Verified Quantum Information Scrambling

Abstract: Quantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout the entire system. This concept underlies the dynamics of thermalization in closed quantum systems, and more recently has emerged as a powerful tool for characterizing chaos in black holes. However, the direct experimental measurement of quantum scrambling is difficult, owing to the exponential complexity of ergodic many-body entangled states. One way to characterize quantum scrambling is to measure an out-of-time-ordered correlation function (OTOC); however, since scrambling leads to their decay, OTOCs do not generally discriminate between quantum scrambling and ordinary decoherence. Here, we implement a quantum circuit that provides a positive test for the scrambling features of a given unitary process. This approach conditionally teleports a quantum state through the circuit, providing an unambiguous litmus test for scrambling while projecting potential circuit errors into an ancillary observable. We engineer quantum scrambling processes through a tunable 3-qubit unitary operation as part of a 7-qubit circuit on an ion trap quantum computer. Measured teleportation fidelities are typically $\sim80\%$, and enable us to experimentally bound the scrambling-induced decay of the corresponding OTOC measurement.

• The paper experimentally verifies quantum information scrambling by implementing a teleportation-based protocol on a 7-qubit ion trap.
• The paper employs a tunable scrambling unitary and projective EPR measurements that achieve teleportation fidelities of 70-80%, effectively dispersing local quantum data.
• The results provide a robust test for distinguishing true quantum scrambling from noise, advancing our understanding of quantum chaos and thermalization.

Essay on "Verified Quantum Information Scrambling"

The paper "Verified Quantum Information Scrambling" presents a detailed experimental investigation into the concept of quantum scrambling using a quantum teleportation protocol. This research builds on theoretical frameworks to experimentally verify the scrambling features of unitary processes on a quantum computer composed of seven trapped ion qubits. By providing a robust litmus test for quantum scrambling, the authors aim to improve our understanding of quantum thermalization and chaos within complex quantum systems, with implications for both fundamental physics and practical quantum information processing.

The experimental setup involves a sequence of interactions between qubits, using a tunable scrambling unitary process within a 7-qubit circuit. The scrambling unitary is deployed with the goal of dispersing localized quantum information across the entire system through entanglement and correlations. The experiment simulates a theoretical model that draws a parallel to information loss in black holes, wherein a quantum state initially accessible to one party (Alice) becomes inaccessible without a specific decoding process. The paper leverages the analogy to black hole dynamics and proposes an explicit teleportation protocol that can distinguish between unitary scrambling, decoherence, and experimental noise.

Key aspects of the experiment include outlining the teleportation protocol that decodes Alice's scrambled quantum state using Bob's entangled quantum memory and an ancillary EPR pair. Here, the authors take advantage of projective EPR measurements to teleport the initial quantum state, showcasing the method's effectiveness in identifying unitary scrambling. Importantly, the protocol counters challenges associated with evaluating out-of-time-ordered correlators (OTOCs) in noisy conditions, as traditional OTOC decay measurements can be confounded by non-unitary processes, suggesting scrambling inaccurately.

Experimentally, the authors employ a quantum computing layout using a trapped ion system, with remarkable state detection fidelity of 99.4% and operational fidelity of single-qubit and two-qubit gates achieving approximately 99% and 98.5%, respectively. The choice of the maximally scrambling unitary $\hat{U}_s$ and its classical counterpart $\hat{U}_c$ are elucidated, with $\hat{U}_s$ demonstrating the ability to array quantum information completely across all subsystems. Contrarily, $\hat{U}_c$, categorized as a classical scrambling operator, affects only phase information without altering population states, rendering it less effective for teleportation except for specific basis states.

A strong focus is given to the numerical results depicted in the experimental data, affirming teleportation fidelities around 70-80% under scrambling conditions. Such outcomes illustrate successful quantum scrambling, allowing the authors to derive an upper bound on quantum scrambling in error-free evolution contexts. Additionally, a deterministic teleportation protocol employs Grover's search function, which evaluates higher-order OTOC dynamics to substantiate findings.

In discussing the implications, the authors propose several future directions, including extending experimental capabilities for larger circuits with Haar random unitaries and probing the role of non-classical scrambling dynamics further. Furthermore, the authors hint at the potential for experimental analogs of gravitational probes within quantum systems, potentially offering novel insights into understanding quantum gravity concerns. The paper's contributions contain relevant advancements both theoretically and experimentally, signifying a rigorous approach to probing chaotic dynamics in quantum systems.

Overall, the research proposes a landmark experiment effectively dissecting the nature of quantum scrambling and delineating between true quantum mechanical processes and experimental artifacts or noise, reinforcing both our theoretical and practical grasp of quantum chaotic systems.