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Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and…

Research on quantum computing has recently gained significant momentum since first physical devices became available. Many quantum algorithms make use of so-called oracles that implement Boolean functions and are queried with highly…

We show how to carry out quantum logical operations (controlled-not and Toffoli gates) on encoded qubits for several encodings which protect against various 1-bit errors. This improves the reliability of these operations by allowing one to…

Controlled commands -- computations whose execution depends on a separate input -- play a central role in reversible Boolean circuits and quantum circuits. However, existing formalisms typically treat control only implicitly, entangled with…

We first show how to construct an O(n)-depth O(n)-size quantum circuit for addition of two n-bit binary numbers with no ancillary qubits. The exact size is 7n-6, which is smaller than that of any other quantum circuit ever constructed for…

We propose protocols for calculating inner product, matrix addition and matrix multiplication based on multiqubit Toffoli-type and the simplest one-qubit operations and employ ancilla measurements to remove all garbage of calculations. The…

The problem of finding efficient decompositions of multi-qubit gates is of importance for quantum computing, especially, in application to existing noisy intermediate-scale quantum devices, whose resources are substantially limited. Here we…

CNOT gates are fundamental to quantum computing, as they facilitate entanglement, a crucial resource for quantum algorithms. Certain classes of quantum circuits are constructed exclusively from CNOT gates. Given their widespread use, it is…

Implementing quantum algorithms on realistic hardware requires translating high-level global operations into sequences of native elementary gates, a process known as quantum compiling. Physical limitations, such as constraints in…

A method for synthesizing quantum gates is presented based on interpolation methods applied to operators in Hilbert space. Starting from the diagonal forms of specific generating seed operators with non-degenerate eigenvalue spectrum one…

We consider a generic elementary gate sequence which is needed to implement a general quantum gate acting on n qubits -- a unitary transformation with 4^n degrees of freedom. For synthesizing the gate sequence, a method based on the…

Elliptic curves over finite fields GF(2^n) play a prominent role in modern cryptography. Published quantum algorithms dealing with such curves build on a short Weierstrass form in combination with affine or projective coordinates. In this…

We introduce new rounding methods to improve the accuracy of finite precision quantum arithmetic. These quantum rounding methods are applicable when multiple samples are being taken from a quantum program. We show how to use multiple…

We use Shor's algorithm for the computation of elliptic curve private keys as a case study for resource estimates in the silicon-photonics-inspired active-volume architecture. Here, a fault-tolerant surface-code quantum computer consists of…

We show that it is possible to reduce the number of two-qubit gates needed for the construction of an arbitrary controlled-unitary transformation by up to two times using a tunable controlled-phase gate. On the platform of linear optics,…

MQuantum algorithms of matrix operations are of great significance in many fields in science and technology. In this paper, by leveraging multi-qubit Toffoli gates and basic single-qubit operations, the quantum algorithms of matrix…

Hardware-efficient circuits employed in Quantum Machine Learning are typically composed of alternating layers of uniformly applied gates. High-speed numerical simulators for such circuits are crucial for advancing research in this field. In…

The design and architecture of a quantum instruction set are paramount to the performance of a quantum computer. This work introduces a gate scheme for qubits with $XX+YY$ coupling that directly and efficiently realizes any two-qubit gate…

Existing quantum systems provide very limited physical qubit counts, trying to execute a quantum algorithm/circuit on them that have a higher number of logical qubits than physically available lead to a compile-time error. Given that it is…

Implementing a quantum circuit on specific hardware with a reduced available gate set is often associated with a substantial increase in the length of the equivalent circuit. This process is also known as transpilation and due to…