Kazuhiro Seki

We demonstrate a dissipative protocol for ground-state preparation of a quantum spin chain on a trapped-ion quantum computer. As a first step, we derive a Kraus representation of a dissipation channel for the protocol recently proposed by Ding et al. [Phys. Rev. Res. 6, 033147 (2024)] that still holds for arbitrary temporal discretization steps, extending the analysis beyond the Lindblad dynamics regime. The protocol guarantees that the fidelity with the ground state monotonically increases (or remains unchanged) under repeated applications of the channel to an arbitrary initial state, provided that the ground state is the unique steady state of the dissipation channel. Using this framework, we implement dissipative ground-state preparation of a transverse-field Ising chain for up to 19 spins on the trapped-ion quantum computer Reimei provided by Quantinuum. Despite the presence of hardware noise, the dynamics consistently converges to a low-energy state far away from the maximally mixed state even when the corresponding quantum circuits contain as many as 4110 entangling gates, demonstrating the intrinsic robustness of the protocol. By applying zero-noise extrapolation, the resulting energy expectation values are systematically improved to agree with noiseless simulations within statistical uncertainties.

We implement the Gutzwiller wave function for attractive SU(3) fermion systems on a quantum computer using a quantum-classical hybrid scheme based on the discrete Hubbard-Stratonovich transformation. In this approach, the nonunitary Gutzwiller operator is decomposed into a linear combination of unitaries constructed from two-qubit fermionic Givens rotation gates, whose rotation angles are dictated by the auxiliary fields. We develop and reformulate two complementary methods to perform the sum over these auxiliary fields. In the first method, the Gutzwiller wave function is probabilistically prepared on the register qubits by projectively postselecting the desired state via measurements of ancilla qubits. We analyze the success rate both analytically and numerically as a function of the Gutzwiller variational parameter $g$ for the Fermi-sea and BCS-like trial states at half filling. The success rate is found to decay exponentially for small $|g|$, but remains finite in the $|g|\to\infty$ limit, with increasing $|g|$. In the second method, we employ importance sampling to address the Gutzwiller variational problem, where the central objective is to estimate the expectation values of observables. We demonstrate the proposed scheme by calculating the energy and triple occupancy of the attractive SU(3) Hubbard model in the framework of digital quantum simulation. Moreover, we present experimental results obtained on a trapped-ion quantum computer for the two-site attractive SU(3) Hubbard model, showing good agreement with exact values within statistical errors.

We perform digital quantum simulations of the noninteracting Su-Schrieffer-Heeger (SSH) model using a parameterized quantum circuit. The circuit comprises two main components: the first prepares the initial state from the product state $|0\rangle^{\otimes L}$, where $L$ is the system size; the second consists of $M$ layers of brick-wall unitaries simulating time evolution. The evolution times, encoded as the rotation angles of quantum gates in the second part, are optimized variationally to minimize the energy. The SSH model exhibits two distinct topological phases, depending on the relative strengths of inter- and intra-cell hopping amplitudes. We investigate the evolution of the energy, entanglement entropy, and mutual information towards topologically trivial and nontrivial ground states. Our results find the follows: (i) When the initial and target ground states belong to the same topological phase, the variational energy decreases exponentially, the entanglement entropy quickly saturates in a system-size-independent manner, and the mutual information remains spatially localized, as the number of layers increases. (ii) When the initial and target ground states belong to different topological phases, the variational energy decreases polynomially, the entanglement entropy initially grows logarithmically before decreasing, and the mutual information spreads ballistically across the entire system, with increasing the number of layers. Furthermore, by calculating the polarization, we identify a topological phase transition occurring at an intermediate circuit layer when the initial and final target states lie in different topological characters. Finally, we experimentally confirm this topological phase transition in an 18-site system using 19 qubits on a trapped-ion quantum computer provided by Quantinuum.

Imaginary-time evolution, an important technique in tensor network and quantum Monte Carlo algorithms on classical computers, has recently been adapted to quantum computing. In this study, we focus on probabilistic imaginary-time evolution (PITE) algorithm and derive its formulation in the context of state-vector-based simulations, where quantum state vectors are directly used to compute observables without statistical errors. We compare the results with those of shot-based simulations, which estimate observables through repeated projective measurements. Applying the PITE algorithm to the Heisenberg chain, we investigate optimal initial conditions for convergence. We further demonstrate the method on the transverse-field Ising model using a state-of-the-art trapped-ion quantum device. Finally, we explore the potential of error mitigation in this framework, highlighting practical considerations for near-term digital quantum simulations.

Complex quantum many-body dynamics spread initially localized quantum information across the entire system. Information scrambling refers to such a process, whose simulation is one of the promising applications of quantum computing. We demonstrate the Hayden-Preskill recovery protocol and the interferometric protocol for calculating out-of-time-ordered correlators to study the scrambling property of a one-dimensional kicked-Ising model on 20-qubit trapped-ion quantum processors. The simulated quantum circuits have a geometrically local structure that exhibits the ballistic growth of entanglement, resulting in the circuit depth being linear in the number of qubits for the entire state to be scrambled. We experimentally confirm the growth of signals in the Hayden-Preskill recovery protocol and the decay of out-of-time-ordered correlators at late times. As an application of the created scrambling circuits, we also experimentally demonstrate the calculation of the microcanonical expectation values of local operators adopting the idea of thermal pure quantum states. Our experiments are made possible by extensively utilizing one of the highest-fidelity quantum processors currently available and, thus, should be considered as a benchmark for the current status of the most advanced quantum computers.