[Paper Review] Diabatic ramping spectroscopy of many-body excited states for trapped-ion quantum simulators

Bryce Yoshimura, Wesley C. Campbell+1 more|arXiv (Cornell University)|Feb 28, 2014

Quantum Information and Cryptography1 references3 citations

TL;DR

This paper proposes diabatic ramping spectroscopy to extract low-lying energy spectra in trapped-ion quantum simulators by intentionally creating excitations via non-adiabatic ramping of the transverse field, followed by time-domain measurement and compressive sensing to reconstruct the frequency spectrum. The method enables efficient, low-data acquisition of many-body excited states, reducing experimental time and making spectroscopy feasible with current technology despite noise and decoherence.

ABSTRACT

Due to the experimental time constraints of state of the art quantum simulations with trapped ions, the direct preparation of the ground state by adiabatically ramping the field of a transverse field Ising model becomes more and more difficult as the number of particles increase. We propose a spectroscopy protocol that intentionally creates excitations through diabatic ramping of the transverse field and measures a low-noise observable as a function of time for a constant field to reveal the structure of the coherent dynamics of the resulting many-body states. To simulate the experimental data, noise from counting statistics and decoherence error are added. Compressive sensing is then applied to Fourier transform the simulated data into the frequency domain and extract the the low-lying energy excitation spectrum. By using compressive sensing, the amount of data in time needed to extract this energy spectrum is sharply reduced making such experiments feasible with current technology.

Motivation & Objective

• To address the challenge of preparing ground states in large trapped-ion quantum simulators due to decreasing energy gaps and finite coherence times.
• To develop a spectroscopic protocol that bypasses adiabatic state preparation by utilizing diabatic excitations as a probe of the many-body spectrum.
• To enable experimental feasibility of measuring low-lying energy spectra with minimal time-domain data using compressive sensing.
• To quantify the robustness of the method against counting statistics and decoherence errors in simulated experimental conditions.

Proposed method

• The protocol applies a diabatic ramp to the transverse magnetic field in a trapped-ion system, creating a coherent superposition of ground and excited states.
• After the ramp, the transverse field is held constant, and a low-noise observable (e.g., total spin) is measured as a function of time.
• The time-domain signal is processed using compressive sensing to reconstruct the frequency spectrum with significantly fewer data points than traditional Fourier transforms.
• The method is tested on the infinite-range transverse field Ising model, equivalent to the Lipkin-Meshkov-Glick (LMG) model, using numerical simulations with added noise.
• Noise from counting statistics and decoherence (with fixed decoherence time τdJ0 = 25) is simulated across 100 realizations to assess robustness.
• The compressive sensing algorithm identifies delta function peaks in the frequency domain, which are compared to exact adiabatic energy differences to validate spectral extraction.

Experimental results

Research questions

• RQ1 Can diabatic ramping spectroscopy extract the low-lying energy spectrum of many-body states in trapped-ion quantum simulators with reduced data requirements?
• RQ2 How does compressive sensing improve the efficiency of spectral reconstruction in the presence of experimental noise and decoherence?
• RQ3 What is the fidelity of spectral peak identification when both counting statistics and decoherence errors are present?
• RQ4 How does the spectral resolution and accuracy vary with transverse magnetic field strength, particularly near the critical point?
• RQ5 Can spurious peaks introduced by noise be reliably distinguished from true energy level transitions?

Key findings

• Compressive sensing successfully extracted the two lowest-lying energy states with average frequency deviations of less than 0.0033 and 0.0077 from exact adiabatic values at different transverse field strengths.
• The standard deviation of extracted peaks across 100 noise-realizations was on the order of 0.001, indicating high precision and reproducibility.
• Spurious delta function peaks appeared primarily at high frequencies and were negligible in number, while low-frequency spurious peaks occurred consistently at three field strengths and were excluded from statistical analysis.
• Spectral extraction performance degraded at low transverse fields due to reduced excitation probability relative to noise, limiting resolution.
• At high transverse fields, low excitation probability led to spurious peaks not associated with physical energy levels, indicating a trade-off in field strength selection.
• The method enables feasible spectroscopy with current experimental setups by sharply reducing the required number of time steps through compressive sensing.