Related papers: Optimization of Lattice Surgery is NP-Hard
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…
We prove upper bounds on the order of convergence of lattice based algorithms for numerical integration in function spaces of dominating mixed smoothness on the unit cube with homogeneous boundary condition. More precisely, we study…
Quantum computing has garnered attention for its potential to solve complex computational problems with considerable speedup. Despite notable advancements in the field, achieving meaningful scalability and noise control in quantum hardware…
A scheme for globally addressing a quantum computer is presented along with its realisation in an optical lattice setup of one, two or three dimensions. The required resources are mainly those necessary for performing quantum simulations of…
Quantum computing promises the possibility of studying the real-time dynamics of nonperturbative quantum field theories while avoiding the sign problem that obstructs conventional lattice approaches. Current and near-future quantum devices…
Graph partitioning is one of an important set of well-known compute-intense (NP-hard) graph problems that devolve to discrete constrained optimization. We sampled solutions to the problem via two different quantum-ready methods to…
Classical simulation of quantum circuits plays a crucial role in validating quantum hardware and delineating the boundaries of quantum advantage. Among the most effective simulation techniques are those based on the stabilizer extent, which…
The problem of minimizing the maximum of $N$ convex, Lipschitz functions plays significant roles in optimization and machine learning. It has a series of results, with the most recent one requiring $O(N\epsilon^{-2/3} + \epsilon^{-8/3})$…
The NP-hard problem of optimizing a quadratic form over the unimodular vector set arises in radar code design scenarios as well as other active sensing and communication applications. To tackle this problem (which we call unimodular…
Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. In deep-space optical communications, current receivers for the…
Logical gates constitute the building blocks of fault-tolerant quantum computation. While quantum error-corrected memories have been extensively studied in the literature, explicit constructions and detailed analyses of thresholds and…
In a capacitated directed graph, it is known that the set of all min-cuts forms a distributive lattice [1], [2]. Here, we describe this lattice as a regular predicate whose forbidden elements can be advanced in constant parallel time after…
One of the most promising routes towards fault-tolerant quantum computation utilizes topological quantum error correcting codes, such as the $\mathbb{Z}_2$ surface code. Logical qubits can be encoded in a variety of ways in the surface…
Simulation of quantum computing on supercomputers is a significant research topic, which plays a vital role in quantum algorithm verification, error-tolerant verification and other applications. Tensor network contraction based on density…
To implement quantum algorithms on a quantum computer, we must overcome the twin problems of fault-tolerance -- how can we realize a relatively noiseless computation by cleverly combining noisy components? -- and compilation -- how can we…
Optimization problems constrained by partial differential equations (PDEs) naturally arise in scientific computing, as those constraints often model physical systems or the simulation thereof. In an implicitly constrained approach, the…
The surface code is a promising platform for a quantum memory, but its threshold under coherent errors remains incompletely understood. We study maximum-likelihood decoding of the square-lattice surface code in the presence of single-qubit…
Motivated by recent progress in quantum hardware and algorithms researchers have developed quantum heuristics for optimization problems, aiming for advantages over classical methods. To date, quantum hardware is still error-prone and…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…