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At large scales, quantum systems may become advantageous over their classical counterparts at performing certain tasks. Developing tools to analyse these systems at the relevant scales, in a manner consistent with quantum mechanics, is…
Quantum simulation of fermionic systems is a promising application of quantum computers, but in order to program them, we need to map fermionic states and operators to qubit states and quantum gates. While quantum processors may be built as…
Exactly solvable models of topologically ordered phases with non-abelian anyons typically require complicated many-body interactions which do not naturally appear in nature. This motivates the "inverse problem" of quantum many-body physics:…
Classical optimization problems can be solved by adiabatically preparing the ground state of a quantum Hamiltonian that encodes the problem. The performance of this approach is determined by the smallest gap encountered during the…
One of the current major challenges surrounding the use of quantum annealers for solving practical optimization problems is their inability to encode even moderately sized problems---the main reason for this being the rigid layout of their…
The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between…
This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…
We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv)…
In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts…
We propose a protocol to realize atomic nonadiabatic holonomic quantum computation (NHQC) with two computational atoms and an auxiliary atom. Dynamics of the system is analyzed in the regime of Rydberg blockade, and robust laser pulses are…
Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to…
We propose a technique for design of quantum Fourier transforms, and ensuing quantum algorithms, in a single interaction step by engineered Hamiltonians of circulant symmetry. The method uses adiabatic evolution and is robust against…
We present two applications of emergent local Hamiltonians to speed up quantum adiabatic protocols for isolated noninteracting and weakly interacting fermionic systems in one-dimensional lattices. We demonstrate how to extract maximal work…
Many-body entangled systems, in particular topologically ordered spin systems proposed as resources for quantum information processing tasks, often involve highly non-local interaction terms. While one may approximate such systems through…
The exponential speedups promised by Hamiltonian simulation on a quantum computer depends crucially on structure in both the Hamiltonian $\hat{H}$, and the quantum circuit $\hat{U}$ that encodes its description. In the quest to better…
To treat a problem with a Quantum Processing Unit (QPU), it must be transformed into a sequence of quantum operations, or gates: this is the quantum description of the problem. These operations are either packed into a query (i.e. quantum…
We propose a protocol to realize quantum simulation and computation in spin systems with long-range interactions. Our approach relies on the local addressing of single spins with external fields parametrized by Walsh functions. This enables…
We propose a hybrid quantum-classical method to investigate the equilibrium physics and the dynamics of strongly correlated fermionic models with spin-based quantum processors. Our proposal avoids the usual pitfalls of fermion-to-spin…
The identification of environmental changes is crucial in many fields. The present research is aimed at investigating the optimal performance for detecting change points in a quantum system when its Hamiltonian suddenly changes at a…
Symmetry plays a crucial role in the design and analysis of quantum protocols. This result shows a canonical circuit decomposition of a $(G \times H)$-invariant quantum comb for compact groups $G$ and $H$ using the corresponding…