Abstract The quantum Rubik's cube exhibits distinctive dual characteristics of high dimensionality and multi‐projection. Its multi‐projection surfaces can present quantum system information from diverse angles, whereas its high‐dimensional nature can be harnessed to probe complex system architectures. In this study, a quantum Rubik's cube is integrated with the Heisenberg model to formulate a novel Hamiltonian form. A fourth‐order quantum Rubik's cube is used to investigate the quantum phase transition, and a fifth‐order Rubik's cube is used to simulate the jumps of electrons across different energy levels, demonstrating the effectiveness of this approach. This holds significant potential for enabling physicists to delve more profoundly into the characteristics and laws of quantum systems, thereby providing substantial support for the theoretical advancement of quantum physics.
Abstract The quantum Rubik's cube exhibits distinctive dual characteristics of high dimensionality and multi‐projection. Its multi‐projection surfaces can present quantum system information from diverse angles, whereas its high‐dimensional nature can be harnessed to probe complex system architectures. In this study, a quantum Rubik's cube is integrated with the Heisenberg model to formulate a novel Hamiltonian form. A fourth‐order quantum Rubik's cube is used to investigate the quantum phase transition, and a fifth‐order Rubik's cube is used to simulate the jumps of electrons across different energy levels, demonstrating the effectiveness of this approach. This holds significant potential for enabling physicists to delve more profoundly into the characteristics and laws of quantum systems, thereby providing substantial support for the theoretical advancement of quantum physics.
This paper explores the potential of algorithmic quantum simulation to accelerate the study and analysis of complex, multi-dimensional dynamical systems. We introduce a novel quantum algorithm designed to efficiently explore the state space of these systems, offering a significant advantage over classical simulation techniques, particularly for systems with intricate dynamics and high dimensionality. The core mechanism focuses on utilizing quantum properties to overcome computational bottlenecks and enable more rapid simulations. We outline the algorithm's architecture, key quantum operations, and potential applications within diverse fields such as physics, chemistry, and materials science. The paper concludes with a discussion of future research directions and the expected impact of this approach on the field of quantum computation.
Quantum computing offers a new paradigm for advancing high-energy physics research by enabling novel methods for representing and reasoning about fundamental quantum mechanical phenomena.Realizing these ideals will require the development of novel computational tools for modeling and simulation, detection and classification, data analysis, and forecasting of high-energy physics (HEP) experiments.While the emerging hardware, software, and applications of quantum computing are exciting opportunities, significant gaps remain in integrating such techniques into the HEP community research programs.Here we identify both the challenges and opportunities for developing quantum computing systems and software to advance HEP discovery science.We describe opportunities for the focused development of algorithms, applications, software, hardware, and infrastructure to support both practical and theoretical applications of quantum computing to HEP problems within the next 10 years.
Abstract These are exciting times for quantum physics as new quantum technologies are expected to soon transform computing at an unprecedented level. Simultaneously network science is flourishing proving an ideal mathematical and computational framework to capture the complexity of large interacting systems. Here we provide a comprehensive and timely review of the rising field of complex quantum networks. On one side, this subject is key to harness the potential of complex networks in order to provide design principles to boost and enhance quantum algorithms and quantum technologies. On the other side this subject can provide a new generation of quantum algorithms to infer significant complex network properties. The field features fundamental research questions as diverse as designing networks to shape Hamiltonians and their corresponding phase diagram, taming the complexity of many-body quantum systems with network theory, revealing how quantum physics and quantum algorithms can predict novel network properties and phase transitions, and studying the interplay between architecture, topology and performance in quantum communication networks. Our review covers all of these multifaceted aspects in a self-contained presentation aimed both at network-curious quantum physicists and at quantum-curious network theorists. We provide a framework that unifies the field of quantum complex networks along four main research lines: network-generalized, quantum-applied, quantum-generalized and quantum-enhanced. Finally we draw attention to the connections between these research lines, which can lead to new opportunities and new discoveries at the interface between quantum physics and network science.
Simulation is a ubiquitous tool for understanding and predicting the behavior of complex systems, ranging from those in natural sciences to those in social studies. When it comes to quantum systems, however, conventional simulation methods encounter fundamental limitations imposed by quantum physics. To overcome this challenge, the concept of using quantum systems to simulate other quantum systems, namely, quantum simulation, has emerged as an indispensable paradigm. In this special issue, we explore the underlying concepts and theoretical frameworks that drive this rapidly developing field.
Abstract Rubik’s Cube is one of the most famous combinatorial puzzles involving nearly 4.3 × 1019 possible configurations. However, only a single configuration matches the solved one. Its mathematical description is expressed by the Rubik’s group, whose elements define how its layers rotate. We develop a unitary representation of the Rubik’s group and a quantum formalism to describe the Cube based on its geometrical constraints. Using single particle quantum states, we describe the cubies as bosons for corners and fermions for edges. By introducing a set of four Ising-like Hamiltonians, we managed to set the solved configuration of the Cube as the global ground state for all the Hamiltonians. To reach the ground state of all the Hamiltonian operators, we made use of a Deep Reinforcement Learning algorithm based on a Hamiltonian reward. The Rubik’s Cube is successfully solved through four phases, each phase driven by a corresponding Hamiltonian reward based on its energy spectrum. We call our algorithm QUBE, as it employs quantum mechanics to tackle the combinatorial problem of solving the Rubik’s Cube. Embedding combinatorial problems into the quantum mechanics formalism suggests new possible algorithms and future implementations on quantum hardware.
Abstract A theoretical scheme is proposed to simulate the quantum phase transitions (QPTs) of the three-level Dicke model. In this designed hybrid system, an ensemble of solid-state spins can simultaneously couple to a superconducting microwave (MW) resonator and a surface-acoustic-wave (SAW) cavity, and then ensure the simulation of the Λ type Dicke model with the acoustic-MW dual-channel transitions. Using a generalized Holstein-Primakoff (HP) mapping in the thermodynamic limit, we derive an effective Hamiltonian that preserves a Z 2 × Z 2 parity symmetry and therefore potentially supports a rich phase diagram. We obtain analytic expressions for the critical couplings of the three phases: the normal, superradiant I and superradiant II phases. We obtain analytic expressions for the critical couplings of three phases: the normal, superradiant I, and superradiant II phases. Among these, we can deterministically identify both first-order (discontinuous) and second-order (continuous) quantum phase transitions with distinct boundary characteristics. Additionally, rigorous diagonalization of the quadratic fluctuation Hamiltonian yields four excitation energies, whose behaviors further clarify the order and continuity of each phase transition. This attempt opens an interesting avenue for simulating multilevel QPTs by jointly using different coupling transducers, including acoustics, mechanics, magnons, and electromagnetics.