Symmetry-protected dissipative preparation of matrix product states

We propose and analyze a method for efficient dissipative preparation of matrix product states that exploits their symmetry properties. Specifically, we construct an explicit protocol that makes use of driven-dissipative dynamics to prepare the Affleck-Kennedy-Lieb-Tasaki (AKLT) states, which features symmetry-protected topological order and non-trivial edge excitations. We show that the use of symmetry allows for robust experimental implementation without fine-tuned control parameters. Numerical simulations show that the preparation time scales polynomially in system size $n$. Furthermore, we demonstrate that this scaling can be improved to $\mathcal{O}(\log^2n)$ by using parallel preparation of AKLT segments and fusing them via quantum feedback. A concrete scheme using excitation of trapped neutral atoms into Rydberg state via Electromagnetically Induced Transparency is proposed, and generalizations to a broader class of matrix product states are discussed

Quantum Computation and Simulation using Fermion-Pair Registers

We propose and analyze an approach to realize quantum computation and simulation using fermionic particles under quantum gas microscopes. Our work is inspired by a recent experimental demonstration of large-scale quantum registers, where tightly localized fermion pairs are used to encode qubits exhibiting long coherence time and robustness against laser intensity noise. We describe how to engineer the SWAP gate and high-fidelity controlled-phase gates by adjusting the fermion hopping as well as Feshbach interaction strengths. Combined with previously demonstrated single-qubit rotations, these gates establish the computational universality of the system. Furthermore, we show that 2D quantum Ising Hamiltonians with tunable transverse and longitudinal fields can be efficient simulated by modulating Feshbach interaction strengths. We present a sample-efficient protocol to characterize engineered gates and Hamiltonian dynamics based on an improved classical shadow process tomography that requires minimal experimental controls. Our work opens up new opportunities to harness existing ultracold quantum gases for quantum information sciences

Exact Quantum Algorithms for Quantum Phase Recognition: Renormalization Group and Error Correction

We explore the relationship between renormalization group (RG) flow and error correction by constructing quantum algorithms that exactly recognize 1D symmetry-protected topological (SPT) phases protected by finite internal Abelian symmetries. For each SPT phase, our algorithm runs a quantum circuit which emulates RG flow: an arbitrary input ground state wavefunction in the phase is mapped to a unique minimally-entangled reference state, thereby allowing for efficient phase identification. This construction is enabled by viewing a generic input state in the phase as a collection of coherent `errors' applied to the reference state, and engineering a quantum circuit to efficiently detect and correct such errors. Importantly, the error correction threshold is proven to coincide exactly with the phase boundary. We discuss the implications of our results in the context of condensed matter physics, machine learning, and near-term quantum algorithms.Comment: 10 pages + appendices v2: extended discussion on RG convergence; added ref