Sub-One-in-a-Million Error in Trapped-Ion Single-Qubit Gates

Last Updated on June 15, 2025 by Sushanta Barman

In a groundbreaking leap for quantum computing, scientists at the University of Oxford have achieved the most precise single-qubit gate operations ever recorded. The team demonstrated error rates as low as \(1.5 \times 10^{-7}\) in a trapped-ion system, a level of precision nearly an order of magnitude better than previous records. This milestone, reported in Physical Review Letters on June 12, 2025, brings us closer to fault-tolerant quantum computers—machines capable of solving problems far beyond the reach of today’s best supercomputers.

The research, conducted at Oxford’s Clarendon Laboratory in collaboration with the University of Osaka, showcases unprecedented control over individual qubits encoded in the hyperfine energy levels of a single calcium-43 ion (\(^{43}Ca^{+}\)). The ion was trapped using a room-temperature microfabricated chip with integrated microwave (MW) control, demonstrating that ultra-precise quantum logic does not require cryogenics or magnetic shielding.

The achievement is significant because high-fidelity single-qubit gates are foundational for scalable quantum computation. Even though two-qubit gates typically draw more attention, many quantum algorithms rely heavily on the reliable operation of single-qubit gates. “Our fastest Clifford gate (4.4 \(\mu\)s) has an error of \(2.9(5) \times 10^{-7}\); this represents a \(20\times \) speedup relative to the previous lowest-error gate,” the team reported.

At the heart of the experiment lies an electronic qubit encoded in the “clock” transition between two hyperfine states in the ground level of the ion—transitions known for their resilience to magnetic field noise. These were manipulated using precisely tuned microwave pulses at 3.123 GHz, generated via a sophisticated drive chain and delivered via an on-chip resonator.

To measure and characterize the error rates, the team used a statistical method known as randomized benchmarking (RB). By applying thousands of pseudorandom sequences of Clifford gates and measuring the resulting qubit state, they estimated the error per gate with high statistical confidence. Their lowest measured error was \(1.5(4) \times 10^{-7}\), and their predictive error model estimated \(1.7(1) \times 10^{-7}\), showing excellent agreement.

The researchers identified and systematically minimized all known sources of gate error. These include:

• Decoherence, mainly from phase noise in the microwave chain, contributed \(\sim 0.64 \times 10^{-7}\).
• Leakage and bit-flip errors, due to residual laser or MW interactions, contributed \(\sim 0.62 \times 10^{-7}\).
• Fast amplitude noise and slow drifts, addressed by automated interleaved calibrations, were suppressed to near-negligible levels.
• Spectator state excitations and Zeeman shift miscalibrations were minimized using shaped pulses and advanced frequency stabilization methods.

One notable innovation was the continuous delivery of microwave power between gate operations, keeping the amplifier thermally stable and minimizing amplitude drift—a major source of systematic error.

These achievements matter because quantum computers require error rates below a certain threshold to implement error correction, a method that allows logical qubits to remain stable over long computations. These results—errors below one part per million—surpass the threshold needed for many fault-tolerant schemes, particularly for surface codes.

Moreover, the team’s methods are not confined to trapped ions. As they write, “The calibration and error characterization methods… are readily applicable to all types of physical qubits.” This makes their results relevant for improving superconducting, semiconductor, and photonic quantum platforms.

The research team plans to further reduce errors by addressing decoherence through hardware improvements like low-noise oscillators and better shielding. There is also interest in exploring non-Markovian errors (errors with memory effects), which standard benchmarking often misses.

In the long term, these advances pave the way for reliable quantum computers that could revolutionize materials science, secure communication, and drug discovery. “We have achieved a new state-of-the-art single-qubit gate error… and presented a breakdown of all known sources of error, which agrees well with the data,” the researchers conclude.

Read the full article: M. C. Smith et al., “Single-Qubit Gates with Errors at the \(10^{−7}\) Level,” Phys. Rev. Lett. 134, 230601 (2025).