Raam Uzdin

Quantum error mitigation (QEM) for dynamic circuits, i.e., those incorporating mid-circuit measurements and feedforward, is important for two key reasons. First, quantum error correction (QEC) circuits are instances of dynamic circuits, and therefore a dynamic circuit-compatible QEM can extend circuit depth and address errors that QEC struggles with. Second, recent studies show that dynamic circuits can significantly outperform purely unitary ones. However, mid-circuit measurement errors remain a major bottleneck. Current solutions rely on readout noise characterization that is vulnerable to temporal noise drifts. To the best of our knowledge, no readout mitigation schemes are resilient to temporal noise drifts. By introducing parity-based noise amplification in repeated measurements, we derive and experimentally demonstrate a drift-resilient protocol for addressing preparation, mid-circuit, and terminating measurement errors without requiring calibration or characterization. Drift resilience increases the longest possible execution time (in terms of shots) and enables flexibility by combining data from non-consecutive times. For platforms such as trapped ions, where the measurements are highly disruptive, we provide an alternative reset-based mitigation scheme. We demonstrate our methods experimentally on IBMQ and Quantinuum hardware. Combined with the Layered-KIK gate error mitigation protocol, the presented readout mitigation approach enables "End-to-end" mitigation for dynamic circuits, that can improve the outcomes of QEC experiments, and that covers the widest range of errors to the best of our knowledge. Other applications of the presented methods include a faster alternative to gate-set tomography and diagnostics of defective qubits during the execution of the target algorithm.

As quantum computers and simulators begin to produce results that cannot be verified classically, it becomes imperative to develop a variety of tools to detect and diagnose experimental errors on these devices. While state or process tomography is a natural way to characterize sources of experimental error, the intense measurement requirements make these strategies infeasible in all but the smallest of quantum systems. In this work, we formulate signatures of unitary evolution based on specific properties of periodically driven quantum systems. The absence of these signatures indicates a break either in the unitarity or periodicity condition on the evolution. We experimentally detect incoherent error on a trapped-ion quantum computer using these signatures. Our method is based on repeated measurements of a single observable, making this a low-cost evaluation of error with measurement requirements that scales according to the character of the dynamics, rather than the system size.

Recently, the principle of \textit{passivity} has been used to set bounds on the evolution of a microscopic quantum system with a thermal initial state. In this work, we experimentally demonstrate the utility of two passivity based frameworks: global passivity and passivity deformation, for the detection of a "hidden" or unaccounted environment. We employ two trapped-ion qubits undergoing unitary evolution, which may optionally be coupled to an unobserved environment qubit. Evaluating the measurement data from the system qubits, we show that global passivity can verify the presence of a coupling to an unobserved environment - a heat leak - in a case where the second law of thermodynamics fails. We also show that passivity deformation is even more sensitive, detecting a heat leak where global passivity fails.

Periodically-driven systems are ubiquitous in science and technology. In quantum dynamics, even a small number of periodically-driven spins leads to complicated dynamics. Hence, it is of interest to understand what constraints such dynamics must satisfy. We derive a set of constraints for each number of cycles. For pure initial states, the observable being constrained is the recurrence probability. We use our constraints for detecting undesired coupling to unaccounted environments and drifts in the driving parameters. To illustrate the relevance of these results for modern quantum systems we demonstrate our findings experimentally on a trapped-ion quantum computer, and on various IBM quantum computers. Specifically, we provide two experimental examples where these constraints surpass fundamental bounds associated with known one-cycle constraints. This scheme can potentially be used to detect the effect of the environment in quantum circuits that cannot be classically simulated. Finally, we show that, in practice, testing an $n$-cycle constraint requires executing only $O(\sqrt{n})$ cycles, which makes the evaluation of constraints associated with hundreds of cycles realistic.

Recently implemented quantum devices such as quantum processors and quantum simulators combine highly complicated quantum dynamics with high-resolution measurements. We present a passivity deformation methodology that sets thermodynamic constraints on the evolution of such quantum devices. This framework enhances the thermodynamic predictive power by simultaneously resolving four of the cardinal deficiencies of the second law in microscopic setups: i) It yields tight bounds even when the environment is microscopic; ii) The ultra-cold catastrophe is resolved; iii) It enables to integrate conservation laws into thermodynamic inequalities for making them tighter; iv) it bounds observables that are not energy-based, and therefore do not appear in the second law of thermodynamics. Furthermore, this framework provides insights to non-thermal environments, correlated environments, and to coarse-graining in microscopic setups. Our findings can be explored and used in physical setups such as trapped ions, superconducting circuits, neutral atoms in optical lattices and more.

The main thread that links classical thermodynamics and the thermodynamics of small quantum systems is the celebrated Clausius inequality form of the second law. However, its application to small quantum systems suffers from two cardinal problems: (i) The Clausius inequality does not hold when the system and environment are initially correlated - a commonly encountered scenario in microscopic setups. (ii) In some other cases, the Clausius inequality does not provide any useful information (e.g. in dephasing scenarios). We address these deficiencies by developing the notion of global passivity and employing it as a tool for deriving thermodynamic inequalities on observables. For initially uncorrelated thermal environments the global passivity framework recovers the Clausius inequality. More generally, global passivity provides an extension of the Clausius inequality that holds even in the presences of strong initial system-environment correlations. Crucially, the present framework provides additional thermodynamic bounds on expectation values. To illustrate the role of the additional bounds we use them to detect unaccounted heat leaks and weak feedback operations ("Maxwell's demons") that the Clausius inequality cannot detect. In addition, it is shown that global passivity can put practical upper and lower bounds on the buildup of system-environment correlation for dephasing interactions. Our findings are highly relevant for experiments in various systems such as ion traps, superconducting circuits, atoms in optical cavities and more.

The heat engine, a machine that extracts useful work from thermal sources, is one of the basic theoretical constructs and fundamental applications of classical thermodynamics. The classical description of a heat engine does not include coherence in its microscopic degrees of freedom. By contrast, a quantum heat engine might possess coherence between its internal states. Although the Carnot efficiency cannot be surpassed, and coherence can be performance degrading in certain conditions, it was recently predicted that even when using only thermal resources, internal coherence can enable a quantum heat engine to produce more power than any classical heat engine using the same resources. Such a power boost therefore constitutes a quantum thermodynamic signature. It has also been shown that the presence of coherence results in the thermodynamic equivalence of different quantum heat engine types, an effect with no classical counterpart. Microscopic heat machines have been recently implemented with trapped ions, and proposals for heat machines using superconducting circuits and optomechanics have been made. When operated with standard thermal baths, however, the machines implemented so far have not demonstrated any inherently quantum feature in their thermodynamic quantities. Here we implement two types of quantum heat engines by use of an ensemble of nitrogen-vacancy centres in diamond, and experimentally demonstrate both the coherence power boost and the equivalence of different heat-engine types. This constitutes the first observation of quantum thermodynamic signatures in heat machines.

Thermal Markovian dynamics is typically obtained by coupling a system to a sufficiently hot bath with a large heat capacity. Here we present a scheme for inducing Markovian dynamics using an arbitrarily small and cold heat bath. The scheme is based on injecting phase noise to the small bath. Several unique signatures of small bath are studied. We discuss realizations in ion traps and superconducting qubits and show that it is possible to create an ideal setting where the system dynamics is indifferent to the internal bath dynamics.

The time evolution of a single particle in a harmonic trap with time dependent frequency omega(t) is well studied. Nevertheless here we show that, when the harmonic trap is opened (or closed) as function of time while keeping the adiabatic parameter mu = [d omega(t)/dt]/omega(t)^2 fixed, a sharp transition from an oscillatory to a monotonic exponential dynamics occurs at mu = 2. At this transition point the time evolution has a third-order exceptional point (EP) at all instants. This situation, where an EP of a time-dependent Hermitian Hamiltonian is obtained at any given time, is very different from other known cases. Our finding is relevant to the dynamics of a single ion in a magnetic, optical, or rf trap, and of diluted gases of ultracold atoms in optical traps.