Related papers: Space-Optimized and Experimental Implementations o…
Applying quantum computing in the computer-aided engineering (CAE) problems are highly expected since quantum computers yield potential exponential speedups for the operations between extremely large matrices and vectors. Although efficient…
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…
We revisit Fermat's factorization method for a positive integer $n$ that is a product of two primes $p$ and $q$. Such an integer is used as the modulus for both encryption and decryption operations of an RSA cryptosystem. The security of…
Noise characterization methods such as randomized benchmarking (RB) are critical for the development of scalable quantum computers. Modern RB protocols for multiqubit systems extract physically relevant error rates by exploiting the…
Cat qubits provide appealing building blocks for quantum computing. They exhibit a tunable noise bias yielding an exponential suppression of bit flips with the average photon number and a protection against the remaining phase errors can be…
Quantum computing is one of the most promising technology advances of the latest years. Once only a conceptual idea to solve physics simulations, quantum computation is today a reality, with numerous machines able to execute quantum…
Quantum phase estimation (QPE) is a key quantum algorithm, which has been widely studied as a method to perform chemistry and solid-state calculations on future fault-tolerant quantum computers. Recently, several authors have proposed…
In this work we propose a high-quality decomposition approach for qubit routing by swap insertion. This optimization problem arises in the context of compiling quantum algorithms onto specific quantum hardware. Our approach decomposes the…
We present a novel and efficient in terms of circuit depth design for Shor's quantum factorization algorithm. The circuit effectively utilizes a diverse set of adders based on the quantum Fourier transform (QFT) Draper's adders to build…
Reversible circuits for modular multiplication $Cx$%$M$ with $x<M$ arise as components of modular exponentiation in Shor's quantum number-factoring algorithm. However, existing generic constructions focus on asymptotic gate count and…
Reasoning about quantum programs remains a fundamental challenge, regardless of the programming model or computational paradigm. Despite extensive research, existing verification techniques are insufficient -- even for quantum circuits, a…
Designing quantum processors is a complex task that demands advanced verification methods to ensure their correct functionality. However, traditional methods of comprehensively verifying quantum devices, such as quantum process tomography,…
Quantum computing has garnered attention for its potential to solve complex computational problems with considerable speedup. Despite notable advancements in the field, achieving meaningful scalability and noise control in quantum hardware…
To efficiently factorize high-dimensional distributed representations to the constituent atomic vectors, one can exploit the compute-in-superposition capabilities of vector-symbolic architectures (VSA). Such factorizers however suffer from…
We study quantum period finding algorithms such as Simon and Shor (and its variants Eker{\aa}-H{\aa}stad and Mosca-Ekert). For a periodic function $f$ these algorithms produce -- via some quantum embedding of $f$ -- a quantum superposition…
We provide a tight analysis of Grover's recent algorithm for quantum database searching. We give a simple closed-form formula for the probability of success after any given number of iterations of the algorithm. This allows us to determine…
Shor's algorithm is one of the most significant quantum algorithms. Shor's algorithm can factor large integers with a certain success probability in polynomial time. However, Shor's algorithm requires an unbearable amount of qubits in the…
We show that $n$-bit integers can be factorized by independently running a quantum circuit with $\tilde{O}(n^{3/2})$ gates for $\sqrt{n}+4$ times, and then using polynomial-time classical post-processing. The correctness of the algorithm…
Ideal quantum algorithms usually assume that quantum computing is performed continuously by a sequence of unitary transformations. However, there always exist idle finite time intervals between consecutive operations in a realistic quantum…
Classical simulation of quantum computation has often been viewed as the method to determine where the horizon of quantum supremacy is located---that is, where quantum computation can no longer be simulated by classical methods. As of now,…