Related papers: Halving the width of Toffoli based constant modula…

While quantum computing holds great potential in combinatorial optimization, electronic structure calculation, and number theory, the current era of quantum computing is limited by noisy hardware. Many quantum compilation approaches can…

To approximate arbitrary unitary transformations on one or more qubits, one must perform transformations which are outside of the Clifford group. The gate most commonly considered for this purpose is the T = diag(1, exp(i \pi/4)) gate. As T…

Numerous scientific developments in this NISQ-era (Noisy Intermediate Scale Quantum) have raised the importance for quantum algorithms relative to their conventional counterparts due to its asymptotic advantage. For resource estimates in…

We developed a general framework for synthesizing target gates by using a finite set of basic gates, which is a crucial step in quantum compilation. When approximating a gate in SU($n$), a naive brute-force search requires a computational…

Current quantum computers are especially error prone and require high levels of optimization to reduce operation counts and maximize the probability the compiled program will succeed. These computers only support operations decomposed into…

The relevance of shallow-depth quantum circuits has recently increased, mainly due to their applicability to near-term devices. In this context, one of the main goals of quantum circuit complexity is to find problems that can be solved by…

Universal quantum entangling gates are a crucial building block in the large-scale quantum computation and quantum communication, and it is an important task to find simple ways to implement them. Here an effective quantum circuit for the…

We describe a simple algorithm for sampling $n$-qubit Clifford operators uniformly at random. The algorithm outputs the Clifford operators in the form of quantum circuits with at most $5n + 2n^2$ elementary gates and a maximum depth of…

Classical simulation of noisy quantum circuits is essential for understanding quantum computing experiments. It enables scalable error characterization, analysis of how noise impacts quantum algorithms, and optimized implementations of…

Let $n\geq 8$ be divisible by 4. The Clifford-cyclotomic gate set $\mathcal{G}_n$ is the universal gate set obtained by extending the Clifford gates with the $z$-rotation $T_n = \mathrm{diag}(1,\zeta_n)$, where $\zeta_n$ is a primitive…

In the near term, programming quantum computers will remain severely limited by low quantum volumes. Therefore, it is desirable to implement quantum circuits with the fewest resources possible. For the common Clifford+T circuits, most…

We focus on the depth optimization of CNOT circuits on hardwares with limited connectivity. We adapt the algorithm from Kutin et al. that implements any $n$-qubit CNOT circuit in depth at most $5n$ on a Linear Nearest Neighbour (LNN)…

Quantum algorithms claim significant speedup over their classical counterparts for solving many problems. An important aspect of many of these algorithms is the existence of a quantum oracle, which needs to be implemented efficiently in…

The circuit-level implementation of a quantum string-matching algorithm, which matches a search string (pattern) of length $M$ inside a longer text of length $N$, has already been demonstrated in the literature to outperform its classical…

We introduce a new quantum layout-aware approach to realize cost-effective $n$-bit gates using the Bloch sphere, for $2 \le n \le 5$ qubits. These $n$-bit gates are entirely constructed from the Clifford+T gates, in the approach of…

Mutually unbiased bases (MUBs) play a crucial role in numerous applications within quantum information science, such as quantum state tomography, error correction, entanglement detection, and quantum cryptography. Utilizing \(2^n + 1\) MUB…

Quantum squaring operation is a useful building block in implementing quantum algorithms such as linear regression, regularized least squares algorithm, order-finding algorithm, quantum search algorithm, Newton Raphson division, Euclidean…

Some physical implementation schemes of quantum computing can apply two-qubit gates only on certain pairs of qubits. These connectivity constraints are commonly viewed as a significant disadvantage. For example, compiling an unrestricted…

Quantum circuits which perform integer arithmetic could potentially outperform their classical counterparts. In this paper, a quantum circuit is considered which performs a specific computational pattern on classically represented integers…

In this paper, we settle the long-standing open problem of the minimum cost of two-qubit gates for simulating a Toffoli gate. More precisely, we show that five two-qubit gates are necessary. Before our work, it is known that five gates are…