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The well-known algorithm for quantum phase estimation requires that the considered unitary is available as a conditional transformation depending on the quantum state of an ancilla register. We present an algorithm converting an unknown…

Orthogonal weight matrices are used in many areas of deep learning. Much previous work attempt to alleviate the additional computational resources it requires to constrain weight matrices to be orthogonal. One popular approach utilizes…

Preparing the ground state of a system is an important task in physics. We propose a quantum algorithm for preparing the ground state of a physical system that can be simulated on a quantum computer. The system is coupled to an ancillary…

We present an approach to simulating quantum computation based on a classical model that directly imitates discrete quantum systems. Qubits are represented as harmonic functions in a 2D vector space. Multiplication of qubit representations…

Simulating physical systems on quantum devices is one of the most promising applications of quantum technology. Current quantum approaches to simulating open quantum systems are still practically challenging on NISQ-era devices, because…

Quantum circuit equivalence checking asks whether two circuits implement the same unitary. It guarantees compiler correctness and safe optimization, yet most existing approaches scale exponentially with the number of qubits or the circuit…

Quantum comparators and modular arithmetic are fundamental in many quantum algorithms. Current research mainly focuses on operations between two quantum states. However, various applications, such as integer factorization, optimization,…

Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…

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…

Tasks such as classification of data and determining the groundstate of a Hamiltonian cannot be carried out through purely unitary quantum evolution. Instead, the inherent non-unitarity of the measurement process must be harnessed.…

Quantum algorithms for computing classical nonlinear maps are widely known for toy problems but might not suit potential applications to realistic physics simulations. Here, we propose how to compute a general differentiable invertible…

Entanglement lies at the core of quantum algorithms designed to solve problems that are intractable by classical approaches. One such algorithm, quantum annealing (QA), provides a promising path to a practical quantum processor. We have…

We introduce a scheme to perform universal quantum computation in quantum cellular automata (QCA) fashion in arbitrary subsystem dimension (not necessarily finite). The scheme is developed over a one spatial dimension $N$-element array,…

Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…

We present an efficient algorithm for twirling a multi-qudit quantum state. The algorithm can be used for approximating the twirling operation in an ensemble of physical systems in which the systems cannot be individually accessed. It can…

Qubit lattice algorithm (QLA) simulations are performed for a two-dimensional (2D) spatially bounded pulse propagating onto a plane interface between two dielectric slabs. QLA is an initial value scheme that consists of a sequence of…

Quantum search is among the most important algorithms in quantum computing. At its core is quantum amplitude amplification, a technique that achieves a quadratic speedup over classical search by combining two global reflections: the oracle,…

We present a general quantum circuit design for finding eigenvalues of non-unitary matrices on quantum computers using the iterative phase estimation algorithm. In particular, we show how the method can be used for the simulation of…

Quantum computing has been increasingly applied in nuclear physics. In this work, we combine quantum computing with the complex scaling method to address the resonance problem. Due to the non-Hermiticity introduced by complex scaling,…

We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the…