Stuart Hadfield
Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand,…
We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve…
Algorithms based on non-unitary evolution have attracted much interest for ground state preparation on quantum computers. One recently proposed method makes use of ancilla qubits and controlled unitary operators to implement weak…
We present Noise-Directed Adaptive Remapping (NDAR), a heuristic algorithm for approximately solving binary optimization problems by leveraging certain types of noise. We consider access to a noisy quantum processor with dynamics that…
Driver Hamiltonians and Mixing Operators that satisfy constraints is an important part of ansatz construction for many quantum algorithms. In this manuscript, we give general algebraic expressions for finding Hamiltonian terms and…
Too often, quantum computer scientists seek to create new algorithms entirely fresh from new cloth when there are extensive and optimized classical algorithms that can be generalized wholesale. At the same time, one may seek to maintain…
Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…
Quantum optimization, both for classical and quantum functions, is one of the most well-studied applications of quantum computing, but recent trends have relied on hybrid methods that push much of the fine-tuning off onto costly classical…
We develop a hardware-efficient ansatz for variational optimization, derived from existing ansatze in the literature, that parametrizes subsets of all interactions in the Cost Hamiltonian in each layer. We treat gate orderings as a…
Quantum Fourier transformations are an essential component of many quantum algorithms, from prime factoring to quantum simulation. While the standard abelian QFT is well-studied, important variants corresponding to \emph{nonabelian} groups…
Quantum computing is one of the most enticing computational paradigms with the potential to revolutionize diverse areas of future-generation computational systems. While quantum computing hardware has advanced rapidly, from tiny laboratory…
Parameterized quantum circuits are attractive candidates for potential quantum advantage in the near term and beyond. At the same time, as quantum computing hardware not only continues to improve but also begins to incorporate new features…
Combinatorial optimization is a broadly attractive area for potential quantum advantage, but no quantum algorithm has yet made the leap. Noise in quantum hardware remains a challenge, and more sophisticated quantum-classical algorithms are…
Diagrammatic representations of quantum algorithms and circuits offer novel approaches to their design and analysis. In this work, we describe extensions of the ZX-calculus especially suitable for parameterized quantum circuits, in…
Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited,…
Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing…
The Quantum Approximate Optimization Algorithm and its generalization to Quantum Alternating Operator Ansatz (QAOA) is a promising approach for applying quantum computers to challenging problems such as combinatorial optimization and…
Simulating general quantum processes that describe realistic interactions of quantum systems following a non-unitary evolution is challenging for conventional quantum computers that directly implement unitary gates. We analyze complexities…
We develop a framework for analyzing layered quantum algorithms such as quantum alternating operator ans\"atze. Our framework relates quantum cost gradient operators, derived from the cost and mixing Hamiltonians, to classical cost…
It is crucial to reduce the resources required to run quantum algorithms and simulate physical systems on quantum computers due to coherence time limitations. With regards to Hamiltonian simulation, a significant effort has focused on…