Laser phase noise and trapped-ion gate errors

Short answer: Laser noise is one of the error sources for trapped-ion gates. A 2023 Physical Review A paper reports that the effect of fast noise on single- and two-qubit gates can be estimated from one number, the noise power spectral density at the qubit response frequency. A recent preprint calculates how correlated laser noise affects Mølmer-Sørensen gates in long ion chains, and a 2005 paper suggests ways to suppress phase decoherence. These are analyses and small-scale measurements.

How fast noise affects gate fidelity

Fast noise, defined as noise at frequencies much higher than the local oscillator linewidth, impacts the fidelity of one- and two-qubit gates in trapped-ion systems. A necessary condition for coherent quantum evolution is a highly stable local oscillator driving these transitions. When this stability is compromised by fast noise, the ability to couple single- or two-qubit levels in a precise manner is reduced.

The 2023 paper analyses and measures the effect of fast noise on single-qubit operations, including resonant rotations and off-resonant sideband transitions. The authors further analyse numerically the effect of fast phase noise on the Mølmer-Sørensen two-qubit gate. The authors report a unified and simple way to estimate the performance of these operations. This estimation relies on a single parameter given by the noise power spectral density at the qubit response frequency. While the analysis focuses on phase noise and trapped-ion systems, it is relevant for other sources of fast noise and for other qubit systems where spinlike qubits are coupled by a common bosonic field.

Correlated noise in long ion chains

Correlated laser frequency noise impacts Mølmer-Sørensen gates in qubit registers based on trapped-ion chains. Using perturbation theory, the preprint's authors calculate gate fidelities in the presence of noise with arbitrary power spectral density for different chain lengths and ion positions. This approach accounts for the simultaneous excitation of multiple phonon modes during gate operation.

The impact of medium-frequency laser noise depends considerably on the positions of the ions in the chain. In contrast, low-frequency noise has a similar effect for different chain lengths and ion positions. Laser frequency noise is known as one of the dominant sources of Mølmer-Sørensen gate error. The noise spectrum of typical laser sources used for trapped-ion quantum state manipulation can vary between setups and contain contributions on the timescale of the inverse gate duration. Consequently, a considerable effect of correlated laser noise on the Mølmer-Sørensen gate could be expected. The gate infidelity can be expressed using the noise power spectral density and a sensitivity function that does not depend on the noise properties and can be inferred from the ideal gate dynamics.

Suppressing phase decoherence

Trapped ion quantum gates are highly susceptible to noise on the applied laser fields in addition to ambient electric and magnetic fields. In most cases, the relevant phases of the laser fields for quantum gates can be sufficiently stable during the evolution of a given gate, with gate speeds typically faster than about 100 microseconds. However, for extended operations involving many successive gates, it will be difficult to maintain optical phase stability over the duration of the quantum computation.

The 2005 paper examines the sensitivity of motional gate schemes to phase fluctuations introduced through noisy external control fields and suggested techniques for suppressing the resulting phase decoherence. Certain gate schemes can be simultaneously insensitive to background magnetic fields, making them quite robust for long-term computations. Special arrangements of the classical driving fields can suppress slow phase decoherence from laser noise and external magnetic field noise. These methods also apply to suppressing long-term phase noise in recent “fast” gate schemes that rely on impulsive spin-dependent optical forces.

Practical implications for hardware design

The 2023 authors say the unified estimate lets one evaluate several operations through a single parameter. They say the analysis, while focused on phase noise and trapped ions, is relevant for other sources of fast noise and for other qubit systems in which spinlike qubits are coupled by a common bosonic field. These are analytical and numerical results, not a hardware demonstration of improved gates.

The sensitivity functions calculated for Mølmer-Sørensen gates for typical experimental parameters provide a basis for assessing noise impacts. Because the sensitivity function does not depend on the specific noise properties, it can be inferred from ideal gate dynamics. This separation allows for the analysis of gate dynamics in the presence of noise with arbitrary power spectral density. The preprint presents this as relevant to long ion chains, where it says laser frequency noise is one of the dominant sources of gate error.

FAQ

What is the primary metric for estimating fast noise impact?

The performance of single- and two-qubit operations can be estimated through a single parameter. This parameter is given by the noise power spectral density at the qubit response frequency. It provides a unified way to assess fidelity degradation across different gate types.

How does ion position affect noise sensitivity?

The impact of medium-frequency laser noise depends considerably on the positions of the ions in the chain. Low-frequency noise, however, has a similar effect for different chain lengths and ion positions. This distinction is critical for analyzing correlated noise in long ion chains.

Can gate schemes suppress phase decoherence?

Yes, certain gate schemes can be simultaneously insensitive to background magnetic fields and slow phase decoherence. Special arrangements of classical driving fields suppress decoherence from laser noise and external magnetic field noise. These techniques make gates more robust for long-term computations.

What is the role of the sensitivity function?

The sensitivity function allows gate infidelity to be expressed in terms of the noise power spectral density. It does not depend on the noise properties and can be inferred from the ideal gate dynamics. This enables the analysis of noise with arbitrary power spectral density.

Is fast noise limited to trapped ions?

No, while the analysis focuses on trapped-ion systems, it is relevant for other sources of fast noise. It also applies to other qubit systems in which spinlike qubits are coupled by a common bosonic field. The underlying physics of phase noise impact is broader than the specific hardware platform.