Related papers: Relative error due to a single bit-flip in floatin…
We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our…
We correct some errors in the two papers published with the above title in Class. Quant. Grav. 19 (2002). In particular, the correct prescription for computing the probabilities is given, in that appropriate normalization factors are…
We develop a classical bit-flip correction method to mitigate measurement errors on quantum computers. This method can be applied to any operator, any number of qubits, and any realistic bit-flip probability. We first demonstrate the…
Gradient-based adversarial attacks using the Cross-Entropy (CE) loss often suffer from overestimation due to relative errors in gradient computation induced by floating-point arithmetic. This paper provides a rigorous theoretical analysis…
Given a random binary sequence $X^{(n)}$ of random variables, $X_{t},$ $t=1,2,...,n$, for instance, one that is generated by a Markov source (teacher) of order $k^{*}$ (each state represented by $k^{*}$ bits). Assume that the probability of…
We give a new explicitly invertible approximation of the normal cumulative distribution function: $\Phi(x) \simeq 1/2 + 1/2 \sqrt{1-{e}^{-x^2\frac{17+{x}^{2}}{26.694+2x^2}}}$, $\forall x \ge 0$, with absolute error $<4.00\cdot 10^{-5}$,…
A family of protocols for quantum weak coin-flipping which asymptotically achieve a bias of 0.192 is described in this paper. The family contains protocols with n+2 messages for all n>1. The case n=2 is equivalent to the protocol of…
To reduce the resource demand of neural network (NN) inference systems, it has been proposed to use approximate memory, in which the supply voltage and the timing parameters are tuned trading accuracy with energy consumption and…
In this paper, we investigate the impact of bit flip errors in FPGA memories in control electronics on quantum computing systems. FPGA memories are integral in storing the amplitude and phase information pulse envelopes, which are essential…
Faced with a sequence of N binary events, such as coin flips (or Ising spins), it is natural to ask whether these events reflect some underlying dynamic signals or are just random. Plausible models for the dynamics of hidden biases lead to…
Consider a universal Turing machine that produces a partial or total function (or a binary stream), based on the answers to the binary queries that it makes during the computation. We study the probability that the machine will produce a…
Given a point set $\mathcal{P}$ and a plane perfect matching $\mathcal{M}$ on $\mathcal{P}$, a flip is an operation that replaces two edges of $\mathcal{M}$ such that another plane perfect matching on $\mathcal{P}$ is obtained. Given two…
I make a rough estimate of the accuracy threshold for fault tolerant quantum computing with concatenated codes. First I consider only gate errors and use the depolarizing channel error model. I will follow P.Shor (quant-ph/9505011) for…
We analyse the forward error in the floating point summation of real numbers, from algorithms that do not require recourse to higher precision or better hardware. We derive informative explicit expressions, and new deterministic and…
Consider $n$ independent, biased coins, each with a known probability of heads. Presented with an ordering of these coins, flip (i.e., toss) each coin once, in that order, until we have observed both a *head* and a *tail*, or flipped all…
In this paper, we will give some estimation for the average error of the prime number theorem.
We develop efficient binary (i.e., 1-bit) and multi-bit coding schemes for estimating the scale parameter of $\alpha$-stable distributions. The work is motivated by the recent work on one scan 1-bit compressed sensing (sparse signal…
Given the importance of floating-point~(FP) performance in numerous domains, several new variants of FP and its alternatives have been proposed (e.g., Bfloat16, TensorFloat32, and Posits). These representations do not have correctly rounded…
Each classical public-coin protocol for coin flipping is naturally associated with a quantum protocol for weak coin flipping. The quantum protocol is obtained by replacing classical randomness with quantum entanglement and by adding a cheat…
We present a new protocol and two lower bounds for quantum coin flipping. In our protocol, no dishonest party can achieve one outcome with probability more than 0.75. Then, we show that our protocol is optimal for a certain type of quantum…