Related papers: Applying Grover's algorithm to AES: quantum resour…
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,…
The AND gate is not reversible$\unicode{x2014}$on qubits. However, it is reversible on qutrits, making it a building block for efficient simulation of qubit computation using qutrits. We first observe that there are multiple two-qutrit…
Quantum noise is a central challenge in quantum computing across many applications. Extensive work has examined how qubits couple to their environment, leading to decoherence and relaxation, which is irreversible. Current studies focus on…
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce…
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's…
A new algorithm for minimization of quantum cost of quantum circuits has been designed. The quantum cost of different quantum circuits of particular interest (eg. circuits for EPR, quantum teleportation, shor code and different quantum…
We review Grover's algorithm by means of a detailed geometrical interpretation and a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are also reviewed. This work is intended for non-specialists which have…
Due to the technical difficulty of building large quantum computers, it is important to be able to estimate how faithful a given implementation is to an ideal quantum computer. The common approach of completely characterizing the…
We introduce the concepts of Grover operators and Grover kernels to systematically analyse Grover's searching algorithms. Then, we investigate a one-parameter family of quantum searching algorithms of Grover's type and we show that the…
The construction of a quantum computer remains a fundamental scientific and technological challenge, in particular due to unavoidable noise. Quantum states and operations can be protected from errors using protocols for fault-tolerant…
As experimental platforms for quantum information processing continue to mature, characterization of the quality of unitary gates that can be applied to their quantum bits (qubits) becomes essential. Eventually, the quality must be…
Gate-level quantum circuits are often derived manually from higher level algorithms. While this suffices for small implementations and demonstrations, ultimately automatic circuit design will be required to realise complex algorithms using…
The von Neumann and quantum R\'enyi entropies characterize fundamental properties of quantum systems and lead to theoretical and practical applications in many fields. Quantum algorithms for estimating quantum entropies, using a quantum…
Quantum data locking is a quantum communication primitive that allows the use of a short secret key to encrypt a much longer message. It guarantees information-theoretical security against an adversary with limited quantum memory. Here we…
Most work in quantum circuit optimization has been performed in isolation from the results of quantum fault-tolerance. Here we present a polynomial-time algorithm for optimizing quantum circuits that takes the actual implementation of…
Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
The difference between classical and quantum algorithms (QA) is following: problem solved by QA is coded in the structure of the quantum operators. Input to QA in this case is always the same. Output of QA says which problem coded. In some…
Circuit cutting allows quantum circuits larger than the available hardware to be executed. Cutting techniques split circuits into smaller subcircuits, run them on the hardware, and recombine results through classical post-processing.…
We consider the possibility of adding noise to a quantum circuit to make it efficiently simulatable classically. In previous works this approach has been used to derive upper bounds to fault tolerance thresholds - usually by identifying a…
We describe an efficient quantum algorithm for the quantum Schur transform. The Schur transform is an operation on a quantum computer that maps the standard computational basis to a basis composed of irreducible representations of the…