Related papers: An efficient quantum circuit analyser on qubits an…
We develop and implement automated methods for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. We show how to handle continuous gate parameters and report a collection…
We develop the first constructive algorithms for compiling single-qubit unitary gates into circuits over the universal $V$ basis. The $V$ basis is an alternative universal basis to the more commonly studied $\{H,T\}$ basis. We propose two…
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…
In a recent work arXiv:2201.07655v2 we showed that there is a constant $\lambda >0$ such that it is possible to efficiently classically simulate a quantum system in which (i) qudits are placed on the nodes of a graph, (ii) each qudit…
Compilation and optimization of quantum circuits are critical components in the execution of algorithms on quantum computers. These components must successfully balance two competing priorities: minimizing the number of expensive resources,…
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…
This paper presents novel methods for optimizing multi-controlled quantum gates, which naturally arise in high-level quantum programming. Our primary approach involves rewriting $U(2)$ gates as $SU(2)$ gates, utilizing one auxiliary qubit…
As quantum devices scale toward practical machine learning applications, the binary qubit paradigm faces expressivity and resource efficiency limitations. Multi-level quantum systems, or qudits, offer a promising alternative by harnessing a…
Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm,…
We discuss the implementation of quantum algorithms for lattice $\Phi^4$ theory on circuit quantum electrodynamics (cQED) system. The field is represented on qudits in a discretized field amplitude basis. The main advantage of qudit systems…
Simpler encoding and decoding networks are necessary for more reliable quantum error correcting codes (QECCs). The simplification of the encoder-decoder circuit for a perfect five-qubit QECC can be derived analytically if the QECC is…
We propose an effective realization of a complete set of elementary quantum gates in the solid-state quantum computer based on the multi-atomic coherent (MAC-) ensembles in the QED cavity. Here, we use the two-ensemble qubit encoding and…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
We present some basic integer arithmetic quantum circuits, such as adders and multipliers-accumulators of various forms, as well as diagonal operators, which operate on multilevel qudits. The integers to be processed are represented in an…
Quantum computers have the potential to solve some important industrial and scientific problems with greater efficiency than classical computers. While most current realizations focus on two-level qubits, the underlying physics used in most…
An important application for near-term quantum computing lies in optimization tasks, with applications ranging from quantum chemistry and drug discovery to machine learning. In many settings --- most prominently in so-called parametrized or…
Efficient decompositions of multi-qubit gates are essential in NISQ applications, where the number of gates or the circuit depth is limited. This paper presents efficient decompositions of CCZ and CCCZ gates, typical multi-qubit gates,…
In this paper, the problem of constructing an efficient quantum circuit for the implementation of an arbitrary quantum computation is addressed. To this end, a basic block based on the cosine-sine decomposition method is suggested which…
This paper concerns the efficient implementation of quantum circuits for qudits. We show that controlled two-qudit gates can be implemented without ancillas and prove that the gate library containing arbitrary local unitaries and one…
Current quantum programming is dominated by low-level, circuit-centric approaches that limit the potential for compiler optimization. This work presents how a high-level programming construct provides compilers with the semantic information…