<p>Coherence is essential for scaling quantum computers, yet its precise quantification remains challenging. In this work, we define the coherence content of a given quantum state and quantify the “quantum character'' of qubits by tracking the temporal evolution of their coherence through the diagonal elements of the density matrix - <i>C</i><sub><i>PDD</i></sub>. Unlike the widely used <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(l_{1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-norm, which lacks direct physical interpretation in observable population dynamics,<i> C</i><sub><i>PDD</i></sub> provides a self-normalized and linearly sensitive quantifier near maximally coherent states. Our analysis spans systems from two qubits to three qubits and beyond, using simulations to examine coherence in light–matter interactions and assess the effects of inter-qubit coupling, detuning, and interaction strength. These results provide a framework for identifying optimal conditions to maintain coherence, thereby enhancing the performance and scalability of future quantum algorithms.</p>

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Quantifying multi-qubit coherence

  • Shivang Pandey,
  • Debabrata Goswami

摘要

Coherence is essential for scaling quantum computers, yet its precise quantification remains challenging. In this work, we define the coherence content of a given quantum state and quantify the “quantum character'' of qubits by tracking the temporal evolution of their coherence through the diagonal elements of the density matrix - CPDD. Unlike the widely used \(l_{1}\) l 1 -norm, which lacks direct physical interpretation in observable population dynamics, CPDD provides a self-normalized and linearly sensitive quantifier near maximally coherent states. Our analysis spans systems from two qubits to three qubits and beyond, using simulations to examine coherence in light–matter interactions and assess the effects of inter-qubit coupling, detuning, and interaction strength. These results provide a framework for identifying optimal conditions to maintain coherence, thereby enhancing the performance and scalability of future quantum algorithms.