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, 10 (1), 5464

Benchmarking an 11-qubit Quantum Computer

Affiliations

Benchmarking an 11-qubit Quantum Computer

K Wright et al. Nat Commun.

Abstract

The field of quantum computing has grown from concept to demonstration devices over the past 20 years. Universal quantum computing offers efficiency in approaching problems of scientific and commercial interest, such as factoring large numbers, searching databases, simulating intractable models from quantum physics, and optimizing complex cost functions. Here, we present an 11-qubit fully-connected, programmable quantum computer in a trapped ion system composed of 13 171Yb+ ions. We demonstrate average single-qubit gate fidelities of 99.5[Formula: see text], average two-qubit-gate fidelities of 97.5[Formula: see text], and SPAM errors of 0.7[Formula: see text]. To illustrate the capabilities of this universal platform and provide a basis for comparison with similarly-sized devices, we compile the Bernstein-Vazirani and Hidden Shift algorithms into our native gates and execute them on the hardware with average success rates of 78[Formula: see text] and 35[Formula: see text], respectively. These algorithms serve as excellent benchmarks for any type of quantum hardware, and show that our system outperforms all other currently available hardware.

Conflict of interest statement

The authors declare no competing interests.

Figures

Fig. 1
Fig. 1
Schematic of the hardware. A linear chain of ions is trapped near a surface electrode trap (trap is not shown). Lasers at 369 and 935 nm (not shown) illuminate all of the ions during cooling, initialization, and detection. Each ion’s fluorescence is imaged through a 0.6 numeric aperture lens (detection optics) and directed onto individual photomultiplier tube channels. Two linearly polarized counterpropagating 355 nm Raman beams are aligned to each qubit-ion, a globally addressing beam that couples to all of the qubits (red) and an individual addressing beam that is focused onto each ion (blue). Acousto-optic modulators (AOMs) modulate the frequency and amplitude of each of these beams to generate single-qubit rotations and XX-gates between arbitrary pairs of qubit ions.
Fig. 2
Fig. 2
Fidelity of native gates. For each qubit pair, we perform an XX-gate and measure the joint populations of the qubit pair as a function of an analysis pulse phase angle. The fidelity of two-qubit gates are plotted as a color scale in the illustration of our all-to-all connectivity in a. For each qubit, we perform randomized benchmarking to determine the fidelity of the single-qubit gates shown in b, which are plotted as the color scale of the nodes in a. We use maximum-likelihood estimation to extract fidelities from the parity and joint-population measurement shown in c. The average two-qubit raw fidelity is 97.5% and all two-qubit gates perform in the range [95.1%, 98.9%]. The distribution of these fidelities are depicted in the histograms above the color bars shown in b, c. The fidelity of all single-qubit gates are enumerated in Supplementary Table 1 and all two-qubit pairs are enumerated in Supplementary Table 2 of the extended data.
Fig. 3
Fig. 3
Bernstein–Vazirani (BV) algorithm. a Shows a textbook implementation of the BV algorithm with hidden bit string 1010101010. b Shows the full output distribution for all 1024 oracle implementations calculated from 500 iterations of each oracle after conditioning on the ancilla. c Shows the probability (inset plot) of detecting the encoded hidden bit string for all 1024 oracle implementations, as a function of the number of ones in the binary representation of the unknown bit string, which is equivalent to the number of two-qubit gates (n), which is maximally 10 in the case of this algorithm. The boxplots highlight the minimum, first quartile, median, third quartile, and maximum of the data. Note that there is only one oracle implementation for n = 0, 10, which explains the lower observed variances for these points. In contrast, there are many more oracles that consist of five two-qubit gates, where each included gate has slightly different fidelity. This leads to increased variance across the full set of five two-qubit gate oracle implementations. The shaded area spans the expected fidelity (excluding crosstalk errors) F2QnF1Q2(n+1)FSPAM10 (where F2Q is the fidelity of two-qubit gates, F1Q is the fidelity of single-qubit gates, and FSPAM is the average SPAM fidelity) if all of our gates share the best measured fidelity or, alternatively, all share the worst fidelity. The result of a shared average fidelity is plotted as a dashed line. The average probability of success is 78% with 899 out of the 1024 oracle implementations exceeding the 23 BQP single-shot success threshold.
Fig. 4
Fig. 4
Hidden Shift (HS) algorithm implementation on 10 qubits. a Shows a textbook implementation of the HS algorithm with hidden shift 1111101010. The circuit for each oracle was measured at least 50 times. We trace out the spectator ion and interpret the binary output state of the 10-qubit register as an integer. The full output distribution is shown in b. c Shows the probability of detecting the encoded shift s for each of the 1024 oracle implementations versus the number of single-qubit gates (m). The shaded area represents the expected fidelity F2Q10F1QmFSPAM10 (where F2Q is the fidelity of two-qubit gates, F1Q is the fidelity of single-qubit gates, and FSPAM is the average SPAM fidelity) if all of our gates share the best measured fidelity or, alternatively, all share the worst fidelity. Additionally, the success probability is reduced by crosstalk onto adjacent ions from the individually addressing Raman beams. This error impacts the result of the HS oracles more than the BV oracles. The result of a shared average fidelity is plotted as a dashed line. The average probability of success is 35%, and 1017 of the 1024 oracle implementations correctly return the hidden shift as the maximal probability state.

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