Practical quantum advantage in quantum simulation

Abstract

Box 1: Example Platforms for Analogue Quantum Simulation Analogue Quantum Simulations are today performed on a variety of platforms [15][16][17][18][19][20], each of which offer distinct features that make them more suitable for specific simulation tasks. Ultracold atoms in optical lattices -Currently up to 3000 atoms in optical potentials with single atom detection and control via so-called quantum gas microscopes. These uniquely implement models of interacting fermionic particles (such as the Hubbard model, see Box 2) or its bosonic variant using bosonic atoms. Spin models can also be engineered, with tailored local parameters and potentials shaped by spatial light modulators [21,22]. Trapped Ions -Currently ca. 50 ions in linear chains (Paul traps) or 2D arrays (Penning traps), with local addressing. Using laser excitations and the collective motion of the array to generate effective interactions, a range of magnetic spin models can be engineered, with tailored long-range interactions. They benefit from readout techniques and manipulation developed for digital quantum computing in ion traps [17]. Atom arrays with Rydberg interactions -Currently ca. 256 atoms held in optical tweezers, with spin models generated by excitation to high-lying electronic states. They benefit from arrangements in arbitrary geometries, and tailored magnetic spin models from different choices in laser excitation to excited states [20]. Superconducting circuits -Currently ca. 50-130 superconducting resonators, which can be used as qubits (spins) or anharmonic oscillators (interacting bosons), with couplings adjusted on the level of individual resonators. As with trapped ions, they benefit directly from architectures and readout techniques in superconducing quantum computers [19,23]. Photonic waveguides or beamsplitter arrays -Currently up to ca. 50-100 channels and photons, either chip-based or with large-scale beamsplitter arrays. They generally implement models for non-interacting bosons, including boson sampling, which is exponentially difficult to reproduce using classical calculations [18,24].Box 2: The Hubbard model A particularly good example of the complex problems addressed in quantum simulation is the determination of low-energy properties and dynamics in a Hubbard model, which is a prototypical model for describing strongly interacting electrons in solids [25]. Although in one dimension the Hubbard model is exactly solvable [26], in two dimensions, it has been a long-term challenge even to find the lowest energy states of this model, although a lot of recent progress has been made [27,28].

Interaction between giant atoms in a one-dimensional structured environment

“…With the technology available today, the model presented here is readily implementable with superconducting qubits coupled to either a microwave photonic crystal [19][20][21] or to a superconducting metamaterial [14,[22][23][24]. Moreover, as it has been showed in recent experiments, this platform can be used for quantum simulation of spinless bosonic models [55,57] and for the implementation of entangling or SWAP gates [14,25].…”

“…In particular, we conclude that preference of a giant-atom design over a small-atom design might depend on the experimental constraints and the intended application. Possible applications include quantum simulation [56,57], as well as implementation of entangling or SWAP gates for quantum computing [14].…”

Overcoming I/O bottleneck in superconducting quantum computing: multiplexed qubit control with ultra-low-power, base-temperature cryo-CMOS multiplexer

“…Quantum information processing on error-corrected quantum computers promises a significant computational advantage over classical computers in solving particular problems that are otherwise intractable [1][2][3][4] . Although many physical systems are under active investigation [5][6][7] , superconducting quantum circuits have emerged as arguably the most developed platform [8][9][10][11] with recent proof-of-principle demonstration of verifiable quantum advantage [12][13][14] .…”

Finite-size criticality in fully connected spin models on superconducting quantum hardware

“…In [23] the authors rigorously analyze the requirements of an algorithm in terms of training data and define generalization bounds for their effective execution on current quantum device. For an overview of the state of the art and future perspectives for quantum simulation, looking at possible quantum advantage in specific applications we refer to [24].…”