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A basic challenge in experimental physics is the extraction of information related to variables that are not directly measured. The challenge is particularly severe in quantum systems where one may be interested in correlations of operators…
This work presents the first finite-time analysis for the last-iterate convergence of average-reward $Q$-learning with an asynchronous implementation. A key feature of the algorithm we study is the use of adaptive stepsizes, which serve as…
A genie-aided decoder for finite dimensional lattice codes is considered. The decoder may exhaustively search through all possible scaling factors $\alpha \in \mathbb{R}$. We show that this decoder can achieve lower word error rate (WER)…
Quantum error correction (QEC) is essential for reliable quantum information processing. Targeting a particular error channel, both the encoding and the recovery channel can be optimized through a biconvex optimization to give a…
Quantum State Tomography is the task of determining an unknown quantum state by making measurements on identical copies of the state. Current algorithms are costly both on the experimental front -- requiring vast numbers of measurements --…
Quantum error correction (QEC) plays an essential role in fault-tolerantly realizing quantum algorithms of practical interest. Among different approaches to QEC, encoding logical quantum information in harmonic oscillator modes has been…
The mean squared error and regularized versions of it are standard loss functions in supervised machine learning. However, calculating these losses for large data sets can be computationally demanding. Modifying an approach of J. Dick and…
Quantum Phase Estimation (QPE) is a cornerstone algorithm for fault-tolerant quantum computation, especially for electronic structure calculations of chemical systems. To accommodate the diverse characteristics of quantum chemical systems,…
In this study, we employed Fourier-based quantum phase estimation (QPE) to calculate X-ray absorption spectroscopy (XAS) spectra. The primary focus of this study is the calculation of the XAS spectra of transition metal $L_{2,3}$-edges,…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
We show polynomial-time quantum algorithms for the following problems: (*) Short integer solution (SIS) problem under the infinity norm, where the public matrix is very wide, the modulus is a polynomially large prime, and the bound of…
Learning problems involving quantum data are natural candidates for demonstrating an advantage in quantum machine learning. Recent results indicate that, for certain tasks and under noiseless conditions, coherent processing of quantum data…
Construction of a fault-tolerant quantum computer remains a challenging problem due to unavoidable noise in quantum states and the fragility of quantum entanglement. However, most of the error-correcting codes increases the complexity of…
Large language models often fail on multi-step reasoning due to fixed reasoning strategies that ignore problem specific difficulty. We introduce CARD (Complexity Agnostic Recursive Decomposition), a framework that predicts problem…
We study phase structure and critical point of finite-temperature QCD in the heavy-quark region applying the hopping parameter expansion (HPE). We first study finite-size scaling on the critical point on $N_t=4$ lattices with large spatial…
We develop a simple and general post-selection strategy for high-rate quantum codes that is transferrable across decoders. After an initial baseline run, the decoder is re-run once per logical observable, and forced in these latter runs to…
We present a procedure for reconstructing the decision function of an artificial neural network as a simple function of the input, provided the decision function is sufficiently symmetric. In this case one can easily deduce the quantity by…
Postselected quantum computation is distinguished from regular quantum computation by accepting the output only if measurement outcomes satisfy predetermined conditions. The output must be accepted with nonzero probability. Methods for…
In the emergent realm of quantum computing, the Variational Quantum Eigensolver (VQE) stands out as a promising algorithm for solving complex quantum problems, especially in the noisy intermediate-scale quantum (NISQ) era. However, the…
We numerically investigate quantum circuit elementary-gate level instantiations of the standard Quantum Phase Estimation (QPE) algorithm for the task of computing the ground-state energy of a quantum magnet; the disordered fully-connected…