arXiv subjects

Smita Bagewadi

Publications and source records attributed to Smita Bagewadi.

3 recordsLinked to original sources

arXiv2024

Limited Parallelization in Gate Operations Leads to Higher Space Overhead and Lower Noise Threshold

In a modern error corrected quantum memory or circuit, parallelization of gate operations is severely restricted due to issues like cross-talk. Hence, there are enough idle qubits not undergoing gate operations either during the computation phase or during the error correction phase, which suffer further decoherence while waiting. Thus, in reality, the space overhead and the noise threshold would depend on the level of gate parallelization. In this paper, we obtain an analytical lower bound on the required space overhead in terms of the level of parallelization for an error correction framework that has more error correction capability than the existing ones. We consider two types of errors: i.i.d. erasure and depolarization. In comparison to the known lower bounds which assume full gate parallelization, our bound is provably strictly larger despite allowing more capability to the error correction framework. This shows the steep price to be paid for lack of gate parallelization. An implication of the bound is that the noise or decoherence threshold, i.e., the noise beyond which no fault-tolerant memory or circuit can be realized, vanishes if the number of parallel gate operations does not scale linearly with the number of physical qubits.

quant-ph↗

arXiv2024

Effect of Correlated Errors on Quantum Memory

Recent results on constant overhead LDPC code-based fault-tolerance against i.i.d. errors naturally lead to the question of fault-tolerance against errors with long-range correlations. Ideally, any correlation can be captured by a joint (system and bath) Hamiltonian. However, an arbitrary joint Hamiltonian is often intractable, and hence, the joint Hamiltonian model with pairwise terms was introduced and developed in a series of foundational works. However, the analysis of the new constant overhead codes in that error model appears to be quite challenging. In this paper, to model correlated errors in quantum memory, we introduce a correlation model which is a generalization of the well-known hidden random fields. This proposed model, which includes stationary and ergodic (non-Markov) error distributions, is shown to capture correlations not captured by the joint Hamiltonian model with pairwise terms. On the other hand, building on non-i.i.d. measure concentration, we show that for a broad class of non-Markov and (possibly) non-stationary error distributions, quantum Tanner codes ensure an exponential retention time (in the number of physical qubits), when the error rate is below a threshold. An implication of these results is that the rate of decay of the correlation with distance does not necessarily differentiate between good and bad correlation.

quant-ph↗

arXiv2024

Learning the Influence Graph of a High-Dimensional Markov Process with Memory

Motivated by multiple applications in social networks, nervous systems, and financial risk analysis, we consider the problem of learning the underlying (directed) influence graph or causal graph of a high-dimensional multivariate discrete-time Markov process with memory. At any discrete time instant, each observed variable of the multivariate process is a binary string of random length, which is parameterized by an unobservable or hidden [0,1]-valued scalar. The hidden scalars corresponding to the variables evolve according to discrete-time linear stochastic dynamics dictated by the underlying influence graph whose nodes are the variables. We extend an existing algorithm for learning i.i.d. graphical models to this Markovian setting with memory and prove that it can learn the influence graph based on the binary observations using logarithmic (in number of variables or nodes) samples when the degree of the influence graph is bounded. The crucial analytical contribution of this work is the derivation of the sample complexity result by upper and lower bounding the rate of convergence of the observed Markov process with memory to its stationary distribution in terms of the parameters of the influence graph.

cs.LG↗