arXiv subjects

Zohar Schwartzman-Nowik

Publications and source records attributed to Zohar Schwartzman-Nowik.

8 recordsLinked to original sources

arXiv2026

Oracle problems as communication tasks and optimization of quantum algorithms

Quantum query complexity studies the number of queries needed to learn some property of a black box. A closely related question is how well an algorithm can succeed with this learning task using only a fixed number of queries. In this work, we propose measuring an algorithm's performance using the mutual information between the output and the actual value. The task of optimizing this mutual information using a single query, is similar to a basic task of quantum communication, where one attempts to maximize the mutual information of the sender and receiver. We make this analogy precise by splitting the algorithm between two agents, obtaining a communication protocol. The oracle's target property plays the role of a message that Alice encodes into a quantum state, which is subsequently sent over to Bob. The first part of the algorithm performs this encoding, and the second part measures the state and aims to deduce the message from the outcome. Moreover, we formally consider the oracle as a separate subsystem, whose state records the unknown oracle identity. Within this construction, Bob's optimal measurement basis minimizes the quantum correlations between the two subsystems. We also find a lower bound on the mutual information, which is related to quantum coherence. These results extend to multiple-query non-adaptive algorithms. As a result, we describe the optimal non-adaptive algorithm that uses at most a fixed number of queries, for any oracle classification problem. Crucially, this mutual-information perspective carries direct practical utility for algorithmic design, providing the theoretical foundation to optimize iterative subroutines in hybrid quantum--classical schemes. Within the present work, we apply this framework to analyze the stage-by-stage information flow and track partial progress in several standard quantum algorithms.

quant-ph↗

arXiv2025

Weak Value Advantage in Overcoming Noise

The weak value exhibits numerous intriguing characteristics, such as values outside the operator spectrum, leading to unexpected phenomena. Nevertheless, the measurement protocol used for measuring the weak value has been the subject of an on-going controversy. In particular, the possibility of gaining a metrological advantage using weak measurements was questioned. A rigorous characterization of this advantage when the primary system is noisy is still missing. We thus consider here the challenge of learning an unknown operator under the influence of noise on the primary system which could lead to bias in the results. For amplitude and phase damping noise channels, we prove that the weak value measurement protocol (WVMP) eliminates the bias to linear order, and this cannot be done with strong measurements. Since the WVMP makes use both of weak entanglement as well as postselection, one might suspect that the advantage is solely due to the postselection aspect of the WVMP. We prove that this is not the case, and that the same advantage of the WVMP is kept even over strong measurement protocols that are allowed to apply postselection. By this we rigorously prove for the first time the existence of settings in which the WVMP possesses a strict advantage in robustness to noise, even over strong measurements augemented with postselection. However, for some noise channels, we show that no advantage is exhibited once both measurement regimes are equipped with postselection.

quant-ph↗

arXiv2025

Generalizing the matching decoder for the Chamon code

Different choices of quantum error-correcting codes can reduce the demands on the physical hardware needed to build a quantum computer. To achieve the full potential of a code, we must develop practical decoding algorithms that can correct errors that have occurred with high likelihood. Matching decoders are very good at correcting local errors while also demonstrating fast run times that can keep pace with physical quantum devices. We implement variations of a matching decoder for a three-dimensional, non-CSS, low-density parity check code known as the Chamon code, which has a non-trivial structure that does not lend itself readily to this type of decoding. The non-trivial structure of the syndrome of this code means that we can supplement the decoder with additional steps to improve the threshold error rate, below which the logical failure rate decreases with increasing code distance. We find that a generalized matching decoder that is augmented by a belief-propagation step prior to matching gives a threshold of 10.5% for depolarizing noise.

quant-ph↗

arXiv2025

Modeling error correction with Lindblad dynamics and approximate channels

We analyze the performance of a quantum error correction code subject to physically motivated noise modeled by a Lindblad master equation. We consider dissipative and coherent single-qubit terms and two-qubit crosstalk, studying how different approximations of the noise capture the success rate of a code. Focusing on the five-qubit code and adapting it to partially correct two-qubit errors in relevant parameter regimes according to the noise model, we find that a composite-channel approximation where every noise term is considered separately captures the behavior in many physical cases up to long timescales, eventually failing due to the effect of noncommuting terms. In contrast, we find that single-qubit approximations do not properly capture the error correction dynamics with two-qubit noise, even for short times. A Pauli approximation going beyond a single-qubit channel is sensitive to the details of the noise, state, and decoder, and succeeds at short timescales relative to the noise strength, beyond which it fails. Furthermore, we point out a mechanism for a Pauli model failure where it underestimates the failure rate of a code even with frequent syndrome projection and correction cycles. These results shed light on the performance of error correction in the presence of realistic noise and can advance the ongoing efforts towards useful quantum error correction.

quant-ph↗

arXiv2023

Quantum circuits for measuring weak values, Kirkwood--Dirac quasiprobability distributions, and state spectra

Weak values and Kirkwood--Dirac (KD) quasiprobability distributions have been independently associated with both foundational issues in quantum theory and advantages in quantum metrology. We propose simple quantum circuits to measure weak values, KD distributions, and spectra of density matrices without the need for post-selection. This is achieved by measuring unitary-invariant, relational properties of quantum states, which are functions of Bargmann invariants, the concept that underpins our unified perspective. Our circuits also enable experimental implementation of various functions of KD distributions, such as out-of-time-ordered correlators (OTOCs) and the quantum Fisher information in post-selected parameter estimation, among others. An upshot is a unified view of nonclassicality in all those tasks. In particular, we discuss how negativity and imaginarity of Bargmann invariants relate to set coherence.

quant-ph↗

arXiv2023

Time-symmetry and topology of the Aharonov-Bohm effect

The Aharonov-Bohm (AB) effect has been highly influential in fundamental and applied physics. Its topological nature commonly implies that an electron encircling a magnetic flux source in a field-free region must close the loop in order to generate an observable effect. In this Letter, we study a variant of the AB effect that apparently challenges this concept. The significance of weak values and nonlocal equations of motion is discussed as part of the analysis, shedding light on and connecting all these fundamental concepts.

quant-ph↗

arXiv2021

Quantum logical entropy: fundamentals and general properties

Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how fundamental concepts of this entropy and other related definitions can be applied to the study of quantum systems, leading to the introduction of the quantum logical entropy. Moreover, we prove several properties of this entropy for generic density matrices that may be relevant to various areas of quantum mechanics and quantum information. Furthermore, we extend the notion of quantum logical entropy to post-selected systems.

quant-ph↗

arXiv2019

Anisotropic Structural Predictor in Glassy Materials

There is a growing evidence that relaxation in glassy materials, both spontaneous and externally driven, is mediated by localized soft spots. Recent progress made it possible to identify the soft spots inside glassy structures and to quantify their degree of softness. These softness measures, however, are typically scalars, not taking into account the tensorial/anisotropic nature of soft spots, which implies orientation-dependent coupling to external deformation. Here we derive from first principles the linear response coupling between the local heat capacity of glasses, previously shown to provide a measure of glassy softness, and external deformation in different directions. We first show that this linear response quantity follows an anomalous, fat-tailed distribution related to the universal $ω^4$ density of states of quasilocalized, nonphononic excitations in glasses. We then construct a structural predictor as the product of the local heat capacity and its linear response to external deformation, and show that it offers enhanced predictability of plastic rearrangements under deformation in different directions, compared to the purely scalar predictor.

cond-mat.soft↗