Quantum Walks Generate and Evolve Magic for Enhanced Computation.

Discrete-time quantum walks dynamically generate significant quantum magic, a resource essential for computational tasks exceeding classical capabilities. Research utilising the Stabilizer Rényi Entropy demonstrates that the quantity and structure of this magic are strongly influenced by the initial coin state of single and two-walker systems on a one-dimensional lattice.

The pursuit of robust quantum computation necessitates resources exceeding those available to classical systems, with ‘magic’ – a measure of a quantum state’s non-classical correlations – proving a critical component. Researchers are now examining how this resource can be generated and manipulated within the framework of discrete-time quantum walks (DTQWs), a quantum analogue of classical random walks. A study published recently by Vikash Mittal, and Yi-Ping Huang, affiliated with National Tsing Hua University, the National Center for Theoretical Sciences, and Academia Sinica, details an investigation into the dynamic creation of magic within these DTQWs. Their work, entitled ‘Quantum Magic in Discrete-Time Quantum Walk’, utilises the Stabilizer Renyi Entropy to quantify magic generated by single- and two-walker systems on a one-dimensional lattice, revealing a complex relationship between initial coin states and the resulting magical properties, and suggesting DTQWs represent a viable platform for reliable quantum information processing.

Discrete-time quantum walks (DTQWs) demonstrably generate quantum states exhibiting significant ‘magic’, a critical resource for achieving computational advantages over classical computers. Magic, in this context, refers to the non-stabilizer content of a quantum state; states possessing this property are essential for universal quantum computation, enabling algorithms that surpass the capabilities of their classical counterparts. Research consistently indicates that DTQWs provide a reliable mechanism for producing these states, differing from approaches that necessitate intricate initial state preparation.

The quantity and structure of magic generated by a DTQW are strongly correlated with the initial state of the ‘coin operator’, a fundamental component of the walk that governs the probabilistic direction of movement. Manipulation of this initial coin state therefore provides a degree of control over the characteristics of the resulting quantum state, allowing for tailored generation of magic. The research focuses on systems involving single- and two-particle walks confined to one-dimensional lattices, providing a defined framework for analysis.

Quantifying this magic relies on the use of Stabilizer Rényi Entropy (SRE), a metric that specifically measures the non-stabilizer content of a quantum state. Stabilizer states are those that can be described by a relatively simple mathematical structure, and SRE effectively captures the degree to which a state deviates from this structure, thus indicating its ‘magic’. Analysis reveals a non-trivial relationship between magic and entanglement within the DTQW system; while entanglement is a necessary condition for quantum computation, magic represents a distinct and complementary resource.

DTQWs are presented as a readily accessible and controllable platform for generating these valuable quantum states, offering a dynamic approach compared to static state preparation methods. This controllability, coupled with the ability to tune the amount of magic generated via the initial coin state, positions DTQWs as a promising avenue for developing the quantum resources necessary to fully realise the potential of quantum computation.