Related papers: RedCarD: A Quantum Assisted Algorithm for Fixed-De…
Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize…
We show the applicability of the Cartan decomposition of Lie algebras to quantum circuits. This approach can be used to synthesize circuits that can efficiently implement any desired unitary operation. Our method finds explicit quantum…
Quantum dynamics simulations (QDSs) are one of the most highly anticipated applications of quantum computing. Quantum circuit depth for implementing Hamiltonian simulation algorithms is commonly time dependent so that long time dynamics…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
Quantum computers can efficiently solve problems which are widely believed to lie beyond the reach of classical computers. In the near-term, hybrid quantum-classical algorithms, which efficiently embed quantum hardware in classical…
Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for translation of bigger unitary gates into elementary quantum operations,…
We provide a new algorithm that translates a unitary matrix into a quantum circuit according to the G=KAK theorem in Lie group theory. With our algorithm, any matrix decomposition corresponding to type-AIII KAK decompositions can be derived…
Accurate computation of the Green's function is crucial for connecting experimental observations to the underlying quantum states. A major challenge in evaluating the Green's function in the time domain lies in the efficient simulation of…
Decoherence of quantum hardware is currently limiting its practical applications. At the same time, classical algorithms for simulating quantum circuits have progressed substantially. Here, we demonstrate a hybrid framework that integrates…
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…
We introduce the flag decomposition as a central tool for unitary synthesis. It lets us carve out a diagonal unitary with $2^n$ degrees of freedom in such a way that the remaining flag circuit is parametrized by the optimal number of…
Unitary synthesis is the process of decomposing a target unitary transformation into a sequence of quantum gates. This is a challenging task, as the number of possible gate combinations grows exponentially with the circuit depth. In this…
Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the…
Recursive Cartan decompositions (CDs) provide a way to exactly factorize quantum circuits into smaller components, making them a central tool for unitary synthesis. Here we present a detailed overview of recursive CDs, elucidating their…
Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational…
Quantum computing is a promising paradigm that may overcome the current computational power bottlenecks. The increasing maturity of quantum processors provides more possibilities for the development and implementation of quantum algorithms.…
Hamiltonian simulation, i.e., simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful…
Despite rapid progress in the field, it is still challenging to discover new ways to take advantage of quantum computation: all quantum algorithms need to be designed by hand, and quantum mechanics is notoriously counterintuitive. In this…
In the Noisy Intermediate Scale Quantum (NISQ) era, finding implementations of quantum algorithms that minimize the number of expensive and error prone multi-qubit gates is vital to ensure computations produce meaningful outputs. Unitary…
Simulation of realistic classical mechanical systems is of great importance to many areas of engineering such as robotics, dynamics of rotating machinery and control theory. In this work, we develop quantum algorithms to estimate quantities…