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arXiv:2502.01824 · SciPost Physics Core

Digital quantum simulation of bosonic systems and quantum complementarity

Victor P. Brasil, Diego S. Starke, Jonas Maziero

Published Nov 24, 2025• 0 citations
arXivHTMLPDF

Abstract

Digital quantum simulation (DQS) has emerged as a powerful approach to investigate complex quantum systems using digital quantum computers. Such systems, like many-particle bosonic systems and intricate optical experimental setups, pose significant challenges for classical simulation methods. In this paper, we utilize a general formalism for the DQS of bosonic systems, which consists of mapping bosonic operators to Pauli operators using the Gray code, in order to simulate interferometric variants of Afshar’s experiment—an intricate optical experiment—on IBM’s quantum computers. We investigated experiments analogous to Afshar’s double-slit experiment performed by Unruh and Pessoa Júnior, exploring discussions on the apparent violation of Bohr’s complementarity principle when considering the entire experimental setup. Based on the aforementioned experiments, we construct a variation of a delayed-choice setup. We also explore another experiment starting with a two-photon initial state. Finally, we analyze these experiments within the framework of an updated quantum complementarity principle, which applies to specific quantum state preparations and remains consistent with the foundational principles of Quantum Mechanics.

DOI
10.21468/scipostphyscore.8.4.086

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Abstract Quantum computers can efficiently simulate quantum systems evolving according to local interactions, making them valuable for exploring quantum many-body dynamics, despite current hardware and algorithmic challenges. In this work, we address the digital quantum simulations of linear optical elements which are inherently bosonic quantum systems. We adopt an encoding scheme based on Gray code to map bosonic states to qubits, which is efficient in terms of qubits and gate counts. Using a beam splitter as a representative example, we demonstrate the construction of quantum algorithms to simulate linear optical elements in quantum computers. To validate our algorithm, we performed a digital quantum simulation of the Hong-Ou-Mandel interference, a two-photon experiment. Our simulations, conducted both in quantum simulators and IBM quantum hardwares, successfully reproduced the characteristics of Hong-Ou-Mandel interference, validating our approach.
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Bohr's Complementarity Principle is a core concept of quantum mechanics. In this article, an updated complementarity relation for the wave and ondulatory aspects of a quantum system is presented and discussed. Two interferometric experiments are implemented in one and two qubit circuits and executed on real hardware. The final state density matrices are reconstructed using quantum state tomography and the complementarity relation is tested via direct computation. Results of the executions are presented both graphically and with a mean squared error analysis for a better comprehension.
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Abstract The parameters of a quantum system grow exponentially with the number of involved quantum particles. Hence, the associated memory requirement to store or manipulate the underlying wavefunction goes well beyond the limit of the best classical computers for quantum systems composed of a few dozen particles, leading to serious challenges in their numerical simulation. This implies that the verification and design of new quantum devices and experiments are fundamentally limited to small system size. It is not clear how the full potential of large quantum systems can be exploited. Here, we present the concept of quantum computer designed quantum hardware and apply it to the field of quantum optics. Specifically, we map complex experimental hardware for high-dimensional, many-body entangled photons into a gate-based quantum circuit. We show explicitly how digital quantum simulation of Boson sampling experiments can be realized. We then illustrate how to design quantum-optical setups for complex entangled photonic systems, such as high-dimensional Greenberger–Horne–Zeilinger states and their derivatives. Since photonic hardware is already on the edge of quantum supremacy and the development of gate-based quantum computers is rapidly advancing, our approach promises to be a useful tool for the future of quantum device design.