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Quantum chemistry and materials science are among the most promising areas for demonstrating algorithmic quantum advantage and quantum utility due to their inherent quantum mechanical nature. Still, large-scale simulations of quantum…
Fault-tolerant quantum error correction (QEC) is crucial for unlocking the true power of quantum computers. QEC codes use multiple physical qubits to encode a logical qubit, which is protected against errors at the physical qubit level.…
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…
Simulating electronic structure on a quantum computer requires encoding of fermionic systems onto qubits. Common encoding methods transform a fermionic system of $N$ spin-orbitals into an $N$-qubit system, but many of the fermionic…
Quantum computing has become a promising computing approach because of its capability to solve certain problems, exponentially faster than classical computers. A $n$-qubit quantum system is capable of providing $2^{n}$ computational space…
Numerical simulation is an important method for verifying the quantum circuits used to simulate low-energy nuclear states. However, real-world applications of quantum computing for nuclear theory often generate deep quantum circuits that…
Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to…
This paper addresses the challenge of scaling quantum computing by employing distributed quantum algorithms across multiple processors. We propose a novel circuit partitioning method that leverages graph partitioning to optimize both qubit…
Establishing an advantage for (white-box) computations by a quantum computer against its classical counterpart is currently a key goal for the quantum computation community. A quantum advantage is achieved once a certain computational…
A Quantum Computer is a new type of computer which can efficiently solve complex problems such as prime factorization. A quantum computer threatens the security of public key encryption systems because these systems rely on the fact that…
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…
Until high-fidelity quantum computers with a large number of qubits become widely available, classical simulation remains a vital tool for algorithm design, tuning, and validation. We present a simulator for the Quantum Approximate…
Current quantum computers require algorithms that use limited resources economically. In quantum machine learning, success hinges on quantum feature maps, which embed classical data into the state space of qubits. We introduce Quantum…
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…
The multiplication of superpositions of numbers is a core operation in many quantum algorithms. The standard method for multiplication (both classical and quantum) has a runtime quadratic in the size of the inputs. Quantum circuits with…
Quantum computing with qudits, an extension of qubits to multiple levels, is a research field less mature than qubit-based quantum computing. However, qudits can offer some advantages over qubits, by representing information with fewer…
Quantum bits have technological imperfections. Additionally, the capacity of a component that can be implemented feasibly is limited. Therefore, distributed quantum computation is required to scale up quantum computers. This dissertation…
Rapid development in quantum computing leads to the appearance of several quantum applications. Quantum Fourier Transformation (QFT) sits at the heart of many of these applications. Existing work leverages SAT solver or heuristics to…
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…
Quantum computations are typically compiled into a circuit of basic quantum gates. Just like for classical circuits, a quantum compiler should optimize the quantum circuit, e.g. by minimizing the number of required gates. Optimizing quantum…