Related papers: Knuth-Bendix Completion Algorithm and Shuffle Alge…
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…
In a previous publication [1] we showed that it is possible to implement universal quantum computation with the anisotropic XY-Heisenberg exchange acting as a single interaction. To achieve this we used encodings of the states of the…
We have reviewed some results on quantized shuffling, and in particular, the grading and structure of this algebra. In parallel, we have summarized certain details about classical shuffle algebras, including Lyndon words (primes) and the…
Faults are stochastic by nature while most man-made systems, and especially computers, work deterministically. This necessitates the linking of probability theory with mathematical logics, automata, and switching circuit theory. This paper…
Recent developments in quantum hardware indicate that systems featuring more than 50 physical qubits are within reach. At this scale, classical simulation will no longer be feasible and there is a possibility that such quantum devices may…
To run quantum algorithms on emerging gate-model quantum hardware, quantum circuits must be compiled to take into account constraints on the hardware. For near-term hardware, with only limited means to mitigate decoherence, it is critical…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
The circuit model of quantum computation can be interpreted as a scattering process. In particular, factorised scattering operators result in integrable quantum circuits that provide universal quantum computation and are potentially less…
It is usually assumed that a quantum computation is performed by applying gates in a specific order. One can relax this assumption by allowing a control quantum system to switch the order in which the gates are applied. This provides a more…
The ZX-calculus is a universal graphical language for qubit quantum computation, meaning that every linear map between qubits can be expressed in the ZX-calculus. Furthermore, it is a complete graphical rewrite system: any equation…
The Heisenberg exchange interaction is a natural method to implement non-local (i.e., multi-qubit) quantum gates in quantum information processing. We consider quantum circuits comprising of $(SWAP)^\alpha $ gates, which are realized…
NISQ devices have several physical limitations and unavoidable noisy quantum operations, and only small circuits can be executed on a quantum machine to get reliable results. This leads to the quantum hardware under-utilization issue. Here,…
Recently it has been shown that Repeat-Until-Success (RUS) circuits can approximate a given single-qubit unitary with an expected number of $T$ gates of about $1/3$ of what is required by optimal, deterministic, ancilla-free decompositions…
We numerically emulate noisy intermediate-scale quantum (NISQ) devices and determine the minimal hardware requirements for two-site hybrid quantum-classical dynamical mean-field theory (DMFT). We develop a circuit recompilation algorithm…
We propose a quantum-classical hybrid algorithm to encode a given arbitrarily quantum state $\vert \Psi \rangle$ onto an optimal quantum circuit $\hat{\mathcal{C}}$ with a finite number of single- and two-qubit quantum gates. The proposed…
In quantum computing, the efficient optimization of Pauli string decompositions is a crucial aspect for the compilation of quantum circuits for many applications, such as chemistry simulations and quantum machine learning. In this paper, we…
We introduce a novel hybrid quantum-classical variational optimization method for unconstrained binary combinatorial optimization problems on gate-model quantum computers, integrating a custom variational ansatz, staged feedback-based dual…
The primary objective of quantum circuit synthesis is to efficiently and accurately realize specific quantum algorithms or operations utilizing a predefined set of quantum gates, while also optimizing the circuit size. It holds a pivotal…
Quantum circuit synthesis is the task of decomposing a given quantum operator into a sequence of elementary quantum gates. Since the finite target gate set cannot exactly implement any given operator, approximation is often necessary. Model…
Compiling arbitrary-connectivity NISQ circuits onto monolithic single-zone neutral-atom devices is constrained by a finite interaction range and a minimum separation between simultaneously addressable sites. Under the minimum-separation…