Related papers: Quantum Approximate Counting with Additive Error: …
Fault-tolerant quantum computations require alternating quantum and classical computations, where the classical computations prove vital in detecting and correcting errors in the quantum computation. Recently, interest in using these…
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…
The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…
We study the exponential time complexity of approximate counting satisfying assignments of CNFs. We reduce the problem to deciding satisfiability of a CNF. Our reduction preserves the number of variables of the input formula and thus also…
We show enough evidence that a structured version of Adiabatic Quantum Computation (AQC) is efficient for most satisfiability problems. More precisely, when the success probability is fixed beforehand, the computational resources grow…
In this paper we show how to generalize the quantum approximate counting technique developed by Brassard, H{\o}yer and Tapp [ICALP 1998] to a more general setting: estimating the number of marked states of a Markov chain (a Markov chain can…
Quantum computers will be able solve important problems with significant polynomial and exponential speedups over their classical counterparts, for instance in option pricing in finance, and in real-space molecular chemistry simulations.…
Quantum measurements are a fundamental component of quantum computing. However, on modern-day quantum computers, measurements can be more error prone than quantum gates, and are susceptible to non-unital errors as well as non-local…
Quantum computing comes with the potential to push computational boundaries in various domains including, e.g., cryptography, simulation, optimization, and machine learning. Exploiting the principles of quantum mechanics, new algorithms can…
We study the complexity of computational problems from quantum physics. Typically, they are studied using the complexity class QMA (quantum counterpart of NP) but some natural computational problems appear to be slightly harder than QMA. We…
Theoretical descriptions of excited states of molecular systems in high-energy regimes are crucial for supporting and driving many experimental efforts at light source facilities. However, capturing their complicated correlation effects…
We prove a query complexity lower bound for $\mathsf{QMA}$ protocols that solve approximate counting: estimating the size of a set given a membership oracle. This gives rise to an oracle $A$ such that $\mathsf{SBP}^A \not\subset…
Recent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and the desired precision. Here we study a…
Quantum computers solve intractable problems which classically require an exponentially long time to compute. With the development of large-scale experiments that claim quantum advantage, a vital issue has now emerged. What are the errors,…
Projective measurements with high quantum efficiency is often assumed to be required for efficient circuit based quantum computing. We argue that this is not the case and show that this fact has actually be known previously though not…
Quantum computing offers significant potential for solving NP-hard combinatorial (optimization) problems that are beyond the reach of classical computers. One way to tap into this potential is by reformulating combinatorial problems as a…
We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions--approximability and distinguishability. Built upon…
The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do not mean the accuracy within the discrete setting, which…
Quantum circuit partitioning (QCP) is a hybrid quantum-classical approach that aims to simulate large quantum systems on smaller quantum computers. A quantum computation is divided into smaller subsystems and results of measurements on…
Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of…