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The preparation of Hamiltonian eigenstates is essential for many applications in quantum computing; the efficiency with which this can be done is of key interest. A canonical approach exploits the quantum phase estimation (QPE) algorithm.…
A frustration-free local Hamiltonian has the property that its ground state minimises the energy of all local terms simultaneously. In general, even deciding whether a Hamiltonian is frustration-free is a hard task, as it is closely related…
We present a theoretical proposal for the implementation of geometric quantum computing based on a Hamiltonian which has a doubly degenerate ground state. Thus the system which is steered adiabatically, remains in the ground-state. The…
Local Hamiltonians with topological quantum order exhibit highly entangled ground states that cannot be prepared by shallow quantum circuits. Here, we show that this property may extend to all low-energy states in the presence of an on-site…
Quantum state tomography, the ability to deduce the density matrix of a quantum system from measured data, is of fundamental importance for the verification of present and future quantum devices. It has been realized in systems with few…
Preparing the ground state of a system of interacting classical particles is an NP-hard problem. Thus, there is in general no better algorithm to solve this problem than exhaustively going through all N configurations of the system to…
Hamiltonian Learning (HL) is essential for validating quantum systems in quantum computing. Not all Hamiltonians can be uniquely recovered from a steady state. HL success depends on the Hamiltonian model and steady state. Here, we analyze…
We give a quasi-polynomial time classical algorithm for estimating the ground state energy and for computing low energy states of quantum impurity models. Such models describe a bath of free fermions coupled to a small interacting subsystem…
A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard approaches, such as variational calculations, consist of writing down a wave function ansatz and minimizing over…
A broad range of quantum optimisation problems can be phrased as the question whether a specific system has a ground state at zero energy, i.e.\ whether its Hamiltonian is frustration free. Frustration-free Hamiltonians, in turn, play a…
Given a generic time-dependent many-body quantum state, we determine the associated parent Hamiltonian. This procedure may require, in general, interactions of any sort. Enforcing the requirement of a fixed set of engineerable Hamiltonians,…
The computational complexity of simulating quantum many-body systems generally scales exponentially with the number of particles. This enormous computational cost prohibits first principles simulations of many important problems throughout…
While general quantum many-body systems require exponential resources to be simulated on a classical computer, systems of non-interacting fermions can be simulated exactly using polynomially scaling resources. Such systems may be of…
One promising field of quantum computation is the simulation of quantum systems, and specifically, the task of ground state energy estimation (GSEE). Ground state preparation (GSP) is a crucial component in GSEE algorithms, and classical…
Heralded multi-photon entanglement generation is a central bottleneck for photonic quantum computing, where resource costs typically skyrocket with target size. We explore efficient methods for generating photon states with tunable…
The stabilizer ground state is defined is the lowest energy stabilizer state with respect to a given Hamiltonian. In many cases it is highly degenerate and does not give a unique stabilizer state. We define the optimal stabilizer ground…
Non-Hermitian (NH) quantum systems demonstrate striking differences from their Hermitian counterparts, leading to claims of NH advantage in areas ranging from metrology to entanglement generation. We show that in the context of quantum…
The hidden subgroup problem~(HSP) is one of the most important problems in quantum computation. Many problems for which quantum algorithm achieves exponential speedup over its classical counterparts can be reduced to the Abelian HSP.…
We study the ground states of lattice Hamiltonians that are invariant under permutations, in the limit where the number of lattice sites, N -> \infty. For spin systems, these are product states, a fact that follows directly from the quantum…
Complexity theory traditionally studies the hardness of solving classical computational problems. In the quantum setting, it is also natural to consider a different notion of complexity, namely the complexity of physically preparing a…