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Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we…
Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to…
The Fermi-Hubbard model is a plausible target to be solved by a quantum computer using the variational quantum eigensolver algorithm. However, problem sizes beyond the reach of classical exact diagonalisation are also beyond the reach of…
Near-term quantum computers will be limited in the number of qubits on which they can process information as well as the depth of the circuits that they can coherently carry out. To-date, experimental demonstrations of algorithms such as…
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.…
Quantum computers have the potential to transform the ways in which we tackle some important problems. The efforts by companies like Google, IBM and Microsoft to construct quantum computers have been making headlines for years. Equally…
We develop a workflow to use current quantum computing hardware for solving quantum many-body problems, using the example of the fermionic Hubbard model. Concretely, we study a four-site Hubbard ring that exhibits a transition from a…
Non-Hermitian physics has emerged as a rich field of study, with applications ranging from $PT$-symmetry breaking and skin effects to non-Hermitian topological phase transitions. Yet most studies remain restricted to small-scale or…
Although quantum computing hardware has evolved significantly in recent years, spurred by increasing industrial and government interest, the size limitation of current generation quantum computers remains an obstacle when applying these…
Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term…
Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
Combinatorial optimization problems pose significant computational challenges across various fields, from logistics to cryptography. Traditional computational methods often struggle with their exponential complexity, motivating exploration…
Combinatorial optimization models a vast range of industrial processes aiming at improving their efficiency. In general, solving this type of problem exactly is computationally intractable. Therefore, practitioners rely on heuristic…
Finding eigenstates of a given many-body Hamiltonian is a long-standing challenge due to the perceived computational complexity. Leveraging on the hardware of a quantum computer accommodating the exponential growth of the Hilbert space size…
Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The…
We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
Hamiltonian simulation is a domain where quantum computers have the potential to outperform their classical counterparts. One of the main challenges of such quantum algorithms is increasing the system size, which is necessary to achieve…
We present experimental results on running 4-qubit unstructured search on IBM quantum processors. Our best attempt attained probability of success around 24.5%. We try several algorithms and use the most recent developments in quantum…