Despite the rapid development of quantum science and technology, errors are inevitable and play a crucial role in quantum simulation and quantum computation. In quantum chaotic systems, coherent errors arising from imperfect Hamiltonian control and incoherent errors induced by coupling to the environment are both exponentially amplified during time evolution due to information scrambling. A fundamental question is how these two classes of errors imprint distinct signatures on the emergent irreversibility of many-body dynamics. In this Letter, we address this question by investigating multi-round time-reversed dynamics in the presence of both coherent and incoherent errors. By applying scramblon theory, we obtain closed-form expressions for the Loschmidt echo over different rounds of time-reversed evolution. For incoherent errors, the error accumulates linearly with the number of rounds, whereas coherent errors exhibit a crossover from quadratic to linear accumulation. These predictions are explicitly verified using the solvable Sachdev-Ye-Kitaev model. Our results provide a theoretical foundation for characterizing and calibrating coherent and incoherent errors in reversed dynamics, with particular relevance to nuclear magnetic resonance systems.
Despite the rapid development of quantum science and technology, errors are inevitable and play a crucial role in quantum simulation and quantum computation. In quantum chaotic systems, coherent errors arising from imperfect Hamiltonian control and incoherent errors induced by coupling to the environment are both exponentially amplified during time evolution due to information scrambling. A fundamental question is how these two classes of errors imprint distinct signatures on the emergent irreversibility of many-body dynamics. In this Letter, we address this question by investigating multi-round time-reversed dynamics in the presence of both coherent and incoherent errors. By applying scramblon theory, we obtain closed-form expressions for the Loschmidt echo over different rounds of time-reversed evolution. For incoherent errors, the error accumulates linearly with the number of rounds, whereas coherent errors exhibit a crossover from quadratic to linear accumulation. These predictions are explicitly verified using the solvable Sachdev-Ye-Kitaev model. Our results provide a theoretical foundation for characterizing and calibrating coherent and incoherent errors in reversed dynamics, with particular relevance to nuclear magnetic resonance systems.
The emergence of the arrow of time in quantum many-body systems stems from the inherent tendency of Hamiltonian evolution to scramble quantum information and increase entanglement. While, in principle, one might counteract this temporal directionality by engineering a perfectly inverted Hamiltonian to reverse entanglement growth, such a scenario is fundamentally unstable because even minor imperfections in the backward evolution can be exponentially amplified, a hallmark of quantum many-body chaos. Therefore, successfully reversing quantum many-body dynamics demands a deep understanding of the underlying structure of quantum information scrambling and chaotic dynamics. In this Letter, by using solid-state nuclear magnetic resonance on a macroscopic ensemble of randomly interacting spins, we measure the out-of-time-ordered correlator and validate key predictions of scramblon theory, a universal theoretical framework for information scrambling. Crucially, this theory enables us to isolate and mitigate errors in the out-of-time-ordered correlator caused by imperfections in the backward evolution. As a result, this protocol uncovers the anticipated exponential behavior of quantum many-body chaos and extracts the quantum Lyapunov exponent in a many-body experimental system for the first time. Our results push the fundamental limits of dynamical reversibility of complex quantum systems, with implications for quantum simulation and metrology.
Quantum information scrambling, the dispersal of local information into many-body degrees of freedom, provides a powerful mechanism for generating large-scale correlations and entanglement essential for quantum-enhanced metrology. However, experimentally verifying such quantum-enhanced metrology remains a demanding task. Here, we correlate thousands of spins by engineering chaotic scrambling dynamics in a solid-state nuclear spin system. By leveraging the newly developed scramblon theory, we reveal exponential scaling in both the quantum Fisher information and the signal response to a phase shift. The signal response achieves a correlation-enabled enhancement of 33(2) dB over uncorrelated spins. After accounting for signal loss due to imperfect time reversal in the readout stage, we obtain a total metrological gain of 18(1) dB with a phase sensitivity of 40(3) μrad. Our results bridge quantum chaos with practical quantum metrology, establishing reversible scrambling dynamics as a powerful resource for precision measurements.
Echoes are ubiquitous phenomena in several branches of physics, ranging from acoustics, optics, condensed matter and cold atoms to geophysics. They are at the base of a number of very useful experimental techniques, such as nuclear magnetic resonance, photon echo and time-reversal mirrors. Particularly interesting physical effects are obtained when the echo studies are performed on complex systems, either classically chaotic, disordered or many-body. Consequently, the term Loschmidt echo has been coined to designate and quantify the revival occurring when an imperfect time-reversal procedure is applied to a complex quantum system, or equivalently to characterize the stability of quantum evolution in the presence of perturbations. Here, we present the articles which discuss the work that has shaped the field in the past few years.
Developing quantum technologies requires the control and understanding of the nonequilibrium dynamics of quantum information in many-body systems. Local information propagates in the system by creating complex correlations known as information scrambling, as this process prevents extracting the information from local measurements. In this paper, we develop a model adapted from solid-state NMR methods, to quantify the information scrambling. The scrambling is measured via time-reversal Loschmidt echo (LE) and multiple quantum coherences experiments that intrinsically contain imperfections. Considering these imperfections, we derive expressions for out-of-time order correlators (OTOCs) to quantify the observable information scrambling based on measuring the number of active spins where the information was spread. Based on the OTOC expressions, decoherence effects arise naturally by the effects of the nonreverted terms in the LE experiment. Decoherence induces localization of the measurable degree of information scrambling. These effects define a localization cluster size for the observable number of active spins that determines a dynamical equilibrium. We contrast the model's predictions with quantum simulations performed with solid-state NMR experiments, that measure the information scrambling with time-reversal echoes with controlled imperfections. An excellent quantitative agreement is found with the dynamics of quantum information scrambling and its localization effects determined from the experimental data. The presented model and derived OTOCs set tools for quantifying the quantum information dynamics of large quantum systems (more than 104 spins) consistent with experimental implementations that intrinsically contain imperfections.
Quantum simulation of many-body systems, particularly using ultracold atoms and trapped ions, presents a unique form of quantum control—it is a direct implementation of a multi-qubit gate generated by the Hamiltonian. As a consequence, it also faces a unique challenge in terms of benchmarking, because the well-established gate benchmarking techniques are unsuitable for this form of quantum control. Here we show that the symmetries of the target many-body Hamiltonian can be used not only to benchmark but to characterize experimental errors in the quantum simulation. We use our results to develop protocols to characterize these errors, which can be implemented using state-of-the-art technology. We consider two forms of errors: (i) unitary errors arising out of systematic errors in the applied Hamiltonian and (ii) canonical non-Markovian errors arising out of random shot-to-shot fluctuations in the applied Hamiltonian. We show that the dynamics of the expectation value of the target Hamiltonian itself, which is ideally constant in time, can be used to characterize these errors. In the presence of errors, the expectation value of the target Hamiltonian shows a characteristic thermalization dynamics, when it satisfies the operator thermalization hypothesis (OTH). That is, an oscillation in the short time followed by relaxation to a steady-state value in the long time limit. We show that while the steady-state value can be used to characterize the coherent errors, the amplitude of the oscillations can be used to estimate the non-Markovian errors. We prove a sandwich theorem to establish a linear relation between the amplitude of the oscillations and the magnitude of the non-Markovian errors. Moreover, by varying the initial state, we show that the steady state values can be used to completely construct the generator of the coherent errors. Using these results, we develop two experimental protocols to characterize the unitary errors based on these results, one of which requires single-qubit addressing and the other one doesn't. We also develop a protocol to characterize non-Markovian errors. Published by the American Physical Society 2024
When a qubit or spin interacts with others under a many-body Hamiltonian, the information it contains progressively scrambles. Here, nuclear spins of an adamantane crystal are used as a quantum simulator to monitor such dynamics through out-of-time-order correlators, while a Loschmidt echo (LE) asses how weak perturbations degrade the information encoded in these increasingly complex states. Both observables involve the implementation of a time-reversal procedure which, in practice, involves inverting the sign of the effective Hamiltonian. Our protocols use periodic radio frequency pulses to modulate the natural dipolar interaction implementing a Hamiltonian that can be scaled down at will. Meanwhile, experimental errors and strength of perturbative terms remain constant and can be quantified through the LE. For each scaling factor, information spreading occurs with a timescale, T_{2}, inversely proportional to the local second moment of the Hamiltonian. We find that, when the reversible interactions dominate over the perturbations, the information scrambled among up to 10^{2} spins can still be recovered. However, we find that the LE decay rate cannot become smaller than a critical value 1/T_{3}≈(0.15±0.02)/T_{2}, which only depends on the interactions themselves, and not on the perturbations. This result shows the emergence of a regime of intrinsic irreversibility in accordance to a central hypothesis of irreversibility, hinted from previous experiments.