Related papers: Quantum Max d-Cut via qudit swap operators
Most quantum computers today are constrained by hardware limitations, particularly the number of available qubits, causing significant challenges for executing large-scale quantum algorithms. Circuit cutting has emerged as a key technique…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
The qubit mapping problem (QMP) focuses on the mapping and routing of qubits in quantum circuits so that the strict connectivity constraints imposed by near-term quantum hardware are satisfied. QMP is a pivotal task for quantum circuit…
The computational cost of simulating quantum many-body systems can often be reduced by taking advantage of physical symmetries. While methods exist for specific symmetry classes, a general algorithm to find the full permutation symmetry…
We present a novel, computationally efficient approach to accelerate quantum optimal control calculations of large multi-qubit systems used in a variety of quantum computing applications. By leveraging the intrinsic symmetry of finite…
The homology of Kontsevich's commutative graph complex parameterizes finite type invariants of odd dimensional manifolds. This {\it graph homology} is also the twisted homology of Outer Space modulo its boundary, so gives a nice point of…
In this paper we develop a classical algorithm of complexity $O(K \, 2^n)$ to simulate parametrized quantum circuits (PQCs) of $n$ qubits, where $K$ is the total number of one-qubit and two-qubit control gates. The algorithm is developed by…
Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing…
The {\sc $c$-Balanced Separator} problem is a graph-partitioning problem in which given a graph $G$, one aims to find a cut of minimum size such that both the sides of the cut have at least $cn$ vertices. In this paper, we present new…
We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality…
As a qubit is a two-level quantum system whose state space is spanned by |0>, |1>, so a qudit is a d-level quantum system whose state space is spanned by |0>,...,|d-1>. Quantum computation has stimulated much recent interest in algorithms…
Distributed quantum computing (DQC) is a promising way to achieve large-scale quantum computing. However, mapping large-sized quantum circuits in DQC is a challenging job; for example, it is difficult to find an ideal cutting and mapping…
The Matching Cut problem is to decide if the vertex set of a connected graph can be partitioned into two non-empty sets $B$ and $R$ such that the edges between $B$ and $R$ form a matching, that is, every vertex in $B$ has at most one…
The Feedback-based Algorithm for Quantum Optimization (FALQON) offers a deterministic alternative to variational quantum algorithms by bypassing classical optimization loops. However, maintaining convergence on large problem instances often…
This paper is devoted to the distributed complexity of finding an approximation of the maximum cut in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any…
The Maximum Independent Set (MIS) problem is a fundamental combinatorial optimization task that can be naturally mapped onto the Ising Hamiltonian of neutral atom quantum processors. Given its connection to NP-hard problems and real-world…
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…
In this paper we study a combinatorial reconfiguration problem that involves finding an optimal sequence of swaps to move an initial configuration of tokens that are placed on the vertices of a graph to a final desired one. This problem…
We study a new problem for cubic graphs: bipartization of a cubic graph $Q$ by deleting sufficiently large independent set $I$. It can be expressed as follows: \emph{Given a connected $n$-vertex tripartite cubic graph $Q=(V,E)$ with…
All known examples confirming the possibility of an exponential separation between classical simulation algorithms and stoquastic adiabatic quantum computing (AQC) exploit symmetries that constrain adiabatic dynamics to effective, symmetric…