相关论文: Lower Bounds for the Size of Nondeterministic Circ…

Quantum Parametric Circuits are constructed as an alternative to reduce the size of quantum circuits, meaning to decrease the number of quantum gates and, consequently, the depth of these circuits. However, determining the optimal circuit…

Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily…

We calculate universal finite-size scaling functions for systems with an n-component order parameter and algebraically decaying interactions. Just as previously has been found for short-range interactions, this leads to a singular…

We show that there is a defining equation of degree at most $\mathsf{poly}(n)$ for the (Zariski closure of the) set of the non-rigid matrices: that is, we show that for every large enough field $\mathbb{F}$, there is a non-zero…

Nondeterminism in neural network optimization produces uncertainty in performance, making small improvements difficult to discern from run-to-run variability. While uncertainty can be reduced by training multiple model copies, doing so is…

We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, polynomial scaling distance and efficient decoding schemes. The code family is based on tessellations of closed,…

For a matrix $M$ and a positive integer $r$, the rank $r$ rigidity of $M$ is the smallest number of entries of $M$ which one must change to make its rank at most $r$. There are many known applications of rigidity lower bounds to a variety…

We show that sharp thresholds for Boolean functions directly imply average-case circuit lower bounds. More formally we show that any Boolean function exhibiting a sharp enough threshold at \emph{arbitrary} critical density cannot be…

Recently, Forbes, Kumar and Saptharishi [CCC, 2016] proved that there exists an explicit $d^{O(1)}$-variate and degree $d$ polynomial $P_{d}\in VNP$ such that if any depth four circuit $C$ of bounded formal degree $d$ which computes a…

Non-deterministic quantum noiseless linear amplifiers are a new technology with interest in both fundamental understanding and new applications. With a noiseless linear amplifier it is possible to perform tasks such as improving the…

The observation that optimum circuit size changes by at most $O(n)$ under a one-point truth table perturbation is implicit in prior work on the Minimum Circuit Size Problem. This note states the bound explicitly for arbitrary fixed finite…

Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity…

The limit of families of two-dimensional conformal field theories has recently attracted attention in the context of AdS/CFT dualities. In our work we analyse the limit of N=(2,2) superconformal minimal models when the central charge…

This paper proposes a "quasi-synchronous" design approach for signal processing circuits, in which timing violations are permitted, but without the need for a hardware compensation mechanism. The case of a low-density parity-check (LDPC)…

In this paper we revisit Safra's determinization constructions for automata on infinite words. We show how to construct deterministic automata with fewer states and, most importantly, parity acceptance conditions. Determinization is used in…

Decoupling has become a central concept in quantum information theory with applications including proving coding theorems, randomness extraction and the study of conditions for reaching thermal equilibrium. However, our understanding of the…

Many promising quantum algorithms in economics, medical science, and material science rely on circuits that are parameterized by a large number of angles. To ensure that these algorithms are efficient, these parameterized circuits must be…

The notion of a non-deterministic logical matrix (where connectives are interpreted as multi-functions) extends the traditional semantics for propositional logics based on logical matrices (where connectives are interpreted as functions).…

Recently, low-resolution LDPC decoders have been introduced that perform mutual information maximizing signal processing. However, the optimal quantization in variable and check nodes requires expensive non-uniform operations. Instead, we…

This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…