Quantum Complexity and Holography

Quantum holography with undetected photons (QHUP) enables the complex amplitude of infrared to be acquired beyond the sensitivity range of silicon based sensors, through induced coherence withoud induced emission. QHUP generally requires multiple phase-shifted holograms to retrieve the complex-amplitude distribution of an object, which limits measurement stability and temporal resolution. Although classical parallel phase-shifting holography provides a favorable balance between temporal and spatial resolution, it has not previously been implemented in QHUP because of the constraints imposed by photon distinguishability. In this study, we propose a quantum eraser-based geometric phase-shifting QHUP. By accurately erasing not only polarization distinguishability but also temporal distinguishability arising from differences in the optical paths, the complex-amplitude distribution of an object can be retrieved in a single shot using a silicon-based image sensor equipped with a polarization-filter array. This single-shot acquisition, combined with real-time processing, enables the observation of dynamic objects in the near-infrared spectral region. To the best of our knowledge, these experimental results constitute the first real-time acquisition of the complex-amplitude distribution of a near-infrared object using QHUP with a silicon-based image sensor equipped with a polarization-filter array. Furthermore, to enhance the reproducibility and applicability of this study, the experimental optical setup, bill of materials, and source code for real-time imaging have been made openly available. The ability to retrieve the complex-amplitude information carried by undetected photons in real time is expected to extend the applicability of QHUP to a wide range of fields, including spectroscopic imaging and semiconductor inspection.Quantum holography with undetected photons (QHUP) enables the complex amplitude of infrared to be acquired beyond the sensitivity range of silicon based sensors, through induced coherence withoud induced emission. QHUP generally requires multiple phase-shifted holograms to retrieve the complex-amplitude distribution of an object, which limits measurement stability and temporal resolution. Although classical parallel phase-shifting holography provides a favorable balance between temporal and spatial resolution, it has not previously been implemented in QHUP because of the constraints imposed by photon distinguishability. In this study, we propose a quantum eraser-based geometric phase-shifting QHUP. By accurately erasing not only polarization distinguishability but also temporal distinguishability arising from differences in the optical paths, the complex-amplitude distribution of an object can be retrieved in a single shot using a silicon-based image sensor equipped with a polarization-filter array. This single-shot acquisition, combined with real-time processing, enables the observation of dynamic objects in the near-infrared spectral region. To the best of our knowledge, these experimental results constitute the first real-time acquisition of the complex-amplitude distribution of a near-infrared object using QHUP with a silicon-based image sensor equipped with a polarization-filter array. Furthermore, to enhance the reproducibility and applicability of this study, the experimental optical setup, bill of materials, and source code for real-time imaging have been made openly available. The ability to retrieve the complex-amplitude information carried by undetected photons in real time is expected to extend the applicability of QHUP to a wide range of fields, including spectroscopic imaging and semiconductor inspection.

arXiv:2609.10907Sep 9, 20260 citations

Holographic nature of quantum reality

Vitaly Kuyukov

Dec 1, 20130 citations

Quantum coincidence holography

Éric Lantz, A. Mosset, Florent Bassignot +1 more

Sep 5, 20180 citations

Weighting gates in circuit complexity and holography

Ibrahim Akal

Abstract Motivated by recent studies of quantum computational complexity in quantum field theory and holography, we discuss how weighting certain classes of gates building up a quantum circuit more heavily than others affects the complexity. Utilizing Nielsen’s geometric approach to circuit complexity, we investigate the effects for a regulated field theory for which the optimal circuit is a representation of $GL(N,\mathbb{R})$ . More precisely, we work out how a uniformly chosen weighting factor acting on the entangling gates affects the complexity and, particularly, its divergent behavior. We show that assigning a higher cost to the entangling gates increases the complexity. Employing penalized and unpenalized complexities for the $\mathcal{F}_{\kappa=2}$ cost, we further find an interesting relation between the latter and that based on the unpenalized $\mathcal{F}_{\kappa=1}$ cost. In addition, we exhibit how imposing such penalties modifies the leading-order UV divergence in the complexity. We show that appropriately tuning the gate weighting eliminates the additional logarithmic factor, thus resulting in a simple power-law scaling. We also compare the circuit complexity with holographic predictions, specifically based on the complexity=action conjecture, and relate the weighting factor to certain bulk quantities. Finally, we comment on certain expectations concerning the role of gate penalties in defining complexity in field theory and also speculate on possible implications for holography.Abstract Motivated by recent studies of quantum computational complexity in quantum field theory and holography, we discuss how weighting certain classes of gates building up a quantum circuit more heavily than others affects the complexity. Utilizing Nielsen’s geometric approach to circuit complexity, we investigate the effects for a regulated field theory for which the optimal circuit is a representation of $GL(N,\mathbb{R})$. More precisely, we work out how a uniformly chosen weighting factor acting on the entangling gates affects the complexity and, particularly, its divergent behavior. We show that assigning a higher cost to the entangling gates increases the complexity. Employing penalized and unpenalized complexities for the $\mathcal{F}_{\kappa=2}$ cost, we further find an interesting relation between the latter and that based on the unpenalized $\mathcal{F}_{\kappa=1}$ cost. In addition, we exhibit how imposing such penalties modifies the leading-order UV divergence in the complexity. We show that appropriately tuning the gate weighting eliminates the additional logarithmic factor, thus resulting in a simple power-law scaling. We also compare the circuit complexity with holographic predictions, specifically based on the complexity=action conjecture, and relate the weighting factor to certain bulk quantities. Finally, we comment on certain expectations concerning the role of gate penalties in defining complexity in field theory and also speculate on possible implications for holography.

arXiv:1903.06156Progress of Theoretical and Experimental PhysicsJul 21, 20215 citations

GL(N,\mathbb{R})

. More precisely, we work out how a uniformly chosen weighting factor acting on the entangling gates affects the complexity and, particularly, its divergent behavior. We show that assigning a higher cost to the entangling gates increases the complexity. Employing penalized and unpenalized complexities for the

\mathcal{F}_{\kappa=2}

cost, we further find an interesting relation between the latter and that based on the unpenalized

\mathcal{F}_{\kappa=1}

cost. In addition, we exhibit how imposing such penalties modifies the leading-order UV divergence in the complexity. We show that appropriately tuning the gate weighting eliminates the additional logarithmic factor, thus resulting in a simple power-law scaling. We also compare the circuit complexity with holographic predictions, specifically based on the complexity=action conjecture, and relate the weighting factor to certain bulk quantities. Finally, we comment on certain expectations concerning the role of gate penalties in defining complexity in field theory and also speculate on possible implications for holography.