Trade-offs between precision and fluctuations in charging finite-dimensional quantum batteries.

Within quantum thermodynamics, many tasks are modeled by processes that require work sources represented by out-of-equilibrium quantum systems, often dubbed quantum batteries, in which work can be deposited or from which work can be extracted. Here we consider quantum batteries modeled as finite-dimensional quantum systems initially in thermal equilibrium that are charged via cyclic Hamiltonian processes. We present optimal or near-optimal protocols for N identical two-level systems and individual d-level systems with equally spaced energy gaps in terms of the charging precision and work fluctuations during the charging process. We analyze the trade-off between these figures of merit as well as the performance of local and global operations.

Entanglement Quantification in Atomic Ensembles.

Entanglement measures quantify nonclassical correlations present in a quantum system, but can be extremely difficult to calculate, even more so, when information on its state is limited. Here, we consider broad families of entanglement criteria that are based on variances of arbitrary operators and analytically derive the lower bounds these criteria provide for two relevant entanglement measures: the best separable approximation and the generalized robustness. This yields a practical method for quantifying entanglement in realistic experimental situations, in particular, when only few measurements of simple observables are available. As a concrete application of this method, we quantify bipartite and multipartite entanglement in spin-squeezed Bose-Einstein condensates of ∼500 atoms, by lower bounding the best separable approximation and the generalized robustness only from measurements of first and second moments of the collective spin operator.

Entangling logical qubits with lattice surgery.

The development of quantum computing architectures from early designs and current noisy devices to fully fledged quantum computers hinges on achieving fault tolerance using quantum error correction1-4. However, these correction capabilities come with an overhead for performing the necessary fault-tolerant logical operations on logical qubits (qubits that are encoded in ensembles of physical qubits and protected by error-correction codes)5-8. One of the most resource-efficient ways to implement logical operations is lattice surgery9-11, where groups of physical qubits, arranged on lattices, can be merged and split to realize entangling gates and teleport logical information. Here we report the experimental realization of lattice surgery between two qubits protected via a topological error-correction code in a ten-qubit ion-trap quantum information processor. In this system, we can carry out the necessary quantum non-demolition measurements through a series of local and entangling gates, as well as measurements on auxiliary qubits. In particular, we demonstrate entanglement between two logical qubits and we implement logical state teleportation between them. The demonstration of these operations-fundamental building blocks for quantum computation-through lattice surgery represents a step towards the efficient realization of fault-tolerant quantum computation.

Fault-tolerant interface between quantum memories and quantum processors.

Topological error correction codes are promising candidates to protect quantum computations from the deteriorating effects of noise. While some codes provide high noise thresholds suitable for robust quantum memories, others allow straightforward gate implementation needed for data processing. To exploit the particular advantages of different topological codes for fault-tolerant quantum computation, it is necessary to be able to switch between them. Here we propose a practical solution, subsystem lattice surgery, which requires only two-body nearest-neighbor interactions in a fixed layout in addition to the indispensable error correction. This method can be used for the fault-tolerant transfer of quantum information between arbitrary topological subsystem codes in two dimensions and beyond. In particular, it can be employed to create a simple interface, a quantum bus, between noise resilient surface code memories and flexible color code processors.

Energetics of correlations in interacting systems.

A fundamental connection between thermodynamics and information theory arises from the fact that correlations exhibit an inherent work value. For noninteracting systems this translates to a work cost for establishing correlations. Here we investigate the relationship between work and correlations in the presence of interactions that cannot be controlled or removed. For such naturally coupled systems, which are correlated even in thermal equilibrium, we determine general strategies that can reduce the work cost of correlations, and illustrate these for a selection of exemplary physical systems.

Coherent controlization using superconducting qubits.

Coherent controlization, i.e., coherent conditioning of arbitrary single- or multi-qubit operations on the state of one or more control qubits, is an important ingredient for the flexible implementation of many algorithms in quantum computation. This is of particular significance when certain subroutines are changing over time or when they are frequently modified, such as in decision-making algorithms for learning agents. We propose a scheme to realize coherent controlization for any number of superconducting qubits coupled to a microwave resonator. For two and three qubits, we present an explicit construction that is of high relevance for quantum learning agents. We demonstrate the feasibility of our proposal, taking into account loss, dephasing, and the cavity self-Kerr effect.

Thermodynamics of creating correlations: Limitations and optimal protocols.

We establish a rigorous connection between fundamental resource theories at the quantum scale. Correlations and entanglement constitute indispensable resources for numerous quantum information tasks. However, their establishment comes at the cost of energy, the resource of thermodynamics, and is limited by the initial entropy. Here, the optimal conversion of energy into correlations is investigated. Assuming the presence of a thermal bath, we establish general bounds for arbitrary systems and construct a protocol saturating them. The amount of correlations, quantified by the mutual information, can increase at most linearly with the available energy, and we determine where the linear regime breaks down. We further consider the generation of genuine quantum correlations, focusing on the fundamental constituents of our universe: fermions and bosons. For fermionic modes, we find the optimal entangling protocol. For bosonic modes, we show that while Gaussian operations can be outperformed in creating entanglement, their performance is optimal for high energies.