Related papers: Computers with closed timelike curves can solve ha…
We show that the time evolution of the wave function of a quantum mechanical many particle system can be implemented very efficiently on a quantum computer. The computational cost of such a simulation is comparable to the cost of a…
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…
If a large Quantum Computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not simulate on a classical Turing machine? In this paper we argue that a QC could solve some relevant physical…
The question of whether or not quantum computers can efficiently solve NP-complete problems is open, although indications are that BQP does not contain NP. Still, many of these problems are natural candidates for solution on quantum…
In principe, General Relativity seems to allow the existence of closed timelike curves (CTC). However, when quantum effects are considered, it is likely that their existence is prevented by some kind of chronological protection mechanism,…
Clocks are a central part of many computing paradigms, and are mainly used to synchronise the delicate operation of switching, necessary to drive modern computational processes. Unfortunately, this synchronisation process is reaching a…
It is well known, and appreciated, that quantum computers have the potential to be the most powerful computational devices ever created. This newfound power comes from a quantum parallelism effect that allows the computer to be in multiple…
The complexity class $PSPACE$ includes all computational problems that can be solved by a classical computer with polynomial memory. All $PSPACE$ problems are known to be solvable by a quantum computer too with polynomial memory and are,…
Concrete computing machines, either sequential or concurrent, rely on an intimate relation between computation and time. We recall the general characteristic properties of physical time and of present realizations of computing systems. We…
Proposed models of closed timelike curves (CTCs) have been shown to enable powerful information-processing protocols. We examine the simulation of models of CTCs both by other models of CTCs and by physical systems without access to CTCs.…
In the last decade, public and industrial research funding has moved quantum computing from the early promises of Shor's algorithm through experiments to the era of noisy intermediate scale quantum devices (NISQ) for solving real-world…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the…
In this comment on S.Lloyd, et al, Phys.Rev.Lett. 106, 040403 (2011), we show that modelling closed timelike curves (CTCs) as post-selected teleportation allows signalling to past times before the creation of the CTC and allows information…
In this paper we discuss analogue computers based on quantum optical systems accelerating dynamic programming for some computational problems. These computers, at least in principle, can be realized by actually existing devices. We estimate…
I study the class of problems efficiently solvable by a quantum computer, given the ability to "postselect" on the outcomes of measurements. I prove that this class coincides with a classical complexity class called PP, or Probabilistic…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…
Shor's algorithm for factoring in polynomial time on a quantum computer\cite{Shor} gives an enormous advantage over all known classical factoring algorithm. We demonstrate how to factor products of large prime numbers using a compiled…
Quantum computers are widely believed have an advantage over classical computers, and some have even published some empirical evidence that this is the case. However, these publications do not include a rigorous proof of this advantage,…