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Tracking Photon Jumps with Repeated Quantum Non-Demolition Parity Measurements
L. Sun, A. Petrenko, Z. Leghtas, B. Vlastakis, G. Kirchmair, K. M. Sliwa, A. Narla, M. Hatridge, S. Shankar, J. Blumoff, L. Frunzio, M. Mirrahimi, M. H. Devoret, R. J. Schoelkopf
TL;DR
The paper tests whether repeated parity measurements can faithfully track photon jumps and error syndromes. It uses repeated parity monitoring with a quantum filter and finds faithful tracking, while cat-state decay bounds the achievable improvement.
Problem
The study asks whether the distribution of photon jumps under repeated monitoring agrees with expectation.
Method
The approach uses repeated parity monitoring and a quantum filter to analyze neighboring parity measurements while mitigating qubit decoherence.
Results
Repeated parity measurement can track error syndromes faithfully, with a filter transition time constant below 1 µs.
Takeaways & Limitations
The analysis projects a factor-of-3 improvement in encoded quantum-bit lifetime, from 12 µs to approximately 36 µs.
Takeaways & Limitations
Decay of the cat states bounds the improvement that parity tracking can achieve.
Abstract
from arXiv · showhide
Quantum error correction (QEC) is required for a practical quantum computer because of the fragile nature of quantum information. In QEC, information is redundantly stored in a large Hilbert space and one or more observables must be monitored to reveal the occurrence of an error, without disturbing the information encoded in an unknown quantum state. Such observables, typically multi-qubit parities such as <XXXX>, must correspond to a special symmetry property inherent to the encoding scheme. Measurements of these observables, or error syndromes, must also be performed in a quantum non-demolition (QND) way and faster than the rate at which errors occur. Previously, QND measurements of quantum jumps between energy eigenstates have been performed in systems such as trapped ions, electrons, cavity quantum electrodynamics (QED), nitrogen-vacancy (NV) centers, and superconducting qubits. So far, however, no fast and repeated monitoring of an error syndrome has been realized. Here, we track the quantum jumps of a possible error syndrome, the photon number parity of a microwave cavity, by mapping this property onto an ancilla qubit. This quantity is just the error syndrome required in a recently proposed scheme for a hardware-efficient protected quantum memory using Schrödinger cat states in a harmonic oscillator. We demonstrate the projective nature of this measurement onto a parity eigenspace by observing the collapse of a coherent state onto even or odd cat states. The measurement is fast compared to the cavity lifetime, has a high single-shot fidelity, and has a 99.8% probability per single measurement of leaving the parity unchanged. In combination with the deterministic encoding of quantum information in cat states realized earlier, our demonstrated QND parity tracking represents a significant step towards implementing an active system that extends the lifetime of a quantum bit.
A. Experiment setup, device parameters, and readout properties
The experiment combines superconducting cavities, a transmon ancilla, and amplified dispersive readout to prepare and monitor cavity photon states. The setup calibrates coherent-state control, characterizes readout imperfections, and measures a cavity lifetime of 55 µs.
- Readout properties: The qubit readout histogram is trimodal, distinguishing |g⟩, |e⟩, and |f⟩ states for digitization.The states are assigned readout values +1, −1, and 0, respectively.
- State preparation: The measured photon-number probabilities agree excellently with a Poisson distribution, indicating good control of the cavity coherent state.The calibration also infers a background photon population nth = 0.02.
- Cavity dynamics: A free parity-evolution fit gives a cavity lifetime of τ0 = 55 µs.The cavity lifetime is obtained from ensemble-averaged parity evolution of a coherent state.
- Measurement limitations: Parity-readout fidelity is mainly limited by qubit decoherence during the measurement.The analysis uses conditional probabilities for positive, negative, and failed readout outcomes.
B. Quantum filter and correlated data
The quantum filter estimates the cavity parity by propagating the photon density matrix through cavity evolution and updating it with each correlated parity measurement. This trajectory-based processing substantially improves agreement with the measured parity dynamics.
- Filter motivation: The quantum filter accounts for qubit decoherence, higher qubit excitations, and readout imperfections when estimating photon-state parity.Its output depends on the entire previous parity trajectory.
- Filter procedure: At each timestep, the filter first evolves the density matrix under cavity decoherence and then applies a Bayesian update from the new parity measurement.The updated estimate becomes the input for the next iteration.
- Parity inference: The filter uses qubit-readout correlations to update knowledge of whether the cavity occupies the even or odd parity manifold.The parity operator is defined as P = P_even − P_odd = e^(iπa†a).
- Readout failures: Zero-correlation outcomes are treated as failed parity measurements, and the filter assigns the density matrix predicted by free cavity evolution.This treatment assumes qubit excitation to |f⟩ is independent of cavity parity.
- Correlated-data analysis: The measured correlation dynamics are predicted from readout probabilities and the even- and odd-parity evolution, with excellent agreement in Fig. S7.The model also reproduces the initial offset caused by asymmetric even- and odd-parity readout fidelities.
- Filter performance: The long-time parity value is reduced mainly by qubit decoherence and imperfections in qubit readout, while filtering substantially improves the result.The large difference between filtered and unfiltered behavior is presented as evidence for filter effectiveness.
C. Statistics of photon jumps
Repeated parity measurements are used to infer photon-jump statistics, with a quantum filter and thresholding improving extraction from noisy trajectories. The measured jump distributions and parity dynamics agree with simulations, supporting faithful error-syndrome tracking.
- C. Statistics of photon jumps: A quantum filter estimates parity from the full measurement trajectory, while a Schmitt trigger digitizes the estimator and counts parity transitions as photon jumps.The trigger thresholds are ±0.9.
- C. Statistics of photon jumps: A transition time constant below 1 µs and a filter response time τ_f ∼2 µs determine how rapidly photon jumps can be resolved.The response time is defined for transitions between estimator thresholds ±0.9.
- C. Statistics of photon jumps: 4% of jumps overlap the filter response for n̄ = 1, increasing to 15% for n̄ = 4, limiting the ability to detect both closely spaced jumps.These probabilities use τ_tot = 49 µs.
- C. Statistics of photon jumps: 98%-2% even/odd mixing after 500 µs reflects the cavity’s steady state of n̄_th = 0.02 photons.The distribution is 98% vacuum and 2% one-photon occupation.
- C. Statistics of photon jumps: 100,000-trajectory Monte Carlo simulations agree well with the experimental jump histograms, demonstrating faithful tracking of repeated parity error syndromes.The simulation includes thermal excitation and finite filter response while neglecting neighboring jumps within τ_f.
D. Quantifying parity tracking performance
The protocol’s performance is governed by a trade-off between missed photon jumps and qubit T1 decay. With optimized timing and current parameters, the authors estimate a substantial improvement in encoded-information lifetime.
- D. Quantifying parity tracking performance: The two principal infidelity sources are missed photon jumps and qubit T1 decay during repeated parity tracking.Measuring too frequently increases qubit-decay errors, whereas measuring too infrequently risks missing photon jumps.
- D. Quantifying parity tracking performance: Qubit T1 decay can impart an arbitrary phase on cat states that is unrecoverable without an auxiliary correction protocol.This bounds the improvement achievable through the demonstrated parity-tracking protocol.
- D. Quantifying parity tracking performance: The effective decay rate is minimized when the two error rates are equal, defining the optimal balance between measurement cadence and waiting time.The measurement model includes τ_M, τ_W, and the qubit-decay dephasing probability P_C(T1).
- D. Quantifying parity tracking performance: τ_M could in principle be reduced to ∼400 ns, with π/χ_qs ∼275 ns and projective measurement lasting just over ∼100 ns.The demonstrated full parity measurement currently takes 1 µs.
- D. Quantifying parity tracking performance: A factor-of-3 lifetime enhancement, from 12 µs to ∼36 µs, is estimated for a quantum bit encoded in the resonator.The optimal waiting time between measurements is estimated as τ_W ∼4 µs.