RQS Seminar

In this talk, Dr Bermúdez will start by reviewing the recent progress of analog quantum simulators based on crystals of trapped atomic ions. He will discuss recent experiments that exploit both the electronic and vibrational degrees of freedom to simulate spin models and bosonic lattice models.

Circuit QED enables the combined use of qubits and oscillator modes. Despite a variety of available gate sets, many hybrid qubit-boson (i.e., oscillator) operations are realizable only through optimal control theory (OCT) which is oftentimes intractable and uninterpretable. We introduce an analytic approach with rigorously proven error bounds for realizing specific classes of operations via two matrix product formulas commonly used in Hamiltonian simulation, the Lie–Trotter and Baker–Campbell–Hausdorff product formulas.

Hamiltonian simulation is one of the most promising applications of quantum computing. Recent experimental results suggest that continuous-time analog quantum simulation would be advantageous over gate-based digital quantum simulation in the Noisy Intermediate-Size Quantum (NISQ) machine era. However, programming such analog quantum simulators is much more challenging due to the lack of a unified interface between hardware and software, and the only few known examples are all hardware-specific.

One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Trapped-ion quantum computers provide a pristine one-dimensional spin system, featuring high isolation from the environment, high-fidelity measurement and preparation of individual spins, and fully connected spin-spin interactions.

Trapped atomic ions are a highly versatile platform for quantum simulation and computation. In this talk, I will provide a brief description of the quantum control that enables both analog and digital modes of quantum simulation on this platform before reporting on two recent results: a digital quantum simulation that measured the first out-of-time-order correlators in a thermal system, and an analog simulation of particles with exotic statistics.

Abstract: The pillars of quantum theory include entanglement and operators' failure to commute. The Page curve quantifies the bipartite entanglement of a many-body system in a random pure state. This entanglement is known to decrease if one constrains extensive observables that commute with each other (Abelian ``charges''). Non-Abelian charges, which fail to commute with each other, are of current interest in quantum information and thermodynamics.

Error-mitigation techniques can enable access to accurate estimates of physical observables that are otherwise biased by noise in pre-fault-tolerant quantum computers. One particularly general error-mitigation technique is probabilistic error cancellation (PEC), which effectively inverts a well-characterized noise channel to produce noise-free estimates of observables. Experimental realizations of this technique, however, have been impeded by the challenge of learning correlated noise in large quantum circuits.

In recent years, there have been rapid breakthroughs in quantum technologies that offer new opportunities for advancing the understanding of basic quantum phenomena; realizing novel strongly correlated systems; and enhancing applications in quantum communication, computation, and sensing. Cutting edge quantum technologies simultaneously require high fidelity quantum-limited measurements and control. Large-scale applications of these capabilities hinge on understanding system-reservoir dynamics of many-body quantum systems, whose Hilbert space grows exponentially with system size.

Previous work by Brakerski et al. (2018) described a 2-party interactive protocol that enables one party to prove that they have quantum computational abilities. The protocol is based on the Learning With Errors (LWE) assumption, a standard computational hardness assumption from classical cryptography. In this talk, I will give an introduction to the protocol of Brakerski et al., and then I will discuss a recent paper of ours that optimizes their protocol and brings it closer to experimental realization.

Quantum computers offer the potential to perform simulations of nuclear processes that are infeasible for classical devices. With a goal of understanding the necessary quantum resources to realize such potential, we estimate the qubit costs and gate costs to simulate an effective nuclear field theory on a cubic lattice, evaluating the various trade-offs in choice of the form of the effective field theory and how this choice interacts with the qubit requirements of encoding the fermionic degrees of freedom into qubits and the gate counts needed for state-of-the-art Hamiltonian simulation.