arXiv subjects

Kausthubh Chandramouli

Publications and source records attributed to Kausthubh Chandramouli.

5 recordsLinked to original sources

arXiv2026

Reliable Sample-Level Quantum Error Mitigation via Dominance-Aware Clustering

Many quantum algorithms for classically difficult optimization tasks must return high-quality bitstrings from finitely many circuit executions, whereas most quantum error-mitigation methods target expectation values. We study sample-level recovery when measured probability mass is distributed around multiple latent bitstrings, called centers. Each component of the measured probability mass is called a source and we assume that each center is associated with one source. We identify dominance-at every coordinate, more than half of a retained region's probability mass comes from one source and agrees with its center-as a sufficient condition under which majority voting recovers that center with exponentially decreasing error probability. We show that nearest-center assignment, as used in clustering algorithms such as the $k$-modes algorithm, can fail to produce dominated regions even when the true centers are known. This failure motivates responsibility thresholding and a local dominance screen, whose combination we call dominance-aware (DA) refinement. Synthetic and simulated MaxCut-QAOA experiments show that DA refinement favors precision, while $k$-modes with DA refinement improves overall center recovery. All procedures are classical post-processing and require no additional quantum-circuit executions.

quant-ph↗

arXiv2026

A Provable Oracle-Free Quantum Algorithm for Nonlinear Dynamics on Hybrid Oscillator-Qubit Processors

We develop a hybrid qubit--qumode algorithm for nonlinear ordinary differential equations of the form $\dot{\mathbf{x}}=\mathbf{f}(\mathbf{x})$ with drift of polynomial degree~$L$. Following the Fokker--Planck route of Tennie and Magri, the algorithm propagates the state density and returns the deterministic trajectory as the peak of that density in the small-noise limit. The discretised generator is carried into a parametrised family of Schrödinger equations by the warped-phase transformation of Jin, Liu, and Yu, and the Fourier-mode parameter of that family is placed on a single continuous-variable qumode. Our central structural result is that the Hermitian parts $H_{1}$ and $H_{2}$ of the discretised generator admit a bipartite Pauli decomposition that sorts the non-zero Pauli strings into $\mathcal{O}(\log N)$ mutually commuting families and factorises each family into a diagonal of degree at most $L$ tensored with a fixed rank-two bond operator. The factorisation renders each family exponential an exact product of $\mathcal{O}(n^{L})$ monomial-controlled momentum displacements, with no intra-family Trotter error. On a $d$-dimensional grid of $N=2^{n}$ points per axis the circuit costs $\mathcal{O}(d^{L+1}n^{L+2})$ gates per Trotter step. No sparse-access oracle and no block encoding is invoked: every gate is fixed in closed form by the polynomial coefficients of the drift. We also prove a bound on the numerical abscissa $λ_{\max}(H_{1})$ that fixes the recovery domain of the warped-phase transform and the post-selection cost. A classical simulation on two nonlinear benchmarks confirms the structural theorems, the shifted recovery, and the accuracy-per-resource advantage of the continuous-variable coupling over a discretised mode register.

quant-ph↗

arXiv2026

Approximate Message Passing for Quantum State Tomography

Quantum state tomography (QST) is an indispensable tool for characterizing many-body quantum systems. However, due to the exponential scaling of the cost of the protocol with system size, many approaches have been developed for quantum states with specific structure, such as low-rank states. In this paper, we show how approximate message passing (AMP), an algorithmic framework for sparse signal recovery, can be used to perform low-rank QST. AMP provides asymptotically optimal performance guarantees for large sparse recovery problems, which suggests its utility for QST. We discuss the design challenges that come with applying AMP to QST, and show that by properly designing the AMP algorithm, we can reduce the reconstruction error by over an order of magnitude compared to existing approaches to low-rank QST. We also performed tomographic experiments on IBM Kingston and considered the effect of device noise on the reliability of the predicted fidelity of state preparation. Our work advances the state of low-rank QST and may be applicable to other quantum tomography protocols.

quant-ph↗

arXiv2025

Statistical Signal Processing for Quantum Error Mitigation

In the noisy intermediate-scale quantum (NISQ) era, quantum error mitigation (QEM) is essential for producing reliable outputs from quantum circuits. We present a statistical signal processing approach to QEM that estimates the most likely noiseless outputs from noisy quantum measurements. Our model assumes that circuit depth is sufficient for depolarizing noise, producing corrupted observations that resemble a uniform distribution alongside classical bit-flip errors from readout. Our method consists of two steps: a filtering stage that discards uninformative depolarizing noise and an expectation-maximization (EM) algorithm that computes a maximum likelihood (ML) estimate over the remaining data. We demonstrate the effectiveness of this approach on small-qubit systems using IBM circuit simulations in Qiskit and compare its performance to contemporary statistical QEM techniques. We also show that our method scales to larger qubit counts using synthetically generated data consistent with our noise model. These results suggest that principled statistical methods can offer scalable and interpretable solutions for quantum error mitigation in realistic NISQ settings.

quant-ph↗

arXiv2022

Automatic Transcription of Drum Strokes in Carnatic Music

The mridangam is a double-headed percussion instrument that plays a key role in Carnatic music concerts. This paper presents a novel automatic transcription algorithm to classify the strokes played on the mridangam. Onset detection is first performed to segment the audio signal into individual strokes, and feature vectors consisting of the DFT magnitude spectrum of the segmented signal are generated. A multi-layer feedforward neural network is trained using the feature vectors as inputs and the manual transcriptions as targets. Since the mridangam is a tonal instrument tuned to a given tonic, tonic invariance is an important feature of the classifier. Tonic invariance is achieved by augmenting the dataset with pitch-shifted copies of the audio. This algorithm consistently yields over 83% accuracy on a held-out test dataset.

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