\times {10}^{-3}$.

Figure 4

The 2Q randomized benchmarking decay curves for each zone and for the combined average across all zones. (a) Standard RB decay curve. The average infidelity per 2Q gate is $1.83(5)\times {10}^{-3}$ across all four gate zones. (b) Decay of fraction of shots without leakage on either qubit as identified by the leakage detection gadget, which gives a measured leakage rate per 2Q gate of $3.9(2)\times {10}^{-4}$ across all four gate zones.

Figure 5

Leakage detection gadget, adapted from Ref. [55]. The gadget uses an ancilla qubit “$a$” to detect whether qubit “$q$” has leaked. The ancilla is initially prepared in $|1⟩$. If $q$ has leaked, the 2Q gates have no logical effect, and $a$ is measured as $|1⟩$. If instead $a$ has leaked, then $a$ will still be measured as $|1⟩$ since the leakage results in the ion being in a bright state. If neither $q$ nor $a$ has leaked, then the gadget (within the barriers in the circuit diagram) acts as $X_a{I}_q$, and $a$ is measured as $|0⟩$.

Figure 6

Mirror benchmarking experiments on H2. The sequence lengths correspond to half the circuit depths, so circuits of length $\ell$ contain $2\ell N$ 2Q gates with full connectivity. Ten random circuits were run at each sequence length with 100 shots per circuit. The average survival probabilities are fit to the model $p(\ell )=A{u}^{\ell -1}$. The parameter $u$ is used to obtain an effective 2Q gate average fidelity for a constant 2Q depolarizing error [57].

Figure 7

Quantum volume $\mathrm{QV}=2^{16}$ measurement on H2. The average and two-sigma confidence intervals of the heavy-output probability are plotted as a function of the circuit index. Passing occurs when the green shaded region (two-sigma confidence interval from semiparametric bootstrap method) is above the dashed gray line at $2/3$, which we satisfy in a data set with 200 randomly generated circuits.

Figure 8

Linear cross-entropy benchmarking fidelity as measured on H2 for classically verifiable random circuits. Each data point displays the combined results from ten circuits, each executed with 100 shots. The details of the best-fit curve are described in Appendix pp3-s3.

Figure 9

GHZ state preparation circuits for (a) log-depth unitary and (b) constant-depth adaptive preparation, here shown for $N=8$, for simplicity.

Figure 10

Populations and parities of $N=20$-, 26-, and 32-qubit GHZ states constructed with a log-depth unitary protocol, and also of a 32-qubit GHZ state produced with a constant-depth adaptive circuit. (a) Populations of $|0{⟩}^{\otimes N}$ and $|1{⟩}^{\otimes N}$. The ideal GHZ state has populations of 0.5 in these two states and zero in all other states. (b) Expectation values of the operator $M_k$ defined in Eq. (7), plotted versus angle ${\theta }_k=k\pi /N$. The ideal GHZ state has values of 1 and $-1$ for even and odd $k$, respectively. The dashed lines denote the averages.

Figure 11

Dynamics of $⟨X⟩$ for a 32-qubit TFIM Hamiltonian simulation vs evolution time. The orange data are obtained by directly implementing each $ZZ$ rotation in every Trotter step using our native parametrized angle $U_{ZZ}(\theta )$ gate with $\theta =2Jt/r$. The green data are obtained by decomposing each $ZZ$ rotation into two $U_{ZZ}(\pi /2)$ (Clifford) gates with some 1Q rotations. Each data point is obtained as the average of 100 shots of the associated Trotterized circuit for that time.

Figure 12

Optimization trajectory of $N=130$, $p=1$ QAOA computed via qubit reuse on H2. The expectation value of the energy as measured experimentally at $p=1$ (blue data) converges well to the best-possible exact value (green line). Uncertainties on the measured value of $⟨H_C⟩$ are plotted but are smaller than the displayed point size (see Appendix pp4-s2 for details). The best sample taken at each iteration (orange data) is also displayed relative to the true max cut (purple line).

Figure 13

Optimization trajectory of $N=32$, $p=2$ QAOA on H2. The expectation value of the energy as measured experimentally at $p=2$ (blue data) surpasses the best-possible exact value for a $p=1$ circuit (green dashed line). The best sample taken at each iteration (orange data) is also displayed relative to the true max cut (purple line).

Figure 14

Logical fidelities of the phase (square, dotted) and bit (circle, dashed) flip repetition codes as a function of distance. As the number of syndrome extraction (SE) rounds increases, more noise is injected into the system, degrading the logical fidelity. For a given number of rounds of SE, as the code distance increases, so does the logical fidelity. All error bars are calculated using jackknife resampling [103], except for those where the sampling number is too low to calculate an error (i.e., 100% fidelities), in which case the statistical rule of three was used [104].

Figure 15

(a) One-dimensional brickwork circuit of length $L=12$ with $t=4$ layers of gates applied to a quantum matrix-product state of bond dimension $\chi =2^{n_b}=2$. (b) HoloQUADS reusing qubits through MCMR to execute the same circuit with a minimal number of qubits. Here, we use $N_{\max }=9$ qubits, but $N_{\max }$ can be adjusted between $n_b+t+2=7$ (maximally serial) and $n_b+L=13$ (maximally parallel). (c) Experimentally measured (dots) correlation function $C^{xx}(r,t)$ for a dual-unitary circuit applied to a length $L=128+t$ solvable $\chi =2$ quantum matrix-product state compared to the exact thermodynamic limit results (solid lines), using $N_{\max }=32$ qubits up to time $t=24$. Error bars are standard deviations of the mean from four 100-shot experiments.

Figure 16

The 1Q RB data with parameters given in Table 5. (a) Decay of survival probability. (b) Decay of unleaked fraction of shots.

Figure 17

The 2Q SU(4) RB data with parameters given in Table 5.

Figure 18

Transport 1Q RB with parameters given in Table 5.

Figure 19

Measurement crosstalk data with parameters given in Table 5.

Figure 20

Reset crosstalk data with parameters given in Table 5.

Figure 21

Decay curves for direct RB of parametrized 2Q gates. The different sets of curves show data for $\theta$ ranging from 0 to $\pi /2$ in increments of $\pi /8$. Each experiment used sequence lengths $\ell =4$, 50, and 100, with ten random circuits per sequence length. The circuits were run in parallel across the four gate zones, and all circuits were run in a random order. The dashed curves are for individual zones, while the solid curve is the average over all zones. The decay curves for $\theta \in \{(\pi /8),(\pi /4),(3\pi /8),(\pi /2)\}$ are fit to the model $p(\ell )=A{r}^{\ell }+1/4$, and the average infidelity is computed using Eq. (b2). For $\theta =0$, the average infidelity is computed using the procedure described in Appendix pp2-s1. The average infidelity versus $\theta$ is shown in Fig. 3.

Figure 22

Quantum volume $\mathrm{QV}=2^{15}$ measurement on H2. The average and two-sigma confidence interval of the heavy-output frequency are plotted as a function of the circuit index. The green-shaded region shows the two-sigma confidence interval from the semiparametric bootstrap method.

Figure 23

(a) Number of Trotter steps used at each simulation time. (b) Absolute Trotter error $|⟨X{⟩}_r-⟨X⟩|$ at each time, where $⟨X{⟩}_r$ is the expectation value using $r$ Trotter steps under a noiseless circuit and $⟨X⟩$ is the exact value at that time. (c) Data value relative to the exact value $|⟨X{⟩}_{\text{exact}}-⟨X{⟩}_{\mathrm{data}}|$ at each simulation time. The data error bars are included to reflect the signal-to-noise ratio.

Figure 24

Energy landscape of an $N=130$, $p=1$ MaxCut QAOA problem. The optimization trace (pink) starts near the maximum in the top left and eventually converges into the potential well in the top right. Individual points at which circuits were evaluated are marked with stars. Note that the landscape is periodic, so the trajectory wraps around the sides of this plot.