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Advanced Quantum Technologies

Probing Quantum Anomalous Heat Flow Using Mid‐Circuit Measurements

Aabhaas Vineet Mallik, Loris Maria Cangemi, Amikam Levy, Emanuele G. Dalla Torre

Published Aug 29, 2025• 3 citations
Publisher

Abstract

Abstract Gate‐based quantum computers are an innovative tool for experimentally studying the core principles of quantum mechanics. This work presents the first observation of quantum anomalous heat flow between two qubits and investigates the role of mid‐circuit measurements in this context. Using mid‐circuit measurements, we designed quantum circuits that violate the semi‐classical heat flow bound, witnessing negativities in the underlying Kirkwood‐Dirac quasiprobability distribution, which indicates the presence of quantum correlations between the subsystems. Mid‐circuit measurements, crucial for probing qubits during the experiment, enabled these observations but also introduced disturbances, such as energy leakage, leading to deviations from theoretical predictions. These noise effects were modeled, providing insight into the limitations of current mid‐circuit measurement techniques.

DOI
10.1002/qute.202500328

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Abstract Gate‐based quantum computers are an innovative tool for experimentally studying the core principles of quantum mechanics. This work presents the first observation of quantum anomalous heat flow between two qubits and investigates the role of mid‐circuit measurements in this context. Using mid‐circuit measurements, we designed quantum circuits that violate the semi‐classical heat flow bound, witnessing negativities in the underlying Kirkwood‐Dirac quasiprobability distribution, which indicates the presence of quantum correlations between the subsystems. Mid‐circuit measurements, crucial for probing qubits during the experiment, enabled these observations but also introduced disturbances, such as energy leakage, leading to deviations from theoretical predictions. These noise effects were modeled, providing insight into the limitations of current mid‐circuit measurement techniques.
Gate-based quantum computers are an innovative tool for experimentally studying the core principles of quantum mechanics. This work presents the first observation of quantum anomalous heat flow between two qubits and investigates the role of mid-circuit measurements in this context. Using mid-circuit measurements, we designed quantum circuits that violate the semi-classical heat flow bound, witnessing negativities in the underlying Kirkwood-Dirac quasiprobability distribution, which indicates the presence of quantum correlations between the subsystems. Mid-circuit measurements, crucial for probing qubits during the experiment, enabled these observations but also introduced disturbances, such as energy leakage, leading to deviations from theoretical predictions. We modeled these noise effects, providing insight into the limitations of current mid-circuit measurement techniques.
We explore the framework based on the Kirkwood-Dirac quasiprobability distribution to quantify the contribution of coherence to work extraction during generic, cyclic quantum evolutions. In particular, we focus on "anomalous processes," counterintuitive scenarios in which, due to the negativity of the quasiprobability distribution, work can be extracted even when individual processes are associated with energy gain. Applying this framework to qubits undergoing sequences of single- and two-qubit gate operations, we identify specific conditions under which such anomalous work exchanges occur. Furthermore, we analyze the quasiprobabilistic structure of deep quantum circuits and establish a compositional relation linking the work statistics of full circuits to those of their constituent gates. Our work highlights the role of coherence in the thermodynamics of basic elements of quantum computation and provides a foundation for systematically studying potential thermodynamic relevance of specific quantum circuits.
Practical quantum computers need to continuously exchange data between classical and quantum subsystems during a computation. Mid-circuit measurements of a qubits state are transferred to the classical electronics layer, and their outcome can inform feedforward operations that close the loop back to the quantum layer. These operations are crucial for fault-tolerant quantum computers, but the quantum-classical loop must be completed before the qubits decohere, presenting a substantial engineering challenge for full-scale systems comprising millions of qubits. Here we perform the first mid-circuit measurements in a system of silicon spin qubits, and show that feedforward operations can be performed without needing to route information to the classical layer. This in-layer approach leverages a backaction-driven control technique that has previously been considered a source of error. We benchmark our in-layer strategy, together with the standard FPGA-enabled approach, and analyse the performance of both methods using gate set tomography. Our results provide the first step towards moving resource-intensive classical processing into the quantum layer, an advance that could solve key engineering challenges, and drastically reduce the power budget of future quantum computers.
The standard approach to deriving fluctuation theorems fails to capture the effect of quantum correlation and coherence in the initial state of the system.Here, we overcome this difficulty and derive the heat-exchange-fluctuation theorem in the full quantum regime by showing that the energy exchange between two locally thermal states in the presence of initial quantum correlations is faithfully captured by a quasiprobability distribution.Its negativities, being associated with proofs of contextuality, are proxies of nonclassicality.We discuss the thermodynamic interpretation of negative probabilities and provide heat-flow inequalities that can only be violated in their presence.Remarkably, testing these fully quantum inequalities, at an arbitrary dimension, is no more difficult than testing traditional fluctuation theorems.We test these results on data collected in a recent experiment studying the heat transfer between two qubits and give examples for the capability of witnessing negative probabilities at higher dimensions.
In classical thermodynamics, heat must spontaneously flow from hot to cold systems. In quantum thermodynamics, the same law applies when considering multipartite product thermal states evolving unitarily. If initial correlations are present, anomalous heat flow can happen, temporarily making cold thermal states colder and hot thermal states hotter. Such an effect can happen due to entanglement but also because of classical randomness, hence lacking a direct connection with nonclassicality. In this work, we introduce scenarios in which anomalous heat flow have a direct link to nonclassicality, defined as the failure of noncontextual models to explain experimental data. We start by extending known noncontextuality inequalities to a setup in which sequential transformations are considered. We then show a class of quantum prepare-transform-measure protocols, characterized by a time interval ( 0 , τ c ) for a given critical time τ c , where anomalous heat flow happens only if a noncontextuality inequality is violated. We also analyze a recent experiment from and find the critical time τ c based on the authors’ experimental parameters. We conclude by investigating heat flow in the evolution of two-qudit systems, showing that our findings are not an artifact of using two-qubit systems.
It is generally considered that the signal output by a quantum circuit is attenuated exponentially fast in the number of gates. This letter explores how algorithms using mid-circuit measurements and classical conditioning as computational tools (and not as error mitigation or correction subroutines) can be naturally resilient to complete decoherence, and maintain quantum states with useful properties even for infinitely deep noisy circuits. Specifically, we introduce a quantum channel built out of mid-circuit measurements and feed-forward, that can be used to compute dynamical correlations at infinite temperature and canonical ensemble expectation values for any Hamiltonian. The unusual property of this algorithm is that in the presence of a depolarizing channel it still displays a meaningful, non-zero signal in the large depth limit. We showcase the noise resilience of this quantum channel on Quantinuum's H1-1 ion-trap quantum computer.