157 research outputs found
Characterizing quantum instruments: from non-demolition measurements to quantum error correction
In quantum information processing quantum operations are often processed
alongside measurements which result in classical data. Due to the information
gain of classical measurement outputs non-unitary dynamical processes can take
place on the system, for which common quantum channel descriptions fail to
describe the time evolution. Quantum measurements are correctly treated by
means of so-called quantum instruments capturing both classical outputs and
post-measurement quantum states. Here we present a general recipe to
characterize quantum instruments alongside its experimental implementation and
analysis. Thereby, the full dynamics of a quantum instrument can be captured,
exhibiting details of the quantum dynamics that would be overlooked with common
tomography techniques. For illustration, we apply our characterization
technique to a quantum instrument used for the detection of qubit loss and
leakage, which was recently implemented as a building block in a quantum error
correction (QEC) experiment (Nature 585, 207-210 (2020)). Our analysis reveals
unexpected and in-depth information about the failure modes of the
implementation of the quantum instrument. We then numerically study the
implications of these experimental failure modes on QEC performance, when the
instrument is employed as a building block in QEC protocols on a logical qubit.
Our results highlight the importance of careful characterization and modelling
of failure modes in quantum instruments, as compared to simplistic
hardware-agnostic phenomenological noise models, which fail to predict the
undesired behavior of faulty quantum instruments. The presented methods and
results are directly applicable to generic quantum instruments.Comment: 28 pages, 21 figure
U(1) Wilson lattice gauge theories in digital quantum simulators
Lattice gauge theories describe fundamental phenomena in nature, but
calculating their real-time dynamics on classical computers is notoriously
difficult. In a recent publication [Nature 534, 516 (2016)], we proposed and
experimentally demonstrated a digital quantum simulation of the paradigmatic
Schwinger model, a U(1)-Wilson lattice gauge theory describing the interplay
between fermionic matter and gauge bosons. Here, we provide a detailed
theoretical analysis of the performance and the potential of this protocol. Our
strategy is based on analytically integrating out the gauge bosons, which
preserves exact gauge invariance but results in complicated long-range
interactions between the matter fields. Trapped-ion platforms are naturally
suited to implementing these interactions, allowing for an efficient quantum
simulation of the model, with a number of gate operations that scales only
polynomially with system size. Employing numerical simulations, we illustrate
that relevant phenomena can be observed in larger experimental systems, using
as an example the production of particle--antiparticle pairs after a quantum
quench. We investigate theoretically the robustness of the scheme towards
generic error sources, and show that near-future experiments can reach regimes
where finite-size effects are insignificant. We also discuss the challenges in
quantum simulating the continuum limit of the theory. Using our scheme,
fundamental phenomena of lattice gauge theories can be probed using a broad set
of experimentally accessible observables, including the entanglement entropy
and the vacuum persistence amplitude
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