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Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the…
We introduce a unitary matrix-product operator (UMPO) based variational method that approximately finds all the eigenstates of fully many-body localized (fMBL) one-dimensional Hamiltonians. The computational cost of the variational…
We present a hybrid classical/quantum algorithm for efficiently solving the eigenvalue problem of many-particle Hamiltonians on quantum computers with limited resources by splitting the workload between classical and quantum processors.…
We present a general framework for finding the time-optimal evolution and the optimal Hamiltonian for a quantum system with a given set of initial and final states. Our formulation is based on the variational principle and is analogous to…
Hybrid quantum-HPC algorithms advance research by delegating complex tasks to quantum processors and using HPC systems to orchestrate workflows and complementary computations. Sample-based quantum diagonalization (SQD) is a hybrid…
The quantum approximate optimization algorithm (QAOA) applies two Hamiltonians to a quantum system in alternation. The original goal of the algorithm was to drive the system close to the ground state of one of the Hamiltonians. This paper…
A universal family of Hamiltonians can be used to simulate any local Hamiltonian by encoding its full spectrum as the low-energy subspace of a Hamiltonian from the family. Many spin-lattice model Hamiltonians -- such as Heisenberg or XY…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…
In this paper, the Quantum Approximate Optimization Algorithm (QAOA) is analyzed by leveraging symmetries inherent in problem Hamiltonians. We focus on the generalized formulation of optimization problems defined on the sets of $n$-element…
Quantum machine learning has emerged as a promising utilization of near-term quantum computation devices. However, algorithmic classes such as variational quantum algorithms have been shown to suffer from barren plateaus due to vanishing…
Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and…
The efficient implementation of matrix arithmetic operations underpins the speedups of many quantum algorithms. We develop a suite of methods to perform matrix arithmetics -- with the result encoded in the off-diagonal blocks of a…
We provide a quantum method for simulating Hamiltonian evolution with complexity polynomial in the logarithm of the inverse error. This is an exponential improvement over existing methods for Hamiltonian simulation. In addition, its scaling…
Hamiltonian simulation is a central task in quantum computing, with wide-ranging applications in quantum chemistry, condensed matter physics, and combinatorial optimization. A fundamental challenge lies in approximating the unitary…
Non-smooth optimization models play a fundamental role in various disciplines, including engineering, science, management, and finance. However, classical algorithms for solving such models often struggle with convergence speed,…
Quantum systems governed by time-dependent Hamiltonians pose significant challenges for the accurate computation of unitary time-evolution operators, which are essential for predicting quantum state dynamics. In this work, we introduce a…
Quantum fluctuations driven by non-stoquastic Hamiltonians have been conjectured to be an important and perhaps essential missing ingredient for achieving a quantum advantage with adiabatic optimization. We introduce a transformation that…
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…
Non-autonomous dynamical systems appear in a very wide range of interesting applications, both in classical and quantum dynamics, where in the latter case it corresponds to having a time-dependent Hamiltonian. However, the quantum…
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…