Quantum computing is an exciting field that uses quantum principles, such as quantum superposition and entanglement, to tackle complex computational problems. Superconducting quantum circuits, based on Josephson junctions, is one of the most promising physical realizations to achieve the long-term goal of building fault-tolerant quantum computers. The past decade has witnessed the rapid development of this field, where many intermediate-scale multi-qubit experiments emerged to simulate nonequilibrium quantum many-body dynamics that are challenging for classical computers. Here, we review the basic concepts of superconducting quantum simulation and their recent experimental progress in exploring exotic nonequilibrium quantum phenomena emerging in strongly interacting many-body systems, e.g., many-body localization, quantum many-body scars, and discrete time crystals. We further discuss the prospects of quantum simulation experiments to truly solve open problems in nonequilibrium many-body systems.
Quantum computing is an exciting field that uses quantum principles, such as quantum superposition and entanglement, to tackle complex computational problems. Superconducting quantum circuits, based on Josephson junctions, is one of the most promising physical realizations to achieve the long-term goal of building fault-tolerant quantum computers. The past decade has witnessed the rapid development of this field, where many intermediate-scale multi-qubit experiments emerged to simulate nonequilibrium quantum many-body dynamics that are challenging for classical computers. Here, we review the basic concepts of superconducting quantum simulation and their recent experimental progress in exploring exotic nonequilibrium quantum phenomena emerging in strongly interacting many-body systems, e.g., many-body localization, quantum many-body scars, and discrete time crystals. We further discuss the prospects of quantum simulation experiments to truly solve open problems in nonequilibrium many-body systems.
Superconducting circuits based on Josephson junctions are regarded as one of the most promising technologies for the implementation of scalable quantum computers. This review presents the basic principles of superconducting qubits and shows the progress of quantum computing and quantum simulation based on superconducting qubits in recent years. The experimental realization of gate operations, readout, error correction codes, as well as some quantum algorithms are summarized, followed by an introduction of quantum simulation. And then some important applications in fields including condensed matter physics, quantum annealing, and quantum chemistry are discussed.
Quantum computing introduces a revolutionary approach to solving problems that are computationally beyond the reach of classical systems. Among its most promising applications is the simulation of many-body systems, where strong particle interactions lead to complex quantum behaviors. Traditional computational techniques often fail due to exponential resource requirements, but quantum simulators can efficiently model these interactions through entanglement and superposition. Recent advances in superconducting qubits, trapped ions, and photonic quantum devices have enabled small- scale experimental demonstrations of spin models, Hubbard systems, and correlated electron dynamics. These developments offer new insights into condensed matter physics and quantum phase transitions. As quantum technologies continue to evolve, they hold the potential to transform the study of materials, superconductivity, and other many-body phenomena with remarkable precision and scalability.
Simulating quantum many-body systems on a classical computer generally requires a computational cost that grows exponential with the number of particles. This computational complexity has been the main obstacle to understanding various fundamental emergent phenomena in condensed matters such as high-Tc superconductivity and the fractional quantum-Hall effect. The difficulty arises because even the simplest models that are proposed to capture those phenomena cannot be simulated on a classical computer. Recognizing this problem in 1981, Richard Feynman envisioned a quantum simulator, an entirely new type of machine that exploits quantum superposition and operates by individually manipulating its constituting quantum particles and their interactions. Recent advances in various experimental platforms from cold atoms in optical lattices, trapped ions, to solid-state systems have brought the idea of Feynman to the realm of reality. Among those, interacting photons in superconducting circuits has been one of the promising platforms thanks to their local controllability and long coherence times. Early theoretical proposals have shown possibilities to realize quantum many-body phenomena of light using coupled cavity arrays such as Mott to superfluid transitions and fractional quantum Hall states. Start-of-the-art experiments include realization of interacting chiral edge states and stroboscopic signatures of localization of interacting photons in a three-site and a nine-site superconducting circuit, respectively. Interacting photons also serve as a natural platform to simulate driven-dissipative quantum many-body phenomena. A 72-site superconducting circuit has also recently been fabricated to study a dissipative phase transition of light.
Simulating quantum many-body systems on a classical computer generally requires a computational cost that grows exponential with the number of particles. This computational complexity has been the main obstacle to understanding various fundamental emergent phenomena in condensed matters such as high-Tc superconductivity and the fractional quantum-Hall effect. The difficulty arises because even the simplest models that are proposed to capture those phenomena cannot be simulated on a classical computer. Recognizing this problem in 1981, Richard Feynman envisioned a quantum simulator, an entirely new type of machine that exploits quantum superposition and operates by individually manipulating its constituting quantum particles and their interactions. Recent advances in various experimental platforms from cold atoms in optical lattices, trapped ions, to solid-state systems have brought the idea of Feynman to the realm of reality. Among those, interacting photons in superconducting circuits has been one of the promising platforms thanks to their local controllability and long coherence times. Early theoretical proposals have shown possibilities to realize quantum many-body phenomena of light using coupled cavity arrays such as Mott to superfluid transitions and fractional quantum Hall states. Start-of-the-art experiments include realization of interacting chiral edge states and stroboscopic signatures of localization of interacting photons in a three-site and a nine-site superconducting circuit, respectively. Interacting photons also serve as a natural platform to simulate driven-dissipative quantum many-body phenomena. A 72-site superconducting circuit has also recently been fabricated to study a dissipative phase transition of light.
Quantum hardware platforms are getting increasingly sophisticated in their ability to simulate condensed matter, including but not limited to strongly-correlated, topological, and non-equilibrium phenomena. This review surveys recent progress in quantum-hardware-based simulations of condensed matter, primarily emphasizing gate-based digital quantum computer simulation, with analog experiments discussed as complementary benchmarks. We first review major hardware platforms, including superconducting qubits, trapped-ions, ultracold atoms, Rydberg arrays, photonic systems, and moire quantum materials. We then introduce the basic ingredients of digital quantum simulation. Building on this foundation, we discuss representative applications to condensed-matter physics, spanning ground-state problems, strongly correlated matter, topological phases, non-equilibrium dynamics, open-system physics, and high-energy-physics-inspired simulations. Finally, we summarize key methodological tools used in state-of-the-art quantum-simulation workflows. We emphasize that present noisy quantum simulations serve not only as near-term demonstrations, but also as prototypes for the encodings, diagnostic protocols and error-control strategies required for future fault-tolerant quantum simulation.
Quantum simulation, as a practical application of noisy quantum computing, has aided the study of exotic quantum matters and the implementation of algorithms that outperform classical approaches. Superconducting qubits, one of the most promising candidates for realizing universal quantum computing, possess state-of-the-art features like easy integration of qubits, long coherence time, and high-fidelity single- and two-qubit gates. These characteristics have enabled applications of digital quantum simulation in the fields of physics, chemistry, and computer science. In this review, we first present the basic concepts of superconducting qubits, quantum gates, and digital quantum simulations. We also explore recent progress in digital quantum simulations using superconducting qubits, especially in relation to quantum chemistry, quantum matters, combinatorial optimization, and quantum machine learning. Finally, we address the current challenges of digital quantum simulation with superconducting qubits, and provide a perspective on the future of the field.