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1. Modulation-agnostic single-shot estimation of quantum measurement confidence

   https://doi.org/10.1103/PhysRevA.108.052203  

   Jabir, M. V.; Annafianto, N. Fajar; Battou, A.; Burenkov, I. A.; Polyakov, Sergey V. (November 2023, Physical Review A)

   n/a (Ed.)

   We experimentally explore single-shot state identification using long alphabets of states and employing different modulation schemes. We use time-resolved quantum measurement and Bayesian inference to identify the input state and demonstrate the advantage of this single-shot measurement over classical state identification. For each single-shot measurement, we estimate the confidence of state identification based on the quantum measurement and demonstrate the physical significance of confidence estimates. Particularly, we show that a set of confidence values correctly represents the probabilities of successful state identification for a given experimental outcome. We investigate the alphabets of coherent states with different modulations and show that confidence estimates yield the reliability of each act of measurement independently of the modulation used. 

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2. The unitary dependence theory for characterizing quantum circuits and states

   https://doi.org/10.1038/s42005-023-01188-y  

   Hu, Zixuan; Kais, Sabre (April 2023, Communications Physics)

   Abstract Most existing quantum algorithms are discovered accidentally or adapted from classical algorithms, and there is the need for a systematic theory to understand and design quantum circuits. Here we develop a unitary dependence theory to characterize the behaviors of quantum circuits and states in terms of how quantum gates manipulate qubits and determine their measurement probabilities. Compared to the conventional entanglement description of quantum circuits and states, the unitary dependence picture offers more practical information on the measurement and manipulation of qubits, easier generalization to many-qubit systems, and better robustness upon partitioning of the system. The unitary dependence theory can be applied to systematically understand existing quantum circuits and design new quantum algorithms. 

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3. Quantum Measurement Classification Using Statistical Learning

   https://doi.org/10.1145/3644823  

   Utt, Zachery; Volya, Daniel; Mishra, Prabhat (June 2024, ACM Transactions on Quantum Computing)

   Interpreting the results of a quantum computer can pose a significant challenge due to inherent noise in these mesoscopic quantum systems. Quantum measurement, a critical component of quantum computing, involves determining the probabilities linked with quantum states post-multiple circuit computations based on quantum readout values provided by hardware. While there are promising classification-based solutions, they can either misclassify or necessitate excessive measurements, thereby proving to be costly. This article puts forth an efficient method to discern the quantum state by analyzing the probability distributions of data post-measurement. Specifically, we employ cumulative distribution functions to juxtapose the measured distribution of a sample against the distributions of basis states. The efficacy of our approach is demonstrated through experimental results on a superconducting transmon qubit architecture, which shows a substantial decrease (88%) in single qubit readout error compared to state-of-the-art measurement techniques. Moreover, we report additional error reduction (12%) compared to state-of-the-art measurement techniques when our technique is applied to enhance existing multi-qubit classification techniques. We also demonstrate the applicability of our proposed method for higher dimensional quantum systems, including classification of single qutrits as well as multiple qutrits. 

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4. Maximum information measurement for qubit states

   https://doi.org/10.1038/s41598-024-62446-9  

   Varga, Árpád; Adam, Peter; Bergou, János A (December 2024, Scientific Reports)

   Abstract We determine the optimal measurement that maximizes the average information gain about the state of a qubit system. The qubit is prepared in one of two known states with known prior probabilities. To treat the problem analytically we employ the formalism developed for the maximum confidence quantum state discrimination strategy and obtain the POVM which optimizes the information gain for the entire parameter space of the system. We show that the optimal measurement coincides exactly with the minimum-error quantum measurement only for two pure states, or when the two states have the same Bloch radius or they are on the same diagonal of the Bloch disk. 

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5. On Fault Tolerant Single-Shot Logical State Preparation and Robust Long-Range Entanglement

   https://doi.org/10.4230/lipics.itcs.2025.16  

   Bergamaschi, Thiago; Liu, Yunchao (January 2025, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Meka, Raghu (Ed.)

   Preparing encoded logical states is the first step in a fault-tolerant quantum computation. Standard approaches based on concatenation or repeated measurement incur a significant time overhead. The Raussendorf-Bravyi-Harrington cluster state [Raussendorf et al., 2005] offers an alternative: a single-shot preparation of encoded states of the surface code, by means of a constant depth quantum circuit, followed by a single round of measurement and classical feedforward [Bravyi et al., 2020]. In this work we generalize this approach and prove that single-shot logical state preparation can be achieved for arbitrary quantum LDPC codes. Our proof relies on a minimum-weight decoder and is based on a generalization of Gottesman’s clustering-of-errors argument [Gottesman, 2014]. As an application, we also prove single-shot preparation of the encoded GHZ state in arbitrary quantum LDPC codes. This shows that adaptive noisy constant depth quantum circuits are capable of generating generic robust long-range entanglement. 

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