Over the last decade, quantum simulation and computation has progressed from a purely scientific testbed of quantum mechanics to a mature field that is starting to offer new insights into materials, quantum effects, and algorithms that are intractable with even the most state-of-the-art classical computation. Simulating certain quantum Hamiltonians that are theorized to be at the heart of high-Tc superconductivity, topological quantum systems such as the fractional quantum Hall effect or fundamental questions of thermalization quickly exceed the available memory of even the most advanced supercomputers – and in fact all memory in the world – due to the exponential growth of the Hilbert space with system size. As postulated by Feynman himself, the computational system best suited for solving quantum problems is to use a quantum system itself, as it can intrinsically represent the entanglement that is the key resource making quantum computing challenging but also promising. Apart from simulating problems in physics and chemistry, there is also tremendous excitement for quantum computers to provide speedups for general algorithms in optimization at a rate that is exponentially faster than existing classical programming. So far only a small class of algorithms has been actually proven to provide such a speedup, most prominently Shor's algorithm which can factor large prime numbers, and several other search and oracle algorithms. In the last two decades, many experiments using ultracold atoms, ions, or superconducting circuits have focused on analog quantum simulation. Here, a model Hamiltonian that is believed to capture all the relevant physics of the system of study is experimentally realized using different building blocks and interactions but replicating condensed matter effects at an increased scale. This has led to a number of bespoke experiments such as BEC/Fermigass machines, quantum gas microscopes and more exotic setups that are purpose built to study a particular effect. More recently, there has been a shift to develop more universal simulation platforms and optical tweezer arrays have emerged as a leading solution due to their high degree of reconfigurability. Through tremendous improvements in the degree of control and measurement of single qubits, error correction has become a viable route to build a true universal digital quantum computer. Even as we transition into the digital age of quantum simulation, certain classes of problems with additional physics constraints such as Fermionic statistics, gauge fields and lattice gauge theories still incur too large of an overhead to be encoded on these digital simulators. In this thesis, we use a highly degenerate twisted cavity to simulate the effect of a magnetic field on a two-dimensional system of interacting photons to enable realization of states of the quantum Hall effect. We design, build, and commission a new lens based cavity apparatus realizing a lowest Landau level for a mesoscopic number of modes. We demonstrate the integration of highly excited Rydberg atoms to mediate strong interactions and demonstrate photon blockade as well as mean field interactions. As a second application of cavities to quantum information leveraging our newfound comfort with intra-cavity optics, and experience with aberration modeling in resonators, we demonstrate a new class of small waist optical resonators enabled by lens-based cavities and then apply our understanding of optical aberrations in cavities to the development of a new class of cavity array. This Cavity Array Microscope (CAM) realizes a large number of cavities (up to currently 600) using only a fixed number of free space optics and is both scalable with constant overhead as well as compatible with Rydberg atoms. This platform provides a route to highly parallel quantum repeater operation or entanglement generation between atom arrays in the future.
Over the last decade, quantum simulation and computation has progressed from a purely scientific testbed of quantum mechanics to a mature field that is starting to offer new insights into materials, quantum effects, and algorithms that are intractable with even the most state-of-the-art classical computation. Simulating certain quantum Hamiltonians that are theorized to be at the heart of high-Tc superconductivity, topological quantum systems such as the fractional quantum Hall effect or fundamental questions of thermalization quickly exceed the available memory of even the most advanced supercomputers – and in fact all memory in the world – due to the exponential growth of the Hilbert space with system size. As postulated by Feynman himself, the computational system best suited for solving quantum problems is to use a quantum system itself, as it can intrinsically represent the entanglement that is the key resource making quantum computing challenging but also promising. Apart from simulating problems in physics and chemistry, there is also tremendous excitement for quantum computers to provide speedups for general algorithms in optimization at a rate that is exponentially faster than existing classical programming. So far only a small class of algorithms has been actually proven to provide such a speedup, most prominently Shor's algorithm which can factor large prime numbers, and several other search and oracle algorithms. In the last two decades, many experiments using ultracold atoms, ions, or superconducting circuits have focused on analog quantum simulation. Here, a model Hamiltonian that is believed to capture all the relevant physics of the system of study is experimentally realized using different building blocks and interactions but replicating condensed matter effects at an increased scale. This has led to a number of bespoke experiments such as BEC/Fermigass machines, quantum gas microscopes and more exotic setups that are purpose built to study a particular effect. More recently, there has been a shift to develop more universal simulation platforms and optical tweezer arrays have emerged as a leading solution due to their high degree of reconfigurability. Through tremendous improvements in the degree of control and measurement of single qubits, error correction has become a viable route to build a true universal digital quantum computer. Even as we transition into the digital age of quantum simulation, certain classes of problems with additional physics constraints such as Fermionic statistics, gauge fields and lattice gauge theories still incur too large of an overhead to be encoded on these digital simulators. In this thesis, we use a highly degenerate twisted cavity to simulate the effect of a magnetic field on a two-dimensional system of interacting photons to enable realization of states of the quantum Hall effect. We design, build, and commission a new lens based cavity apparatus realizing a lowest Landau level for a mesoscopic number of modes. We demonstrate the integration of highly excited Rydberg atoms to mediate strong interactions and demonstrate photon blockade as well as mean field interactions. As a second application of cavities to quantum information leveraging our newfound comfort with intra-cavity optics, and experience with aberration modeling in resonators, we demonstrate a new class of small waist optical resonators enabled by lens-based cavities and then apply our understanding of optical aberrations in cavities to the development of a new class of cavity array. This Cavity Array Microscope (CAM) realizes a large number of cavities (up to currently 600) using only a fixed number of free space optics and is both scalable with constant overhead as well as compatible with Rydberg atoms. This platform provides a route to highly parallel quantum repeater operation or entanglement generation between atom arrays in the future.
Quantum computing promises to revolutionize several scientific and technological domains through fundamentally new ways of processing information. Among its most compelling applications is digital quantum simulation, where quantum computers are used to replicate the behavior of other quantum systems. This could enable the study of problems that are otherwise intractable on classical computers, transforming fields such as quantum chemistry, condensed matter physics, and materials science. Despite this potential, realizations of practical quantum advantage for relevant problems are hindered by imperfections of current devices. This also affects quantum hardware based on superconducting circuits which is among the most advanced and scalable platforms. The envisaged long-term solution of fault-tolerant quantum computers that correct their own errors remains out of reach mainly due to the associated qubit number overhead. As a result, the field has developed strategies that combine quantum and classical resources, exploit hardware-native operations, and employ error mitigation techniques to extract meaningful results from noisy data. This doctoral thesis contributes to this broader effort by exploring methods for advancing quantum simulation across the full computational stack, including hardware-level innovations, refined techniques for noise modeling and error mitigation, and algorithmic improvements enabled by efficient measurement processing.
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.
Envisioned by Richard Feynman in the early 1980s, quantum simulation has received dramatic impetus thanks to the development of a variety of plateforms able to emulate a wide class of quantum Hamiltonians.During the past decade, most of the quantum simulators have implemented rather well-known models, hence permitting a direct comparison with theoretical calculations and a precise benchmarking of their reliability.The field has now reached a maturity such that one can address difficult problems, which cannot be solved efficiently using classical algorithms.These advances provide unprecedented opportunities to explore previously unreachable fields, test theoretical predictions, and inspire novel approaches.This contribution is an elementary introduction to quantum simulation.We discuss the challenges, define both digital and analog quantum simulators, and list the demanding conditions they require.We also provide a brief account of the contributions gathered in the dossier on Quantum simulation in the Compte rendus Physique of the French Academy of Sciences [1][2][3][4][5][6].The latter completes excellent reviews that appeared previously, see for instance . Universal models and the role of simulations in many-body physicsUnderstanding the behavior of macroscopic quantum systems is a major challenge of modern physics.The basic laws of low-energy physics are by now quite well known at the microscopic, say atomic, scale.Conversely, many fundamental questions remain open, and even debated, about the collective dynamics at the macroscopic scale.By "macroscopic scale", here we mean systems made up of a huge number of constituents, or degrees of freedom, say 10 6 , 10 23 , or even more, as relevant in condensed matter physics or in astrophysics, for instance.Such huge systems cannot be treated exactly, be it a the classical level and, even worse, at the quantum level.Yet, it is the main outcome of the thermodynamic approach that the collective behavior of a macroscopic system can drastically differ from that of its elementary constituents.For instance, the elementary interactions between the H 2 O molecules are fundamentally unchanged when a water bucket turns from the liquid phase to the solid phase at zero degree Celsius.Similarly, the interactions between the microscopic magnetic moments do not show any brutal change when a magnetic material gets magnetized underneath the Curie temperature.Hence, the dramatic effects observed in macroscopic systems are governed by large-scale instabilities, without obvious counterparts at the microscopic level.This observation takes a universal character, summarized in the celebrated motto "More is Different" [15].Such so-called emerging phenomena also appear in quantum systems, where new effects that are impossible in the classical world show up below some critical temperature or at zero temperature when some interaction parameter passes through a critical value.Celebrated examples include the superfluid transition in helium or super-conducting transitions and other metal-insulator transitions in electronic systems.Strikingly enough at first sight, while emerging phenomena only appear in very large scale macroscopic systems, their germs are contained in the mutual interactions of their elementary constituents.Hence, local two-body interactions are sufficient to explain a huge class of phase transitions, such as the liquid-solid and magnetic transitions mentioned above.The Boltzmann statistical approach proved particularly successful in describing this connection between the microscopic and macroscopic scales.To understand emerging phenomena on grounds as fundamental as possible, the programme is now well established: One tries to identify the basic microscopic terms that seem to be relevant and disregards all the other microscopic details.One then elaborates a model, as generic as possible, likely to reproduce the main experimental observations.The most usual examples are the Ising and Heisenberg models for magnetic transitions, or the Hubbard model for metal-insulator transitions [16][17][18].Then all is left to do is to check that the phenomenon of interest indeed emerges from the dynamics of the simplified model.The realization of this programme is nothing but a simulation.It consists in building up a simplified system that mimics the main properties of a real system.
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.