Related papers: Stabilizer Circuits, Quadratic Forms, and Computin…
Optimal quantum linear equation solvers provide complexity $O(\kappa\log(1/\epsilon))$, where $\kappa$ is the condition number and $\epsilon$ is the allowable error. The optimal solver using a discrete adiabatic approach [PRX Quantum 3,…
Outcome probability estimation via classical methods is an important task for validating quantum computing devices. Outcome probabilities of any quantum circuit can be estimated using Monte Carlo sampling, where the amount of negativity…
We show that the cost of strong simulation of quantum circuits using $t$ $T$ gate magic states exhibits non-trivial reductions on its upper bound for $t=1$, $t=2$, $t=3$, and $t=6$ with odd-prime-qudits. This agrees with previous numerical…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
This study explores the qubit mapping through the integration of Quasi-Orthogonal Space-Time Block Codes (QOSTBCs) with Quaternion Orthogonal Designs (QODs) in quantum error correction (QEC) frameworks. QOSTBCs have gained prominence for…
Comparator circuits are a natural circuit model for studying bounded fan-out computation whose power sits between nondeterministic branching programs and general circuits. Despite having been studied for nearly three decades, the first…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
Quantum circuits are time dependent diagrams describing the process of quantum computation. Usually, a quantum algorithm must be mapped into a quantum circuit. Optimal synthesis of quantum circuits is intractable and heuristic methods must…
Existing numerical optimizers deployed in quantum compilers use expensive $\mathcal{O}(4^n)$ matrix-matrix operations. Inspired by recent advances in quantum machine learning (QML), QFactor-Sample replaces matrix-matrix operations with…
Characterizing quantum magic -- the resource enabling computational advantage beyond stabilizer circuits -- is subtle in qubit systems because established measures can give conflicting information about the same state. We introduce C(rho),…
We show that coarse graining arguments invented for the analysis of multi-spin systems on a randomly triangulated surface apply also to the O(n) model on a random lattice. These arguments imply that if the model has a critical point with…
The quantum stabilizer formalism became foundational for understanding error correction soon after the realization of the first useful quantum error correction codes. Stabilizers provide a way to describe sets of quantum states which are…
In practical applications, quantum systems are inevitably subject to significant uncertainties, including unknown initial states, imprecise physical parameters, and unmodeled environmental noise, all of which pose major challenges to robust…
The work proposes an extension of the quantum circuit formalism where qubits (wires) are circular instead of linear. The left-to-right interpretation of a quantum circuit is replaced by a circular representation which allows to select the…
We investigate the problem of evaluating the output probabilities of Clifford circuits with nonstabilizer product input states. First, we consider the case when the input state is mixed, and give an efficient classical algorithm to…
Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by…
We define a class of stochastic processes based on evolutions and measurements of quantum systems, and consider the complexity of predicting their long-term behavior. It is shown that a very general class of decision problems regarding…
Motivated by recent Linear Programming solvers, we design dynamic data structures for maintaining the inverse of an $n\times n$ real matrix under $\textit{low-rank}$ updates, with polynomially faster amortized running time. Our data…
For an $n$-element matroid $M$ given by an $n \times n$ matrix representation over a finite field $\mathbb F$ and an integer $k$, we present an $(O_{k,\mathbb F}(n^2)+O(n^\omega))$-time algorithm that either finds a branch-decomposition of…
We propose a new method to extend the size of a quantum computation beyond the number of physical qubits available on a single device. This is accomplished by randomly inserting measure-and-prepare channels to express the output state of a…