arXiv subjects

Victor Kasatkin

Publications and source records attributed to Victor Kasatkin.

7 recordsLinked to original sources

arXiv2026

Quantum Error Correction and Dynamical Decoupling: Better Together or Apart?

Quantum error correction/detection (QEC/QED) and dynamical decoupling (DD) are tools for protecting quantum information. A natural goal is to combine them to outperform either approach alone. Such a benefit is not automatic: physical DD can conflict with encoded subspace, and QEC performance is governed by the errors that survive decoding, not just those DD suppresses. We analyze a hybrid memory cycle where DD is implemented logically (LDD) using normalizer elements of an $[[n,k,d]]$ stabilizer code, followed by a round of syndrome measurement and recovery (or, in the detection setting, postselection on a trivial syndrome). In an effective Pauli model with physical error probability $p$, LDD suppression factor $p_{DD}$, and recovery imperfection rate $p_{QEC}$ (or $p_{QED}$), we derive closed-form entanglement-fidelity expressions for QEC-only, QED-only, LDD-only, physical DD, and the hybrid LDD+QEC protocol. The formulas are expressed via a small set of code-dependent weight enumerator polynomials, making the role of the decoder and the LDD group explicit. For ideal recovery LDD+QEC outperforms QEC-only iff the conditional fraction of uncorrectable Pauli errors is larger in the LDD-suppressed sector than in the unsuppressed sector. In the low-noise regime, a sufficient design rule guaranteeing hybrid advantage is that LDD suppresses at least one minimum-weight uncorrectable Pauli error for the chosen recovery map. We show how stabilizer-equivalent choices of LDD generators can enforce this condition. We supplement our analysis with numerical results for the $[[7,1,3]]$ Steane code and a $[[13,1,3]]$ code, mapping regions of hybrid-protocol advantage in parameter space beyond the small-$p$ regime. Our work illustrates the need for co-design of the code, decoder, and logical decoupling group, and clarifies the conditions under which the hybrid LDD+QEC protocol is advantageous.

quant-ph↗

arXiv2026

Demonstration of Exponential Quantum Speedup with Constant-Depth Compiled Circuits for Simon's Problem

We demonstrate exponential algorithmic quantum speedup for a restricted-Hamming-weight version of Simon's problem, in which the hidden string $b$ is promised to satisfy $\text{HW}(b)\le w$ for a Hamming-weight cutoff $w$, on present-day superconducting quantum processors. We introduce a hardware-aware compilation strategy that reduces the quantum part of each Simon query circuit to constant depth. The resulting compiled circuits have $O(1)$ depth, require only linear nearest-neighbor connectivity, map directly onto common device layouts, and avoid additional routing and SWAP overhead. Implemented on IBM's $156$-qubit Boston and $120$-qubit Miami processors, these circuits achieve sufficient fidelity to exhibit algorithmic quantum speedup without error suppression. Using the number-of-queries-to-solution (NTS) metric, we observe exponential speedup over the classical lower-bound benchmark for all restricted-Hamming-weight cutoffs $w\ge 4$ on Boston and across low-to-intermediate Hamming-weight cutoffs on Miami; at higher Hamming-weight cutoffs on Miami, we still observe polynomial speedup. The same construction also enables unrestricted instances of Simon's problem, corresponding to $w=n$ for problem size $n$, over the finite problem-size ranges for which our NTS computation is feasible; in this regime, the observed scaling advantage is not limited to the restricted-Hamming-weight setting. These results show that careful hardware-aware compilation can make quantum speedup experimentally accessible for a canonical hidden-subgroup problem in the NISQ regime.

quant-ph↗

arXiv2025

Demonstration of High-Fidelity Entangled Logical Qubits using Transmons

Quantum error correction (QEC) codes are necessary to fault-tolerantly operate quantum computers. However, every such code is inherently limited by its inability to detect logical errors. Here, we propose and implement a method that leverages dynamical decoupling (DD) to drastically suppress logical errors. The key to achieving this is to use the logical operators of the QEC code as DD pulses, which we refer to as logical dynamical decoupling (LDD). The resulting hybrid QEC-LDD strategy is in principle capable of handling arbitrary weight errors. We test QEC-LDD using IBM transmon devices and the [[4,2,2]] code, demonstrating performance that significantly exceeds the capabilities of using either this code or DD in isolation. We present a method that allows for the detection of logical errors affecting logically encoded Bell states, which, in this case, arise primarily from crosstalk among physical qubits. Building on this, we experimentally demonstrate high-fidelity entangled logical qubits.

quant-ph↗

arXiv2024

Detecting Quantum and Classical Phase Transitions via Unsupervised Machine Learning of the Fisher Information Metric

The detection of quantum and classical phase transitions in the absence of an order parameter is possible using the Fisher information metric (FIM), also known as fidelity susceptibility. Here, we propose and investigate an unsupervised machine learning (ML) task: estimating the FIM given limited samples from a multivariate probability distribution of measurements made throughout the phase diagram. We utilize an unsupervised ML method called ClassiFIM (developed in a companion paper) to solve this task and demonstrate its empirical effectiveness in detecting both quantum and classical phase transitions using a variety of spin and fermionic models, for which we generate several publicly available datasets with accompanying ground-truth FIM. We find that ClassiFIM reliably detects both topological (e.g., XXZ chain) and dynamical (e.g., metal-insulator transition in Hubbard model) quantum phase transitions. We perform a detailed quantitative comparison with prior unsupervised ML methods for detecting quantum phase transitions. We demonstrate that ClassiFIM is competitive with these prior methods in terms of appropriate accuracy metrics while requiring significantly less resource-intensive training data compared to the original formulation of the prior methods. In particular, ClassiFIM only requires classical (single-basis) measurements. As part of our methodology development, we prove several theorems connecting the classical and quantum fidelity susceptibilities through equalities or bounds. We also significantly expand the existence conditions of the fidelity susceptibility, e.g., by relaxing standard differentiability conditions. These results may be of independent interest to the mathematical physics community.

quant-ph↗

arXiv2024

ClassiFIM: An Unsupervised Method To Detect Phase Transitions

Estimation of the Fisher Information Metric (FIM-estimation) is an important task that arises in unsupervised learning of phase transitions, a problem proposed by physicists. This work completes the definition of the task by defining rigorous evaluation metrics distMSE, distMSEPS, and distRE and introduces ClassiFIM, a novel machine learning method designed to solve the FIM-estimation task. Unlike existing methods for unsupervised learning of phase transitions, ClassiFIM directly estimates a well-defined quantity (the FIM), allowing it to be rigorously compared to any present and future other methods that estimate the same. ClassiFIM transforms a dataset for the FIM-estimation task into a dataset for an auxiliary binary classification task and involves selecting and training a model for the latter. We prove that the output of ClassiFIM approaches the exact FIM in the limit of infinite dataset size and under certain regularity conditions. We implement ClassiFIM on multiple datasets, including datasets describing classical and quantum phase transitions, and find that it achieves a good ground truth approximation with modest computational resources. Furthermore, we independently implement two alternative state-of-the-art methods for unsupervised estimation of phase transition locations on the same datasets and find that ClassiFIM predicts such locations at least as well as these other methods. To emphasize the generality of our method, we also propose and generate the MNIST-CNN dataset, which consists of the output of CNNs trained on MNIST for different hyperparameter choices. Using ClassiFIM on this dataset suggests there is a phase transition in the distribution of image-prediction pairs for CNNs trained on MNIST, demonstrating the broad scope of FIM-estimation beyond physics.

cs.LG↗

arXiv2023

Which differential equations correspond to the Lindblad equation?

The Lindblad master equation can always be transformed into a first-order linear ordinary differential equation (1ODE) for the coherence vector. We pose the inverse problem: given a finite-dimensional, non-homogeneous 1ODE, does a corresponding Lindblad equation exist? If so, what are the corresponding Hamiltonian and Lindblad operators? We provide a general solution to this problem, including a complete positivity test in terms of the parameters of the 1ODE. We also derive a host of properties relating the two representations (master equation and 1ODE), which are of independent interest.

quant-ph↗

arXiv2015

Fredholm modules and the Beilinson-Bloch regulator

We prove an operator-theoretic reconstruction of the Beilinson-Bloch regulator for compact Riemann surfaces, using loop operators and the Connes-Karoubi character for Fredholm modules. The proof includes a new computation of the Connes-Karoubi character for Steinberg symbols of the circle, which relies on the Helton-Howe determinant theory, but not on the Carey-Pincus theory of joint torsion.

math.OA↗