Quantum Simulation in the Era of Practical Quantum Computers

Abstract

Understanding the computational power of quantum devices has become a central focus of modern physics, driven in part by the promise of new discoveries in fundamental science. The properties of quantum many-body systems are encoded in a Hilbert space whose dimension grows exponentially with the number of constituent degrees of freedom, and the intricate patterns of quantum correlations that such systems develop resist the compression on which classical methods rely. As a result, many quantities of central physical interest, most notably real-time dynamics and non-equilibrium phenomena, lie beyond the reach of even the most powerful classical supercomputers. Quantum computers evade this barrier by construction: because the device is itself a controllable quantum system, it can store and evolve many-body states with resources that scale only polynomially in the system size. The simulation of physical systems is therefore among the primary applications of quantum computation, and arguably its original motivation. Although errors and noise still limit the coherence times of current hardware, quantum simulators have now reached the stage of being functional scientific instruments, capable of practical simulations that challenge their classical counterparts. Extracting scientific value from these devices, however, requires more than raw hardware capability. Generic, hardware-agnostic algorithms are often prohibitively expensive on near-term machines, and so specialized methods must be developed that are informed by the physics of the problem itself. Insights from quantum many-body theory, the symmetries and gauge invariance of the target system, the structure of its correlations and entanglement, and the way errors propagate through its dynamics, can be built directly into simulation, measurement, and error-suppression protocols, dramatically reducing the resources they demand. Developing such physics-informed methods is the unifying theme of this dissertation. The research presented here contributes to both the practical and conceptual formulations of quantum simulation, for systems spanning a range of subfields from condensed matter to high-energy physics. The first part develops time evolution algorithms in both analog and digital settings. A framework for quantifying and optimizing algorithmic errors in Rydberg-atom simulators is presented, revealing that at a given level of device noise there exists an optimal time step. A hardware-efficient digitization of \sutwo lattice gauge theory (LGT) is then presented that remains resource efficient at all values of the gauge coupling; quantum circuits implementing time evolution are constructed and simulations are performed on superconducting quantum hardware. The second part of this thesis focuses on the efficient measurement of observables relevant for quantum simulation. Building on the investigation of the non-equilibrium dynamics of an \sutwo LGT, its quantum complexity is measured experimentally with the aid of a novel error mitigation technique. Classical shadows protocols are then developed that leverage gauge invariance to achieve an exponential reduction in sample complexity compared to standard local schemes. Finally, a tomographic protocol based on a novel ansatz for non-Gaussian states is introduced and used to efficiently measure the build-up of level repulsion in a system of weakly interacting fermions, opening new avenues for studying non-equilibrium dynamics and thermalization. The dissertation concludes with new approaches for combining fault tolerance with near-term simulation techniques, demonstrated through experiments on quantum devices. By balancing circuit depth against the protection afforded by fault-tolerant gadgets, beyond break-even performance is achieved for the calculation of local observables relevant to quantum simulation.