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Repeated multi-qubit readout and feedback with a mixed-species trapped-ion register
Vlad Negnevitsky, Matteo Marinelli, Karan Mehta, Hsiang-Yu Lo, Christa Flühmann, Jonathan P. Home
TL;DR
The study examines how gate and readout imperfections shape repeated parity measurement and feedback. It characterizes stabilizer correlations and models the sequence; correlations under nominally commuting corrections were about 10% lower than without feedback, and the model reproduced feedback-event correlations reasonably well.
Problem
The study examines how gate and readout imperfections shape correlations during repeated parity measurement and feedback.
Source: Methods · p. 7Method
The authors characterize Bell-state correlations and simulate repeated parity measurements using depolarization and leakage channels.
Source: Methods · p. 7Results
Correlations were ≈10% lower with nominally commuting corrections than without feedback, while simulations reasonably reproduced observed feedback-event correlations.
Source: Methods · pp. 7–8Takeaways & Limitations
The simulation accounts for observed feedback-event correlations and supports the arguments made about those correlations.
Source: Methods · p. 8
Abstract
from arXiv · showhide
Quantum error correction will be essential for realizing the full potential of large-scale quantum information processing devices. Fundamental to its experimental realization is the repetitive detection of errors via projective measurements of quantum correlations among qubits, and correction using conditional feedback. Performing these tasks repeatedly requires a system in which measurement and feedback decision times are short compared to qubit coherence times, where the measurement reproduces faithfully the desired projection, and for which the measurement process has no detrimental effect on the ability to perform further operations. Here we demonstrate up to 50 sequential measurements of correlations between two beryllium-ion qubits using a calcium ion ancilla, and implement feedback which allows us to stabilize two-qubit subspaces as well as Bell states. Multi-qubit mixed-species gates are used to transfer information from qubits to the ancilla, enabling quantum state detection with negligible crosstalk to the stored qubits. Heating of the ion motion during detection is mitigated using sympathetic recooling. A key element of the experimental system is a powerful classical control system, which features flexible in-sequence processing to implement feedback control. The methods employed here provide a number of essential ingredients for scaling trapped-ion quantum computing, and provide new opportunities for quantum state control and entanglement-enhanced quantum metrology.
Methods
The methods combine a mixed-species ion register, repeated parity readout and feedback, and measurements and simulations to characterize the resulting correlations. They also specify how qubit and motional coherence, pulse phases, and state-detection fidelity are managed or assessed.
State detection
- Bright and dark fluorescence distributions have means of 25 and 0.2 counts, respectively, yielding state-detection error around 0.5% per ion.Impure polarization causes optical pumping and substantial departures from Poissonian distributions.Source: Methods · p. 5
Ion register and motional modes
- A three-ion Be+-Ca+-Be+ chain uses its 1.56 MHz in-phase axial mode for MS gates; field-insensitive Be+ qubits have coherence times over 1 second.The ions are cooled before each run, including Ca+ sideband cooling on the lowest-frequency mode; automatic recrystallization can keep a three-ion crystal trapped for 4–6 hours.Source: Methods · pp. 5–6, Figure 4 · p. 5
Pulse and phase control
- Ramsey sequences with the 90 beam pair cancel sensitivity to slow path-length phase drift, while readout-block time references and dynamic phase updates compensate pulse-phase shifts.Stark shifts from USZ, USX, CX, and CZ are compensated by adjusting future gate phases in embedded software.Source: Methods · p. 6
Parity-measurement fidelity
- FND compares Ca+ readout probabilities with input Be+ parity probabilities, whereas FQSP measures the conditional probability that the post-measurement Be+ subspace matches the Ca+ outcome.Both measures are averaged over input-state preparation phases.Source: Methods · pp. 6–7
Bell-state fidelity estimation
- Beryllium Bell-state fidelity is estimated from ZZ, XX, and YY correlations, with CZ preprocessing used for Ψ states before the XX and YY analyses.The feedback-dependent phases of analysis pulses must also be updated.Source: Methods · p. 7
Bell-state stabilization correlations
- Correlations were ≈10% lower with nominally commuting CX/CZ corrections than without feedback, despite calibration experiments expecting 1% gate errors.The comparison concerns successive stabilizer measurements; ideally, the corresponding commuting correction leaves their correlation at 1.Source: Methods · p. 7
- With readout errors dominating, SZ correlations following CZ corrections were 30–50% anti-correlated, versus perfect anti-correlation in the ideal feedback case.In the steady state, readout errors can lead to correction of an already uncorrupted subspace, giving 50% anti-correlation.Source: Methods · p. 7
Simulation and modelling
- Monte Carlo density-matrix simulations combine ideal parity-mapping unitaries with depolarization, calcium projection, and probabilistic leakage, but leakage alone does not reproduce the observed dynamics.Adding a gradual 3–5% parity-detection bias produces a good match across datasets, and the simulation reasonably reproduces observed feedback-event correlations; the noise model is acknowledged as simplified.Source: Methods · pp. 7–8