Related papers: On exact counting and quasi-quantum complexity

We introduce a variational algorithm based on the quantum alternating operator ansatz (QAOA) for the approximate solution of computationally hard counting problems. Our algorithm, dubbed VQCount, is based on the equivalence between random…

There's something really strange about quantum mechanics. It's not just that cats can be dead and alive at the same time, and that entanglement seems to violate the principle of locality; quantum mechanics seems to be what Aaronson calls…

We analyze the forward error in the floating point summation of real numbers, for computations in low precision or extreme-scale problem dimensions that push the limits of the precision. We present a systematic recurrence for a martingale…

We define counting classes #P_R and #P_C in the Blum-Shub-Smale setting of computations over the real or complex numbers, respectively. The problems of counting the number of solutions of systems of polynomial inequalities over R, or of…

We explore the space "just above" BQP by defining a complexity class PDQP (Product Dynamical Quantum Polynomial time) which is larger than BQP but does not contain NP relative to an oracle. The class is defined by imagining that quantum…

We gather and examine in detail gate decomposition techniques for continuous-variable quantum computers and also introduce some new techniques which expand on these methods. Both exact and approximate decomposition methods are studied and…

The formula-evaluation problem is defined recursively. A formula's evaluation is the evaluation of a gate, the inputs of which are themselves independent formulas. Despite this pure recursive structure, the problem is combinatorially…

It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum…

This paper studies the important problem of quantum classification of Boolean functions from a entirely novel perspective. Typically, quantum classification algorithms allow us to classify functions with a probability of $1.0$, if we are…

This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…

We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer…

Bosonic rotation codes, introduced here, are a broad class of bosonic error-correcting codes based on phase-space rotation symmetry. We present a universal quantum computing scheme applicable to a subset of this class--number-phase…

We consider the problem of identifying the defectives from a population of items via a non-adaptive group testing framework with a random pooling-matrix design. We analyze the sufficient number of tests needed for approximate set…

With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability $p$. The…

Recent demonstrations on specialized benchmarks have reignited excitement for quantum computers, yet whether they can deliver an advantage for practical real-world problems remains an open question. Here, we show that probabilistic…

Unconstrained binary integer programming (UBIP) poses significant computational challenges due to its discrete nature. We introduce a novel reformulation approach using a piecewise cubic function that transforms binary constraints into…

We re-examine a non-Gaussian quantum error correction code designed to protect optical coherent-state qubits against errors due to an amplitude damping channel. We improve on a previous result [Phys. Rev. A 81, 062344 (2010)] by providing a…

In this thesis, we develop algorithms similar to the Gaussian elimination algorithm in symplectic and split orthogonal similitude groups. As an application to this algorithm, we compute the spinor norm for split orthogonal groups. Also, we…

Computational validation is vital for all large-scale quantum computers. One needs computers that are both fast and accurate. Here we apply precise, scalable, high order statistical tests to data from large Gaussian boson sampling (GBS)…

In this work we define an universal arithmetical algorithm, by means of the standard quantum mechanical formalism, called universal qm-arithmetical algorithm. By universal qm-arithmetical algorithm any decidable arithmetical formula…