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We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
This paper proves the threshold result, which asserts that quantum computation can be made robust against errors and inaccuracies, when the error rate, $\eta$, is smaller than a constant threshold, $\eta_c$. The result holds for a very…
A quantum computer -- i.e., a computer capable of manipulating data in quantum superposition -- would find applications including factoring, quantum simulation and tests of basic quantum theory. Since quantum superpositions are fragile, the…
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…
In theory, quantum computers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantum computers must operate with noisy devices…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
The purpose of this little survey is to give a simple description of the main approaches to quantum error correction and quantum fault-tolerance. Our goal is to convey the necessary intuitions both for the problems and their solutions in…
We prove the existence of (one-way) communication tasks with a subconstant versus superconstant asymptotic gap, which we call "doubly infinite," between their quantum information and communication complexities. We do so by studying the…
In this perspective article, we revisit and critically evaluate prevailing viewpoints on the capabilities and limitations of near-term quantum computing and its potential transition toward fully fault-tolerant quantum computing. We examine…
Many quantum technologies are now reaching a high level of maturity and control, and it is likely that the first demonstrations of suppression of naturally occurring quantum noise using small topological error correcting codes will soon be…
We initiate a systematic study of pseudo-deterministic quantum algorithms. These are quantum algorithms that, for any input, output a canonical solution with high probability. Focusing on the query complexity model, our main contributions…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
A leading approach to algorithm design aims to minimize the number of operations in an algorithm's compilation. One intuitively expects that reducing the number of operations may decrease the chance of errors. This paradigm is particularly…
Fault-tolerant schemes can use error correction to make a quantum computation arbitrarily ac- curate, provided that errors per physical component are smaller than a certain threshold and in- dependent of the computer size. However in…
As techniques for fault-tolerant quantum computation keep improving, it is natural to ask: what is the fundamental lower bound on redundancy? In this paper, we obtain a lower bound on the redundancy required for $\epsilon$-accurate…
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation…
Quantum systems, in general, output data that cannot be simulated efficiently by a classical computer, and hence is useful for solving certain mathematical problems and simulating quantum many-body systems. This also implies, unfortunately,…
Quantum error mitigation techniques can reduce noise on current quantum hardware without the need for fault-tolerant quantum error correction. For instance, the quasiprobability method simulates a noise-free quantum computer using a noisy…