Arrow of time and its reversal on IBM quantum computer (1712.10057v2)

Abstract: Uncovering the origin of the arrow of time remains a fundamental scientific challenge. Within the framework of statistical physics, this problem was inextricably associated with the second law of thermodynamics, which declares that entropy growth proceeds from the system's entanglement with the environment. It remains to be seen, however, whether the irreversibility of time is a fundamental law of nature or whether, on the contrary, it might be circumvented. Here we show that, while in nature the complex conjugation needed for time reversal is exponentially improbable, one can design a quantum algorithm that includes complex conjugation and thus reverses a given quantum state. Using this algorithm on an IBM quantum computer enables us to experimentally demonstrate a backward time dynamics for an electron scattered on a two-level impurity.

• The paper introduces an experimental quantum algorithm that reverses time evolution in a controlled electron scattering setup, achieving approximately 85% fidelity in two-qubit systems.
• It employs quantum circuits with control, NOT, and Toffoli gates to model scattering dynamics on a two-level impurity, quantifying the impact of gate errors and decoherence.
• The study highlights that natural time-reversal events are virtually impossible, underscoring the complexity of entanglement and paving the way for advanced quantum reversibility research.

Arrow of Time and its Reversal on IBM Quantum Computer

The paper "Arrow of Time and its Reversal on IBM Quantum Computer," authored by G. B. Lesovik et al., presents an exploration of the fundamental question of time irreversibility within the framework of quantum mechanics. The research explores whether the arrow of time, as dictated by the Second Law of Thermodynamics, is an indelible principle or can be experimentally circumvented. This paper leverages the capabilities of a quantum computer to experimentally demonstrate the reversal of time dynamics for an electron scattered on a two-level impurity.

Summary and Findings

The paper begins by outlining the historical context of time's irreversibility, rooted in classical statistical mechanics and progressing through quantum mechanical conjectures by Landau, von Neumann, and Wigner. These conjectures essentially tie irreversibility to the measurement process and the entanglement-induced complexity, rendering time-reversal operations exponentially improbable in nature.

The authors propose a quantum algorithm capable of implementing the time-reversal operation by performing complex conjugation of quantum states, a task improbable in a natural setting but feasible on a quantum computer. Using IBM's quantum computing resources, they experimentally validate this algorithm by reversing the time evolution of a quantum state, specifically targeting a scenario involving an electron scattering off a two-level impurity.

Key Results

1. Model and Implementation:
   • The paper models the scattering process as a unitary evolution involving a two-level system (representing the impurity) and employs quantum circuits to simulate scattering dynamics. The time-reversal operation is executed by utilizing the control, NOT, and Toffoli gates native to quantum computation.
   • This model successfully demonstrates that under controlled conditions, time reversal can be executed with a fidelity dependent on quantum gate errors and coherence times.
2. Time-Reversal Complexity:
   • A significant insight is the quantification of time-reversal complexity, suggesting that spontaneous time-reversal events are practically non-existent within the universe's lifetime due to the entanglement and complexity involved, even for a single particle in free space.
3. Experimental Validation:
   • The experiment culminated with time-reversal fidelities of approximately 85% for two-qubit systems and 49% for three-qubit systems, indicating the current limits imposed by gate errors and decoherence within quantum computers but also marking a significant step toward understanding time reversibility in a quantum regime.

Implications and Future Directions

The potential implications of this research are manifold:

• Practical Applications: While the immediate applications in technology might be constrained by current quantum hardware limitations, the concepts could evolve to improve simulation techniques that require precise control over quantum states, such as error correction algorithms in quantum information processing.
• Theoretical Insights: This paper contributes fundamentally to our understanding of time symmetry in quantum mechanics and provides a platform for probing deeper into the nature of reversibility in quantum processes and systems with larger state spaces.
• Further Developments: Future exploration may extend this work to more complex systems, possibly incorporating interactions between multiple particles and impurities, with an aim to uncover the full scope of time-reversal operations and scalability challenges within larger, more entangled quantum systems.

In summary, this paper serves as an important demonstration of leveraging quantum computers to test hypotheses about time's arrow, and it establishes a foundation for further experiments aimed at probing quantum mechanics' fundamental limits. As quantum computing technology advances, the precision and complexity of such experiments can only be expected to augment, continuing to unravel new insights into the nature of time within our quantum universe.