Related papers: Resilient functions: Optimized, simplified, and ge…

As quantum computing hardware steadily increases in qubit count and quality, one important question is how to allocate these resources to mitigate the effects of hardware noise. In a transitional era between noisy small-scale and fully…

For an $n$-qubit system, a rational function on the space of mixed states which is invariant with respect to the action of the group of local symmetries may be viewed as a detailed measure of entanglement. We show that the field of all such…

We provide new query complexity separations against sensitivity for total Boolean functions: a power $3$ separation between deterministic (and even randomized or quantum) query complexity and sensitivity, and a power $2.22$ separation…

We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In…

Recent works explore deep learning's success by examining functions or data with hierarchical structure. To study the learning complexity of functions with hierarchical structure, we study the noise stability of functions with tree…

We study the circuit complexity of boolean functions in a certain infinite basis. The basis consists of all functions that take value $1$ on antichains over the boolean cube. We prove that the circuit complexity of the parity function and…

The generalized rotating-wave approximation with counter-rotating interactions has been applied to a biased qubit-oscillator system. Analytical expressions are explicitly given for all eigenvalues and eigenstates. For a flux qubit coupled…

The dynamics of noise-resilient Boolean networks with majority functions and diverse topologies is investigated. A wide class of possible topological configurations is parametrized as a stochastic blockmodel. For this class of networks, the…

Quantum annealing is an optimization technique which potentially leverages quantum tunneling to enhance computational performance. Existing quantum annealers use superconducting flux qubits with short coherence times, limited primarily by…

Boolean functions with high algebraic immunity are important cryptographic primitives in some stream ciphers. In this paper, two methodologies for constructing binary minimal codes from sets, Boolean functions and vectorial Boolean…

Unconditionally secure non-relativistic bit commitment is known to be impossible in both the classical and the quantum worlds. But when committing to a string of n bits at once, how far can we stretch the quantum limits? In this paper, we…

We generalize the construction of elliptic stable envelopes to actions of connected reductive groups and give a direct inductive proof of their existence and uniqueness in a rather general situation. We show these have powerful enumerative…

We consider classical and entanglement-assisted versions of a distributed computation scheme that computes nonlinear Boolean functions of a set of input bits supplied by separated parties. Communication between the parties is restricted to…

We introduce the nested canalyzing depth of a function, which measures the extent to which it retains a nested canalyzing structure. We characterize the structure of functions with a given depth and compute the expected activities and…

The reversible logic can be used in various research areas, e.g. quantum computation, cryptography and signal processing. In the paper we study reversible logic circuits with additional inputs, which consist of NOT, CNOT and…

A long-investigated problem in circuit complexity theory is to decompose an $n$-input or $n$-variable Majority Boolean function (call it $M_n$) using $k$-input ones ($M_k$), $k < n$, where the objective is to achieve the decomposition using…

Random selection, leader election, and collective coin flipping are fundamental tasks in fault-tolerant distributed computing. We study these problems in the full-information model where despite decades of study, key gaps remain in our…

Shannon proved that almost all Boolean functions require a circuit of size $\Theta(2^n/n)$. We prove a quantum analog of this classical result. Unlike in the classical case the number of quantum circuits of any fixed size that we allow is…

We develop a general method for lower bounding the variance of sequences in arithmetic progressions mod $q$, summed over all $q \leq Q$, building on previous work of Liu, Perelli, Hooley, and others. The proofs lower bound the variance by…

We demonstrate how robust entanglement of quantum dot molecular system in a voltage controlled junction can be generated. To improve the quantum information characteristics of this system, we propose an applicable protocol which contains…