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Quantum state discrimination of three-level systems via a nonlinear protocol

P. V. Pyshkin, Orsolya Kálmán, T. Kiss

Published Jun 15, 2018• 0 citations
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A cavity quantum electrodynamical scenario is proposed for implementing a Schr\"odinger microscope capable of amplifying differences between nonorthogonal atomic quantum states. The scheme involves an ensemble of identically prepared two-level atoms interacting pairwise with a single mode of the radiation field as described by the Tavis-Cummings model. By repeated measurements of the cavity field and of one atom within each pair a measurement-induced nonlinear quantum transformation of the relevant atomic states can be realized. The intricate dynamical properties of this nonlinear quantum transformation, which exhibits measurement-induced chaos, allow approximate orthogonalization of atomic states by purification after a few iterations of the protocol and thus the application of the scheme for quantum state discrimination.
We explore the effects of driving a cavity at a large photon number in a circuit-QED experiment where the “matterlike” part corresponds to a unique Andreev level in a superconducting weak link. The three many-body states of the weak link, corresponding to the occupation of the Andreev level by 0, 1, or 2 quasiparticles, lead to different cavity frequency shifts. We show how the nonlinearity inherited by the cavity from its coupling to the weak link affects the state discrimination and the photon number calibration. Both effects require treating the evolution of the driven system beyond the dispersive limit. In addition, we observe how transition rates between the circuit states (quantum and parity jumps) are affected by the microwave power, and compare the measurements with a theory accounting for the “dressing” of the Andreev states by the cavity. Published by the American Physical Society 2024
Accurate and timely quantum state discrimination is critical for quantum computing, particularly in protocols requiring mid-circuit measurement (MCM) and conditional feed-forward. While classical state readout in transistors is near-instantaneous, identifying the state of superconducting qubits remains latency-limited and error-prone. Existing approaches rely on post-processing measurement data transferred to host computers, introducing delays on the order of milliseconds -- vastly exceeding the coherence time of quantum states, which typically last only hundreds of microseconds. To bridge this latency gap, we present an in-situ machine learning (ML) inference engine implemented on a field-programmable gate array (FPGA), enabling real-time quantum state discrimination within 40 ns. Our system supports both two-level (qubit) and three-level (qutrit) systems and performs inference directly on digitized readout signals without host-side intervention. This low-latency operation facilitates mid-circuit measurements, where qubit states are measured and reused within a single quantum circuit, and enables real-time conditional operations essential for quantum error correction. Crucially, fast and accurate mid-circuit readout is a prerequisite for implementing practical fault-tolerant error correction, where errors must be detected and corrected within a single circuit cycle to preserve logical state coherence. We validate our system using superconducting transmon devices, demonstrating robust discrimination fidelity across multiple qubit and qutrit channels. Further, we implement a conditional qutrit logic protocol based on FPGA-resident state classification, highlighting the practical benefits of our approach for NISQ-era quantum algorithms and scalable fault-tolerant architectures.