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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…

We propose a sampling-based simulation for fault-tolerant quantum error correction under coherent noise. A mixture of incoherent and coherent noise, possibly due to over-rotation, is decomposed into Clifford channels with a quasiprobability…

We propose a linear-size synthesis of the multi-controlled Toffoli gate on qudits with at most one borrowed ancilla. This one ancilla can even be saved when the qudit dimension is odd. Our synthesis leads to improvements in various quantum…

The rotation of subspaces by a chosen angle is a fundamental quantum computing operation, with applications in error correction and quantum algorithms such as the Quantum Approximate Optimization Algorithm, the Variational Quantum…

We provide a method for compiling approximate multi-controlled single qubit gates into quantum circuits without ancilla qubits. The total number of elementary gates to decompose an n-qubit multi-controlled gate is proportional to 32n, and…

Many synthesis approaches for reversible and quantum logic have been proposed so far. However, most of them generate circuits with respect to simple metrics, i.e. gate count or quantum cost. On the other hand, to physically realize…

We present an algorithm for building a circuit that approximates single qubit unitaries with precision {\epsilon} using O(log(1/{\epsilon})) Clifford and T gates and employing up to two ancillary qubits. The algorithm for computing our…

We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve…

In this paper we show that it is possible to adapt a qudit scheme for creating a controlled-Toffoli created by Ralph et al. [Phys. Rev. A 75 011213] to be applicable to qubits. While this scheme requires more gates than standard schemes for…

Due to the unreliability and limited capacity of existing quantum computer prototypes, quantum circuit simulation continues to be a vital tool for validating next generation quantum computers and for studying variational quantum algorithms,…

One of the major promises of quantum computing is the realization of SIMD (single instruction - multiple data) operations using the phenomenon of superposition. Since the dimension of the state space grows exponentially with the number of…

In some quantum algorithms, arithmetic operations are of utmost importance for resource estimation. In binary quantum systems, some efficient implementation of arithmetic operations like, addition/subtraction, multiplication/division,…

Single-qubit gates are in many quantum platforms applied using a linear drive resonant with the qubit transition frequency which is often theoretically described within the rotating-wave approximation (RWA). However, for fast gates on…

Implementing the group arithmetic is a cost-critical task when designing quantum circuits for Shor's algorithm to solve the discrete logarithm problem. We introduce a tool for the automatic generation of addition circuits for ordinary…

We describe methods to construct digital quantum simulation algorithms for quantum spin systems on a regular lattice with local interactions. In addition to tools such as the Trotter-Suzuki expansion and graph coloring, we also discuss the…

Quantum circuits for basic mathematical functions such as the square root are required to implement scientific computing algorithms on quantum computers. Quantum circuits that are based on Clifford+T gates can easily be made fault tolerant…

Quantum Entanglement is a fundamentally important resource in Quantum Information Science; however, generating it in practice is plagued by noise and decoherence, limiting its utility. Entanglement distillation and forward error correction…

In this work, approximate eight-bit floating-point operations performed using simple integer operations is discussed. For two-bit mantissa formats, faithful rounding can always be obtained for the considered operations. For all operations,…

Multi-controlled Toffoli gates are fundamental building blocks in quantum computation, with applications in quantum arithmetic, simulation, and search algorithms. In fault-tolerant architectures, their realization is constrained by the high…

The synthesis of a quantum circuit consists in decomposing a unitary matrix into a series of elementary operations. In this paper, we propose a circuit synthesis method based on the QR factorization via Householder transformations. We…