Related papers: On The Capacity Of Noisy Computations
Model explanations can be valuable for interpreting and debugging predictive models. We study a specific kind called Concept Explanations, where the goal is to interpret a model using human-understandable concepts. Although popular for…
Channel capacities quantify the optimal rates of sending information reliably over noisy channels. Usually, the study of capacities assumes that the circuits which sender and receiver use for encoding and decoding consist of perfectly…
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 this paper, we first consider a channel that is contaminated by two independent Gaussian noises $S ~ N(0,Q)$ and $Z_0 ~ N(0,N_0)$. The capacity of this channel is computed when independent noisy versions of $S$ are known to the…
The reliability of logical operations is indispensable for the reliable operation of computational systems. Since the down-sizing of micro-fabrication generates non-negligible noise in these systems, a new approach for designing…
Over-the-air computation has the potential to increase the communication-efficiency of data-dependent distributed wireless systems, but is vulnerable to eavesdropping. We consider over-the-air computation over block-fading additive white…
We consider fault-tolerant quantum computation in the context where there are no fresh ancilla qubits available during the computation, and where the noise is due to a general quantum channel. We show that there are three classes of noisy…
Cloud-based quantum computing, coupled with the rapid progress in quantum algorithms, brings to the forefront the question of verifiability in delegated quantum computations. In the current landscape of noisy quantum devices, this question…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…
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,…
The maximum rates for information transmission through noisy quantum channels has primarily been developed for memoryless channels, where the noise on each transmitted state is treated as independent. Many real world communication channels…
We present a family of additive quantum error-correcting codes whose capacities exceeds that of quantum random coding (hashing) for very noisy channels. These codes provide non-zero capacity in a depolarizing channel for fidelity parameters…
We consider the problem of reliable communication over multiple-access channels (MAC) where the channel is driven by an independent and identically distributed state process and the encoders and the decoder are provided with various degrees…
This paper considers a sequential estimation and sensor scheduling problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process, and makes a decision as…
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…
This work considers a Poisson noise channel with an amplitude constraint. It is well-known that the capacity-achieving input distribution for this channel is discrete with finitely many points. We sharpen this result by introducing upper…
Recent experimental achievements motivate an ever-growing interest from companies starting to feel the limitations of classical computing. Yet, in light of ongoing privacy scandals, the future availability of quantum computing through…
Transmitting data reliably over noisy communication channels is one of the most important applications of information theory, and well understood when the channel is accurately modelled by classical physics. However, when quantum effects…
The channel capacity of a nonlinear, dispersive fiber-optic link is revisited. To this end, the popular Gaussian noise (GN) model is extended with a parameter to account for the finite memory of realistic fiber channels. This finite-memory…
Usual scenarios of fault-tolerant computation are concerned with the fault-tolerant realization of quantum algorithms that compute classical functions, such as Shor's algorithm for factoring. In particular, this means that input and output…