Related papers: Quantum Advantage for All
We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum algorithm with time complexity q^(3/8) (log q)^O(1) is…
A robust definition of quantum runtime is essential for assessing the performance of quantum algorithms and claims of quantum advantage. While for most classical hardware the total runtime is well approximated by computation plus a weakly…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
Quantum computation by adiabatic evolution, as described in quant-ph/0001106, will solve satisfiability problems if the running time is long enough. In certain special cases (that are classically easy) we know that the quantum algorithm…
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…
In machine learning, fewer features reduce model complexity. Carefully assessing the influence of each input feature on the model quality is therefore a crucial preprocessing step. We propose a novel feature selection algorithm based on a…
To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…
A recently introduced classical simulation method for universal quantum computation with magic states operates by repeated sampling from probability functions [M. Zurel et al. PRL 260404 (2020)]. This method is closely related to sampling…
Simulating the time evolution of a physical system at quantum mechanical levels of detail -- known as Hamiltonian Simulation (HS) -- is an important and interesting problem across physics and chemistry. For this task, algorithms that run on…
Quantum computing exploits quantum phenomena such as superposition and entanglement to realize a form of parallelism that is not available to traditional computing. It offers the potential of significant computational speed-ups in quantum…
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…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
Although quantum algorithms realizing an exponential time speed-up over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we…
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…
In this thesis, we introduce a new quantum Turing machine (QTM) model that supports general quantum operators, together with its pushdown, counter, and finite automaton variants, and examine the computational power of classical and quantum…
Quantum annealing offers a promising paradigm for solving NP-hard combinatorial optimization problems, but its practical application is severely hindered by two challenges: the complex, manual process of translating problem descriptions…
Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum accelerated simulated…
Quantum computational supremacy arguments, which describe a way for a quantum computer to perform a task that cannot also be done by a classical computer, typically require some sort of computational assumption related to the limitations of…
Quantum computing is the process of performing calculations using quantum mechanics. This field studies the quantum behavior of certain subatomic particles for subsequent use in performing calculations, as well as for large-scale…
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…