Related papers: Hardness of approximation for ground state problem…
An instance of Max CSP is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satisfied constraints. Max CSP captures many well-known problems (such as Max…
We study the complexity of approximate counting Constraint Satisfaction Problems (#CSPs) in a bounded degree setting. Specifically, given a Boolean constraint language $\Gamma$ and a degree bound $\Delta$, we study the complexity of…
We study the Equitable Connected Partition (ECP for short) problem, where we are given a graph G=(V,E) together with an integer p, and our goal is to find a partition of V into p parts such that each part induces a connected sub-graph of G…
Solving electronic structure problems is considered one of the most promising applications of quantum computing. However, due to limitations imposed by the coherence time of qubits in the Noisy Intermediate Scale Quantum (NISQ) era or the…
Ground State Energy Estimation (GSEE) is a central problem in quantum chemistry and condensed matter physics, demanding efficient algorithms to solve complex electronic structure calculations. This work introduces a structured benchmarking…
Quadratic assignment problems are a fundamental class of combinatorial optimization problems which are ubiquitous in applications, yet their exact resolution is NP-hard. To circumvent this impasse, it was proposed to regularize such…
Estimating ground state energies of many-body Hamiltonians is a central task in many areas of quantum physics. In this work, we give quantum algorithms which, given any $k$-body Hamiltonian $H$, compute an estimate for the ground state…
Quantum computers can accurately compute ground state energies using phase estimation, but this requires a guiding state that has significant overlap with the true ground state. For large molecules and extended materials, it becomes…
Ground states of local Hamiltonians can be generally highly entangled: any quantum circuit that generates them (even approximately) must be sufficiently deep to allow coupling (entanglement) between any pair of qubits. Until now this…
The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…
Quantum PCP conjecture is one of the most influential open problems in quantum complexity theory, which states that approximating the ground state energy for a sparse local Hamiltonian upto a constant is QMA-complete. However, even though…
In this work we develop theoretical techniques for analysing the performance of the quantum approximate optimization algorithm (QAOA) when applied to random boolean constraint satisfaction problems (CSPs), and use these techniques to…
In the lead up to fault tolerance, the utility of quantum computing will be determined by how adequately the effects of noise can be circumvented in quantum algorithms. Hybrid quantum-classical algorithms such as the variational quantum…
A quantum circuit must be preprocessed before implementing on NISQ devices due to the connectivity constraint. Quantum circuit mapping (QCM) transforms the circuit into an equivalent one that is compliant with the NISQ device's architecture…
A classic result due to Schaefer (1978) classifies all constraint satisfaction problems (CSPs) over the Boolean domain as being either in $\mathsf{P}$ or $\mathsf{NP}$-hard. This paper considers a promise-problem variant of CSPs called…
Constraint satisfaction problems (CSPs) consist of a set of variables taking values from some finite domain and a set of local constraints on these variables. The objective is to find an assignment to the variables that maximizes the…
Motivated by understanding the power of quantum computation with restricted number of qubits, we give two complete characterizations of unitary quantum space bounded computation. First we show that approximating an element of the inverse of…
We present a quantum-classical hybrid algorithm for calculating the ground state and its energy of the quantum many-body Hamiltonian by proposing an adaptive construction of a quantum state for the quantum-selected configuration interaction…
We consider the task of approximating the ground state energy of two-local quantum Hamiltonians on bounded-degree graphs. Most existing algorithms optimize the energy over the set of product states. Here we describe a family of shallow…
The promise constraint satisfaction problem (PCSP) is a recently introduced vast generalisation of the constraint satisfaction problem (CSP) that captures approximability of satisfiable instances. A PCSP instance comes with two forms of…