Quantum algorithms and applications
Optimized quantum algorithms for simulating the Schwinger effect - https://arxiv.org/abs/2508.16831.
We studied the problem of simulating Schwinger effect on a quantum computer, by analyzing the performances of two Hamiltonian simulation methods, one based on interaction picture, and the other based on product formula. For our own sake, we rederived the analysis and quantum circuits for the interaction-picture based algorithm. Our comparison considers the parameter regimes (physical parameters regarding initial state and model parameters, and simulation parameters such as the size of the lattice and electric-field cutoff), so that Schwinger effect (proliferation of particle-antiparticle pairs) is expected to be observed in splitting/scattering experiments.
A comprehensive framework to simulate real-time chemical dynamics on a fault-tolerant quantum computer - https://arxiv.org/abs/2504.06348.
We introduced a quantum simulation framework for simulating quantum chemical dynamics, including the state preparation of reactants, time-evolution, and extracting the products. Notably, our improved block-encoding techniques results in a 3-8x improvement compared to the previous state-of-the-art in quantum resource estimates.
Quantum sampling algorithms for quantum state preparation and matrix block-encoding - https://arxiv.org/abs/2405.11436.
We introduced a general framework of efficient quantum state preparation and matrix block-encoding, for structured wavefunctions and matrices. Our techniques make essential use of rejection sampling techniques and give rise to exponential improvements compared to an arbitrary state preparation/block-encoding, when the underlying structure can be exploited.
Quantum algorithms from fluctuation theorems: Thermal-state preparation, Quantum 6, 825 (2022).
Talk at QIP 2023
We introduced a new quantum algorithm for preparing quantum states at thermal equilibrium, based on fluctuation theorems. The underlying idea is to start from a closeby, yet efficiently preparable, thermal state of a simpler Hamiltonian, and implement the block-encoding of the exponential of the work operator.
We studied the concept of fast-forwarding quantum evolution, i.e., simulating a time evolution of amount t, in time o(t), generalized the definition to encompass polynomial fast-forwarding in addition to exponential fast-forwarding. We analyzed three general class of systems, where polynomial and exponential fast-forwarding appears: Hamiltonians with block-diagonal structure due to symmetries, low-energy subspace of positive Hamiltonians, quadratice fermionic and bosonic systems.
Hamiltonian simulation in the low-energy subspace, npj Quantum information, 7, article number: 119 (2021).
Talk at QIP 2021
We studied the performance of the product formula in the low-energy subspace of the Hamiltonian. Our detailed analysis proved that the product formula performs more efficiently when the input state is supported in the low-energy subspace. We developed techniques to treat the leakage of the quantum system towards higher energies, and the lower Trotter error within the low-energy subspace that compete with each other. We showed that these two competing effects balances out to still give rise to an improved complexity for the Hamiltonian simulation.
Quantum error correction
Quantum error detection at low-energies, JHEP Volume 2019, article number 21, (2019).
Quantum error correcting codes in eigenstates of translation-invariant spin chains, Phys. Rev. Lett. 123, 110502.
Tensor networks - General theory and topological order
Boson condensation and instability in the tensor network representation of string-net states, Phys. Rev. B 98, 125112.
Matrix product representation of locality preserving unitaries, Phys. Rev. B 98, 245122.
Anyons and matrix product operator algebras, Annals of Physics Volume 378, March 2017.
Matrix product operators for symmetry-protected topological phases: Gauging and edge theories, Phys. Rev. B 94, 205150.
Characterizing topological order with matrix product operators, Annales Henri Poincaré Volume 22 (2021).
Talk at QIP2015
Quantum marginal problem
Recoupling coefficients and quantum entropies, Annales Henri Poincaré Volume 19 (2018).
Talk at QIP2013