Tracking Photon Jumps with Repeated Quantum Non-Demolition Parity Measurements (1311.2534v1)

Abstract: 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 Schr\"{o}dinger 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.

• The paper demonstrates real-time photon jump tracking using repeated, high-fidelity (99.8%) quantum non-demolition parity measurements in a circuit QED system.
• It employs a three-dimensional cQED architecture and combines Ramsey-type sequences with dispersive readout to map photon parity onto a transmon qubit, enabling high-fidelity cat state confirmation via Wigner tomography.
• The work advances quantum error correction by accurately detecting 85% of photon jumps, thereby improving error syndrome identification and paving the way for fault-tolerant quantum memory designs.

Tracking Photon Jumps with Repeated Quantum Non-Demolition Parity Measurements

The paper, co-authored by researchers from Yale University and INRIA Paris-Rocquencourt, presents an advanced quantum measurement methodology that tracks photon jumps via quantum non-demolition (QND) parity measurements in a circuit quantum electrodynamics (cQED) framework. This work tackles a key challenge in quantum error correction (QEC): accurately identifying error syndromes without disturbing the underlying quantum information.

Summary of Experimental Setup and Methodology

The authors utilize a three-dimensional cQED architecture consisting of a superconducting transmon qubit coupled to dual waveguide cavities. The primary objective is to track the photon number parity in a low-frequency storage cavity using the transmon qubit and a high-frequency cavity for fast readout. A controlled-phase gate is realized via strong dispersive coupling, enabling the mapping of the cavity photon parity onto the qubit state.

During the experiment, photon parity is repeatedly measured by combining Ramsey-type sequences with dispersive readouts. Remarkably, the parity measurement is achieved with a 99.8% QND fidelity, a critical metric indicating minimal disturbance to the quantum system during measurement. The parity measurement collapses a coherent superposition into even or odd Schrödinger cat states, confirmed by Wigner tomography that reveals high-fidelity cat states with interference patterns—a haLLMark of quantum behavior.

Numerical Results and Analysis

The implementation achieves a rapid sequence of parity measurements at intervals significantly shorter than the cavity's photon lifetime, demonstrating the ability to monitor photon jumps in real time. Analysis of single-shot traces highlights variability in jump statistics, with some traces exhibiting multiple jump events within the measurement window. A quantum filter is applied to mitigate decoherence effects, improving the reliability of detecting photon jumps.

Crucially, the fidelity of capturing photon jump statistics suggests that 85% of jumps were accurately detected for states with an average photon number of $\bar{n}=4$. Furthermore, the ensemble averaged parity dynamics corroborate the projective nature of individual measurements, exhibiting distinct extremal values reflective of the even or odd photon-number eigenspace.

Implications for Quantum Error Correction and Future Directions

The implications of this work for QEC are substantial. The demonstrated QND parity measurements offer a viable path toward indirect monitoring of photon loss errors, a persistent issue impeding quantum memory lifetimes. By projecting quantum states into degenerate subspaces, the paper aligns with methodologies necessary for fault-tolerant quantum computing architectures.

Future directions will likely involve reducing the probability of missed photon jumps, which the authors propose might be achieved with extended cavity lifetimes and optimized measurement strategies. Additionally, addressing ancilla-induced error pathways remains vital to fully realizing a fault-tolerant and error-corrected quantum memory.

In conclusion, this paper delivers a significant advancement in the measurement techniques crucial for quantum information processing. The successful tracking of photon number parity signals a leap forward in the pursuit of practical QEC, holding profound implications for the development of robust quantum computational systems.