Center for Theoretical Physics

In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the conventional Monte Carlo approach, such as the sign-problem afflicted regimes of finite baryon density, topological terms, and out-of-equilibrium dynamics. First proof-of-concept quantum computations of lattice gauge theories in (1+1) dimensions have been accomplished, and first resource-efficient quantum algorithms for lattice gauge theories in (1+1) and (2+1) dimensions have been developed. The path towards quantum computations of (3+1)-dimensional lattice gauge theories, including Lattice QCD, requires many incremental steps of improving both quantum hardware and quantum algorithms. After reviewing these requirements and recent advances, we discuss the main challenges and future directions.

We present an update of the Fermilab Lattice and MILC Collaborations project to compute the form factors for semileptonic \(B_{(s)}\)-meson decays. Our calculation uses the highly improved staggered quark (HISQ) action for sea and valence quarks, and ensembles with up, down, strange, and charm quarks in the sea. Using a highly improved action with the MILC Collaboration's gauge ensembles with lattice spacings down to \(a\approx0.03\) fm, allows the heavy valence quarks to be treated with the same discretization as the light and strange quarks. This unified treatment of the valence quarks allows for absolutely normalized vector currents, bypassing the need for perturbative matching, which has been a source of uncertainty in previous calculations of \(B\)-meson decay form factors by our collaboration. All preliminary form-factor results are blinded.

The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these fine-grained error-correction methods can incur significant overhead for quantum algorithms of increasing complexity. We present a first step in achieving error correction at the level of quantum algorithms by combining a unified perspective on modern quantum algorithms via quantum signal processing (QSP). An error model of under- or over-rotation of the signal processing operator parameterized by \(\epsilon < 1\) is introduced. It is shown that while Pauli \(Z\)-errors are not recoverable without additional resources, Pauli \(X\) and \(Y\) errors can be arbitrarily suppressed by coherently appending a noisy `recovery QSP.' Furthermore, it is found that a recovery QSP of length \(O(2^k c^{k^2} d)\) is sufficient to correct any length-\(d\) QSP with \(c\) unique phases to \(k^{th}\)-order in error \(\epsilon\). Allowing an additional assumption, a lower bound of \(\Omega(cd)\) is shown, which is tight for \(k = 1\), on the length of the recovery sequence. Our algorithmic-level error correction method is applied to Grover's fixed-point search algorithm as a demonstration.

With the vast data-collecting capabilities of current and future high-energy collider experiments, there is an increasing demand for computationally efficient simulations. Generative machine learning models enable fast event generation, yet so far these approaches are largely constrained to fixed data structures and rigid detector geometries. In this paper, we introduce EPiC-GAN - equivariant point cloud generative adversarial network - which can produce point clouds of variable multiplicity. This flexible framework is based on deep sets and is well suited for simulating sprays of particles called jets. The generator and discriminator utilize multiple EPiC layers with an interpretable global latent vector. Crucially, the EPiC layers do not rely on pairwise information sharing between particles, which leads to a significant speed-up over graph- and transformer-based approaches with more complex relation diagrams. We demonstrate that EPiC-GAN scales well to large particle multiplicities and achieves high generation fidelity on benchmark jet generation tasks.