Related papers: Constant-Optimized Quantum Circuits for Modular Mu…
In this study, we propose a new method for constrained combinatorial optimization using variational quantum circuits. Quantum computers are considered to have the potential to solve large combinatorial optimization problems faster than…
Optimizing the size and depth of CNOT circuits is an active area of research in quantum computing and is particularly relevant for circuits synthesized from the Clifford + T universal gate set. Although many techniques exist for finding…
We show that several quantum circuit families can be simulated efficiently classically if it is promised that their output distribution is approximately sparse i.e. the distribution is close to one where only a polynomially small, a priori…
Digital circuits based on residue number systems have been considered to produce a pseudo-random behavior. The present work is an initial step towards the complete implementation of those systems for similar applications using quantum…
The synthesis approaches for quantum circuits typically aim at minimizing the number of lines or gates. Given the tight restrictions on those logical resources in physical implementations, we propose to view the problem fundamentally…
Efficient arithmetic circuit design for resourceconstrained hardware involves challenging combinatorial optimization problems, among which Multiple Constant Multiplication (MCM) is a prominent example. MCM aims at implementing…
The paper proposes an implicit (i.e., machine-independent) complexity approach to studying computation by polynomial-size, constant-depth circuits with gates counting modulo a constant through the lens of discrete ordinary differential…
The integer factorization problem (IFP) underpins the security of RSA, yet becomes efficiently solvable on a quantum computer through Shor's algorithm. Regev's recent high-dimensional variant reduces the circuit size through lattice-based…
We show the applicability of the Cartan decomposition of Lie algebras to quantum circuits. This approach can be used to synthesize circuits that can efficiently implement any desired unitary operation. Our method finds explicit quantum…
Quantum arithmetic circuits have practical applications in various quantum algorithms. In this paper, we address quantum addition on 2-dimensional nearest-neighbor architectures based on the work presented by Choi and Van Meter (JETC 2012).…
We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…
Shor's factoring algorithm is one of the most anticipated applications of quantum computing. However, the limited capabilities of today's quantum computers only permit a study of Shor's algorithm for very small numbers. Here we show how…
In quantum computing the decoherence time of the qubits determines the computation time available and this time is very limited when using current hardware. In this paper we minimize the execution time (the depth) for a class of circuits…
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…
We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure…
Quantum computers allow a near-exponential speed-up for specific applications when compared to classical computers. Despite recent advances in the hardware of quantum computers, their practical usage is still severely limited due to a…
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,…
We demonstrate a technique for optimizing quantum circuits that is analogous to classical windowing. Specifically, we show that small table lookups can allow control qubits to be iterated in groups instead of individually. We present…
We consider a version of Shor's quantum factoring algorithm such that the quantum Fourier transform is replaced by an extremely simple one where decomposition coefficients take only the values of $1,i,-1,-i$. In numerous calculations which…
There is a folkloric belief that a depth-$\Theta(m)$ quantum circuit is needed to estimate the trace of the product of $m$ density matrices (i.e., a multivariate trace), a subroutine crucial to applications in condensed matter and quantum…