John Goold

One of the promising applications of digital quantum processors is the simulation of many-body quantum systems. They have been already used to investigate several ergodicity violating mechanisms, which were initially discovered in synthetic quantum matter, such as many-body localisation, Hilbert space fragmentation and quantum many-body scars (QMBS). In addition to conventional QMBS, a recently discovered mechanism for ergodicity violation are the so-called asymptotic quantum many-body scars (AQMBS). These become more stable as system size is increased, leading to progressively longer thermalisation timescales. In this work, we show a connection between gapless excitations and AQMBS in certain qudit-based models. We then consider a 2-local model, hosting both conventional and asymptotic scars, in which the AQMBS states are gapless excitations of a ground state localisation transition. By exploiting the structure of the found AQMBS states and the all-to-all connectivity of the Quantinuum H1-1 quantum processor, we prepare these states in logarithmic circuit depth, and probe their thermalisation behaviour under Floquet dynamics. Performing simulations on up to N = 20 qubits and up to 418 entangling ZZ gates, we find slower thermalisation times as the system size is increased, providing the first experimental signatures of asymptotic scars.

Within the framework of microscopic thermodynamics, correlations can play a crucial role for energy extraction. Our work sheds light on this connection by demonstrating that entanglement governs the amount of extractable energy in a controllable setting. We experimentally investigate a fundamental link between information, encoded in tunable non-classical correlations and quantified by quantum state tomography, and its utility as fuel for energy extraction. We realize an agent-demon protocol involving two trapped-ion qubits, and show that by implementing an appropriate feedback policy, the demon can optimize the energy extraction process, capitalizing on the correlations between the system's constituents. By quantifying both the concurrence of the two-qubit resource state and the energy extraction gain from applying the feedback policy, we corroborate the connection between information and energy, solidifying the role of non-classical correlations as a resource for thermodynamic processes.

Quantum statistical mechanics allows us to extract thermodynamic information from a microscopic description of a many-body system. A key step is the calculation of the density of states, from which the partition function and all finite-temperature equilibrium thermodynamic quantities can be calculated. In this work, we devise and implement a quantum algorithm to perform an estimation of the density of states on a digital quantum computer which is inspired by the kernel polynomial method. Classically, the kernel polynomial method allows to sample spectral functions via a Chebyshev polynomial expansion. Our algorithm computes moments of the expansion on quantum hardware using a combination of random state preparation for stochastic trace evaluation and a controlled unitary operator. We use our algorithm to estimate the density of states of a non-integrable Hamiltonian on the Quantinuum H1-1 trapped ion chip for a controlled register of 18 qubits. This not only represents a state-of-the-art calculation of thermal properties of a many-body system on quantum hardware, but also exploits the controlled unitary evolution of a many-qubit register on an unprecedented scale.

Many complex systems can spontaneously oscillate under non-periodic forcing. Such self-oscillators are commonplace in biological and technological assemblies where temporal periodicity is needed, such as the beating of a human heart or the vibration of a cello string. While self-oscillation is well understood in classical non-linear systems and their quantized counterparts, the spontaneous emergence of periodicity in quantum systems without a semi-classical limit is more elusive. Here, we show that this behavior can emerge within the repeated-interaction description of open quantum systems. Specifically, we consider a many-body quantum system that undergoes dissipation due to sequential coupling with auxiliary systems at random times. We develop dynamical symmetry conditions that guarantee an oscillatory long-time state in this setting. Our rigorous results are illustrated with specific spin models, which could be implemented in trapped-ion quantum simulators.

We propose and analyze a mechanism for rectification of spin transport through a small junction between two spin baths or leads. For interacting baths we show that transport is conditioned on the spacial asymmetry of the quantum junction mediating the transport, and attribute this behavior to a gapped spectral structure of the lead-system-lead configuration. For non-interacting leads a minimal quantum model that allows for spin rectification requires an interface of only two interacting two-level systems. We obtain approximate results with a weak-coupling Born-master-equation in excellent agreement with matrix-product-state calculations that are extrapolated in time by mimicking absorbing boundary conditions. These results should be observable in controlled spin systems realized with cold atoms, trapped ions, or in electrons in quantum dot arrays.

We realize a heat engine using a single electron spin as a working medium. The spin pertains to the valence electron of a trapped $^{40}$Ca$^+$ ion, and heat reservoirs are emulated by controlling the spin polarization via optical pumping. The engine is coupled to the ion's harmonic-oscillator degree of freedom via spin-dependent optical forces. The oscillator stores the work produced by the heat engine and therefore acts as a flywheel. We characterize the state of the flywheel by reconstructing the Husimi $\mathcal{Q}$ function of the oscillator after different engine runtimes. This allows us to infer both the deposited energy and the corresponding fluctuations throughout the onset of operation, starting in the oscillator ground state. In order to understand the energetics of the flywheel, we determine its ergotropy, i.e. the maximum amount of work which can be further extracted from it. Our results demonstrate how the intrinsic fluctuations of a microscopic heat engine fundamentally limit performance.

Very recently, interferometric methods have been proposed to measure the full statistics of work performed on a driven quantum system [Dorner et al. Phys. Rev. Lett. 110 230601 (2013)] and [Mazzola et al. Phys. Rev. Lett. 110 230602 (2013)]. The advantage of such schemes is that they replace the necessity to make projective measurements by performing phase estimation on an appropriately coupled ancilla qubit. These proposals are one possible route to the tangible experimental exploration of quantum thermodynamics, a subject which is the centre of much current attention due to the current control of mesoscopic quantum systems. In this Letter we demonstrate that a modification of the phase estimation protocols can be used in order to measure the heat distribution of a quantum process. In addition we demonstrate how our scheme may be implemented using ion trap technology. Our scheme should pave the way for the first experimental explorations of the Landauer principle and hence the intricate energy to information conversion in mesoscopic quantum systems.