arXiv subjects

Sumeet Khatri

Publications and source records attributed to Sumeet Khatri.

At least 19 recordsLinked to original sources

arXiv2026

Constant Overhead Entanglement Distillation via Scrambling

High-fidelity quantum entanglement enables key quantum networking capabilities such as secure communication and distributed quantum computing, but long-distance entanglement distribution is limited by noise and loss. Entanglement distillation protocols address this problem by extracting high-fidelity Bell pairs from multiple noisy ones. The primary objective is minimizing the resource overhead: the number of noisy input pairs needed to distill each high-fidelity output pair. While protocols achieving optimal overhead are known in theory, they often require complex decoding operations that make practical implementation challenging. We circumvent this challenge by introducing protocols that use quantum scrambling -- the spreading of quantum information under chaotic dynamics -- through random Clifford operations. Based on this scrambling mechanism, our protocol maintains asymptotically \emph{constant} overhead, independent of the desired output error rate $\bar{\varepsilon}$, and can be implemented with shallow quantum circuits of depth $O(\mathrm{poly} \log \log \bar{\varepsilon}^{-1})$ and memory $O(\mathrm{poly} \log \bar{\varepsilon}^{-1})$. Our protocol remains effective even with noisy quantum gates. By incorporating error correction, our protocol achieves state-of-the-art performance: starting with pairs of 10% initial infidelity, we require only 7 noisy inputs per output pair to distill a single Bell pair with infidelity $\bar{\varepsilon}=10^{-12}$, substantially outperforming existing schemes. We demonstrate the utility of our protocols for quantum repeater networks.

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arXiv2025

$k$-Positive Maps: New Characterizations and a Generation Method

We study $k$-positive linear maps on matrix algebras and address two problems, (i) characterizations of $k$-positivity and (ii) generation of non-decomposable $k$-positive maps. On the characterization side, we derive optimization-based conditions equivalent to $k$-positivity that (a) reduce to a simple check when $k=d$, (b) reveal a direct link to the spectral norm of certain order-3 tensors (aligning with known NP-hardness barriers for $k<d$), and (c) recast $k$-positivity as a novel optimization problem over separable states, thereby connecting it explicitly to separability testing. On the generation side, we introduce a Lie-semigroup-based method that, starting from a single $k$-positive map, produces one-parameter families that remain $k$-positive and non-decomposable for small enough times. We illustrate this by generating such families for $d=3$ and $d=4$. We also formulate a semi-definite program (SDP) to test an equivalent form of the positive partial transpose (PPT) square conjecture (and do not find any violation of the latter). Our results provide practical computational tools for certifying $k$-positivity and a systematic way to sample $k$-positive non-decomposable maps.

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arXiv2025

Reinforcement learning of quantum circuit architectures for molecular potential energy curves

Quantum chemistry and optimization are two of the most prominent applications of quantum computers. Variational quantum algorithms have been proposed for solving problems in these domains. However, the design of the quantum circuit ansatz remains a challenge. Of particular interest is developing a method to generate circuits for any given instance of a problem, not merely a circuit tailored to a specific instance of the problem. To this end, we present a reinforcement learning (RL) approach to learning a problem-dependent quantum circuit mapping, which outputs a circuit for the ground state of a Hamiltonian from a given family of parameterized Hamiltonians. For quantum chemistry, our RL framework takes as input a molecule and a discrete set of bond distances, and it outputs a bond-distance-dependent quantum circuit for arbitrary bond distances along the potential energy curve. The inherently non-greedy approach of our RL method contrasts with existing greedy approaches to adaptive, problem-tailored circuit constructions. We demonstrate its effectiveness for the four-qubit and six-qubit lithium hydride molecules, as well as an eight-qubit H$_4$ chain. Our learned circuits are interpretable in a physically meaningful manner, thus paving the way for applying RL to the development of novel quantum circuits for the ground states of large-scale molecular systems.

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arXiv2025

Thermalization with partial information

A many-body system, whether in contact with a large environment or evolving under complex dynamics, can typically be modeled as occupying the thermal state singled out by Jaynes' maximum entropy principle. Here, we find analogous fundamental principles identifying a noisy quantum channel $\mathcal{T}$ to model the system's dynamics, going beyond the study of its final equilibrium state. Our maximum channel entropy principle states that $\mathcal{T}$ should maximize the channel's entropy, suitably defined, subject to any available macroscopic constraints. These may correlate input and outputs, and may lead to restricted or partial thermalizing dynamics including thermalization with average energy conservation. This principle is reinforced by an independent extension of the microcanonical derivation of the thermal state to channels, which leads to the same $\mathcal{T}$. Our technical contributions include a derivation of the general mathematical structure of $\mathcal{T}$, a custom postselection theorem relating an arbitrary permutation-invariant channel to nearby i.i.d. channels, as well as novel typicality results for quantum channels for noncommuting constraints and arbitrary input states. We propose a learning algorithm for quantum channels based on the maximum channel entropy principle, demonstrating the broader relevance of $\mathcal{T}$ beyond thermodynamics and complex many-body systems.

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arXiv2025

Maximum channel entropy principle and microcanonical channels

The thermal state plays a number of significant roles throughout physics, information theory, quantum computing, and machine learning. It arises from Jaynes' maximum-entropy principle as the maximally entropic state subject to linear constraints, and is also the reduced state of the microcanonical state on the system and a large environment. We formulate a maximum-channel-entropy principle, defining a thermal channel as one that maximizes a channel entropy measure subject to linear constraints on the channel. We prove that thermal channels exhibit an exponential form reminiscent of thermal states. We study examples including thermalizing channels that conserve a state's average energy, as well as Pauli-covariant and classical channels. We propose a quantum channel learning algorithm based on maximum channel entropy methods that mirrors a similar learning algorithm for quantum states. We then demonstrate the thermodynamic relevance of the maximum-channel-entropy channel by proving that it resembles the action on a single system of a microcanonical channel acting on many copies of the system. Here, the microcanonical channel is defined by requiring that the linear constraints obey sharp statistics for any i.i.d. input state, including for noncommuting constraint operators. Our techniques involve convex optimization methods to optimize recently introduced channel entropy measures, typicality techniques involving noncommuting operators, a custom channel postselection technique, as well as Schur-Weyl duality. As a result of potential independent interest, we prove a constrained postselection theorem for quantum channels. The widespread relevance of the thermal state throughout physics, information theory, machine learning, and quantum computing, inspires promising applications for the analogous concept for quantum channels.

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arXiv2025

Reducing classical communication costs in multiplexed quantum repeaters using hardware-aware quasi-local policies

Future quantum networks will have nodes equipped with multiple quantum memories, allowing for multiplexing and entanglement distillation strategies in order to increase fidelities and reduce waiting times for end-to-end entanglement distribution. In this work, we introduce \textit{quasi-local} policies for multiplexed quantum repeater chains. In fully-local policies, nodes make decisions based only on knowledge of their own states. In our quasi-local policies, nodes have increased knowledge of the state of the repeater chain, but not necessarily full, global knowledge. Our policies exploit the observation that for most decisions the nodes have to make, they only need to have information about the connected region of the chain they belong to, and not the entire chain. In this way, we not only obtain improved performance over local policies, but we reduce the classical communication (CC) costs inherent to global-knowledge policies. Our policies also outperform the well-known and widely studied nested purification and doubling swapping policy in practically relevant parameter regimes. We also carefully examine the role of entanglement distillation. Via analytical and numerical results, we identify the parameter regimes in which distillation makes sense and is useful. In these regimes, we also address the question: "Should we distill before swapping, or vice versa?" Finally, to provide further practical guidance, we propose an experimental implementation of a multiplexing-based repeater chain, and experimentally demonstrate the key element, a high-dimensional biphoton frequency comb. We then evaluate the anticipated performance of our multiplexing-based policies in such a real-world network through simulation results for two concrete memory platforms, namely rare-earth ions and diamond vacancies.

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arXiv2025

Quantum reinforcement learning of classical rare dynamics: Enhancement by intrinsic Fourier features

Rare events are essential for understanding the behavior of non-equilibrium and industrial systems. It is of ongoing interest to develop methods for effectively searching for rare events. With the advent of quantum computing and its potential advantages over classical computing for applications like sampling certain probability distributions, the question arises whether quantum computers could also provide an advantage or inspire new methods for sampling the statistics of rare events. In this work, we propose a quantum reinforcement learning (QRL) method for studying rare dynamics, and we investigate their benefits over classical approaches based on neural networks. As a proof-of-concept example, we demonstrate that our QRL agents can learn and generate the rare dynamics of random walks, and we are able to explain this success as well as the different contributing factors to it via the intrinsic Fourier features of the parameterized quantum circuit. Furthermore, we show better learning behavior with fewer parameters compared to classical approaches. This is the first investigation of QRL applied to generating rare events and suggests that QRL is a promising method to study their dynamics and statistics.

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arXiv2024

Towards a General Framework for Practical Quantum Network Protocols

The quantum internet is one of the frontiers of quantum information science. It will revolutionize the way we communicate and do other tasks, and it will allow for tasks that are not possible using the current, classical internet. The backbone of a quantum internet is entanglement distributed globally in order to allow for such novel applications to be performed over long distances. Experimental progress is currently being made to realize quantum networks on a small scale, but much theoretical work is still needed in order to understand how best to distribute entanglement and to guide the realization of large-scale quantum networks, and eventually the quantum internet, especially with the limitations of near-term quantum technologies. This work provides an initial step towards this goal. The main contribution of this thesis is a mathematical framework for entanglement distribution protocols in a quantum network, which allows for discovering optimal protocols using reinforcement learning. We start with a general development of quantum decision processes, which is the theoretical backdrop of reinforcement learning. Then, we define the general task of entanglement distribution in a quantum network, and we present ground- and satellite-based quantum network architectures that incorporate practical aspects of entanglement distribution. We combine the theory of decision processes and the practical quantum network architectures into an overall entanglement distribution protocol. We also define practical figures of merit to evaluate entanglement distribution protocols, which help to guide experimental implementations.

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arXiv2024

A resource- and computationally-efficient protocol for multipartite entanglement distribution in Bell-pair networks

Multipartite entangled states, such as Greenberger--Horne--Zeilinger (GHZ) states, are important resources in multiparty quantum networking tasks. We consider protocols for generating such states from networks of Bell pairs and local operations and classical communication. We present a computationally-efficient protocol for generating GHZ states that is also efficient with respect to the number of consumed Bell pairs, (local) gates, and Bell-pair sources. Our protocol: (1) requires $O(N)$ gates in a network with $N$ nodes, independent of the network topology; (2) has time complexity $O(N^2)$, avoiding the Steiner tree and any other computationally-hard problem; (3) maintains a near-optimal number of consumed Bell pairs. Numerically, our protocol outperforms those based on (approximate) Steiner trees with respect to number of gates and Bell-pair sources. We prove that the minimal Bell-pair source cost is given by solving the graph-theoretic dominating set problem, and we demonstrate numerically that our protocol is nearly optimal for this quantity. Finally, we analytically characterize the impact of noisy Bell pairs and gates on the fidelity of the distributed GHZ states.

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arXiv2024

Experimental measurement and a physical interpretation of quantum shadow enumerators

Throughout its history, the theory of quantum error correction has heavily benefited from translating classical concepts into the quantum setting. In particular, classical notions of weight enumerators, which relate to the performance of an error-correcting code, and MacWilliams' identity, which helps to compute enumerators, have been generalized to the quantum case. In this work, we establish a distinct relationship between the theoretical machinery of quantum weight enumerators and a seemingly unrelated physics experiment: we prove that Rains' quantum shadow enumerators - a powerful mathematical tool - arise as probabilities of observing fixed numbers of triplets in a Bell sampling experiment. This insight allows us to develop here a rigorous framework for the direct measurement of quantum weight enumerators, thus enabling experimental and theoretical studies of the entanglement structure of any quantum error-correcting code or state under investigation. On top of that, we derive concrete sample complexity bounds and physically-motivated robustness guarantees against unavoidable experimental imperfections. Finally, we experimentally demonstrate the possibility of directly measuring weight enumerators on a trapped-ion quantum computer. Our experimental findings are in good agreement with theoretical predictions and illuminate how entanglement theory and quantum error correction can cross-fertilize each other once Bell sampling experiments are combined with the theoretical machinery of quantum weight enumerators.

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arXiv2024

Perturbative gadgets for gate-based quantum computing: Non-recursive constructions without subspace restrictions

Perturbative gadgets are a tool to encode part of a Hamiltonian, usually the low-energy subspace, into a different Hamiltonian with favorable properties, for instance, reduced locality. Many constructions of perturbative gadgets have been proposed over the years. Still, all of them are restricted in some ways: Either they apply to some specific classes of Hamiltonians, they involve recursion to reduce locality, or they are limited to studying time evolution under the gadget Hamiltonian, e.g., in the context of adiabatic quantum computing, and thus involve subspace restrictions. In this work, we fill the gap by introducing a versatile universal, non-recursive, non-adiabatic perturbative gadget construction without subspace restrictions, that encodes an arbitrary many-body Hamiltonian into the low-energy subspace of a three-body Hamiltonian and is therefore applicable to gate-based quantum computing. Our construction requires $rk$ additional qubits for a $k$-body Hamiltonian comprising $r$ terms. Besides a specific gadget construction, we also provide a recipe for constructing similar gadgets, which can be tailored to different properties, which we discuss.

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arXiv2024

Online learning of quantum processes

Among recent insights into learning quantum states, online learning and shadow tomography procedures are notable for their ability to accurately predict expectation values even of adaptively chosen observables. In contrast to the state case, quantum process learning tasks with a similarly adaptive nature have received little attention. In this work, we investigate online learning tasks for quantum processes. Whereas online learning is infeasible for general quantum channels, we show that channels of bounded gate complexity as well as Pauli channels can be online learned in the regret and mistake-bounded models of online learning. In fact, we can online learn probabilistic mixtures of any exponentially large set of known channels. We also provide a provably sample-efficient shadow tomography procedure for Pauli channels. Our results extend beyond quantum channels to non-Markovian multi-time processes, with favorable regret and mistake bounds, as well as a shadow tomography procedure. We complement our online learning upper bounds with mistake as well as computational lower bounds. On the technical side, we make use of the multiplicative weights update algorithm, classical adaptive data analysis, and Bell sampling, as well as tools from the theory of quantum combs for multi-time quantum processes. Our work initiates a study of online learning for classes of quantum channels and, more generally, non-Markovian quantum processes. Given the importance of online learning for state shadow tomography, this may serve as a step towards quantum channel variants of adaptive shadow tomography.

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arXiv2024

Fast and reliable entanglement distribution with quantum repeaters: principles for improving protocols using reinforcement learning

Future quantum technologies such as quantum communication, quantum sensing, and distributed quantum computation, will rely on networks of shared entanglement between spatially separated nodes. In this work, we provide improved protocols/policies for entanglement distribution along a linear chain of nodes, both homogeneous and inhomogeneous, that take practical limitations such as photon losses, non-ideal measurements, and quantum memories with short coherence times into account. For a wide range of parameters, our policies improve upon previously known policies, such as the "swap-as-soon-as-possible" policy, with respect to both the waiting time and the fidelity of the end-to-end entanglement. This improvement is greatest for the most practically relevant cases, namely, for short coherence times, high link losses, and highly asymmetric links. To obtain our results, we model entanglement distribution using a Markov decision process, and then we use the Q-learning reinforcement learning (RL) algorithm to discover new policies. These new policies are characterized by dynamic, state-dependent memory cutoffs and collaboration between the nodes. In particular, we quantify this collaboration between the nodes. Our quantifiers tell us how much "global" knowledge of the network every node has. Finally, our understanding of the performance of large quantum networks is currently limited by the computational inefficiency of simulating them using RL or other optimization methods. Thus, in this work, we present a method for nesting policies in order to obtain policies for large repeater chains. By nesting our RL-based policies for small repeater chains, we obtain policies for large repeater chains that improve upon the swap-as-soon-as-possible policy, and thus we pave the way for a scalable method for obtaining policies for long-distance entanglement distribution.

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arXiv2024

Exponentially tighter bounds on limitations of quantum error mitigation

Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault tolerant schemes. Recently, error mitigation has been successfully applied to reduce noise in near-term applications. In this work, however, we identify strong limitations to the degree to which quantum noise can be effectively `undone' for larger system sizes. Our framework rigorously captures large classes of error mitigation schemes in use today. By relating error mitigation to a statistical inference problem, we show that even at shallow circuit depths comparable to the current experiments, a superpolynomial number of samples is needed in the worst case to estimate the expectation values of noiseless observables, the principal task of error mitigation. Notably, our construction implies that scrambling due to noise can kick in at exponentially smaller depths than previously thought. They also impact other near-term applications, constraining kernel estimation in quantum machine learning, causing an earlier emergence of noise-induced barren plateaus in variational quantum algorithms and ruling out exponential quantum speed-ups in estimating expectation values in the presence of noise or preparing the ground state of a Hamiltonian.

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arXiv2024

Noise-induced shallow circuits and absence of barren plateaus

Motivated by realistic hardware considerations of the pre-fault-tolerant era, we comprehensively study the impact of uncorrected noise on quantum circuits. We first show that in the task of estimating observable expectation values any noise truncates most quantum circuits to effectively logarithmic depth. We then prove that quantum circuits under any non-unital noise do not exhibit barren plateaus for cost functions composed of local observables. However, by using the effective shallowness, we also design an efficient classical algorithm to estimate observable expectation values within any constant additive accuracy, with high probability over the choice of the circuit, in any circuit architecture. Taken together, our results establish that, unless we carefully engineer quantum circuits to take advantage of the noise, noisy quantum circuits are unlikely to offer an advantage over shallow ones for algorithms that output observable expectation value estimates, such as many variational quantum machine learning proposals.

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arXiv2024

Principles of Quantum Communication Theory: A Modern Approach

This is a preliminary version of a book in progress on the theory of quantum communication. We adopt an information-theoretic perspective throughout and give a comprehensive account of fundamental results in quantum communication theory from the past decade (and earlier), with an emphasis on the modern one-shot-to-asymptotic approach that underlies much of today's state-of-the-art research in this field. In Part I, we cover mathematical preliminaries and provide a detailed study of quantum mechanics from an information-theoretic perspective. We also provide an extensive and thorough review of quantum entropies, and we devote an entire chapter to the study of entanglement measures. Equipped with these essential tools, in Part II we study classical communication (with and without entanglement assistance), entanglement distillation, quantum communication, secret key distillation, and private communication. In Part III, we cover the latest developments in feedback-assisted communication tasks, such as quantum and classical feedback-assisted communication, LOCC-assisted quantum communication, and secret key agreement.

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arXiv2023

On the design and analysis of near-term quantum network protocols using Markov decision processes

The quantum internet is one of the frontiers of quantum information science research. It will revolutionize the way we communicate and do other tasks, and it will allow for tasks that are not possible using the current, classical internet. The backbone of a quantum internet is entanglement distributed globally in order to allow for such novel applications to be performed over long distances. Experimental progress is currently being made to realize quantum networks on a small scale, but much theoretical work is still needed in order to understand how best to distribute entanglement, especially with the limitations of near-term quantum technologies taken into account. This work provides an initial step towards this goal. In this work, we lay out a theory of near-term quantum networks based on Markov decision processes (MDPs), and we show that MDPs provide a precise and systematic mathematical framework to model protocols for near-term quantum networks that is agnostic to the specific implementation platform. We start by simplifying the MDP for elementary links introduced in prior work, and by providing new results on policies for elementary links. In particular, we show that the well-known memory-cutoff policy is optimal. Then we show how the elementary link MDP can be used to analyze a quantum network protocol in which we wait for all elementary links to be active before creating end-to-end links. We then provide an extension of the MDP formalism to two elementary links, which is useful for analyzing more sophisticated quantum network protocols. Here, as new results, we derive linear programs that give us optimal steady-state policies with respect to the expected fidelity and waiting time of the end-to-end link.

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arXiv2023

Quantum metrology in the finite-sample regime

In quantum metrology, one of the major applications of quantum technologies, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cramér-Rao bound. Yet, the latter is no longer guaranteed to carry an operational meaning in the regime where few measurement samples are obtained, which we illustrate through a simple example. We instead propose to quantify the quality of a metrology protocol by the probability of obtaining an estimate with a given accuracy. This approach, which we refer to as probably approximately correct (PAC) metrology, ensures operational significance in the finite-sample regime. The accuracy guarantees hold for any value of the unknown parameter, unlike the Cramér-Rao bound which assumes it is approximately known. We establish a strong connection to multi-hypothesis testing with quantum states, which allows us to derive an analogue of the Cramér-Rao bound which contains explicit corrections relevant to the finite-sample regime. We further study the asymptotic behavior of the success probability of the estimation procedure for many copies of the state and apply our framework to the example task of phase estimation with an ensemble of spin-1/2 particles. Overall, our operational approach allows the study of quantum metrology in the finite-sample regime and opens up a plethora of new avenues for research at the interface of quantum information theory and quantum metrology.

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