Related papers: Bounds on the Power of Constant-Depth Quantum Circ…

This paper proves that the computational power of quantum interactive proof systems, with a double-exponentially small gap in acceptance probability between the completeness and soundness cases, is precisely characterized by EXP, the class…

Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…

We present a compact quantum circuit for factoring a large class of integers, including some whose classical hardness is expected to be equivalent to RSA (but not including RSA integers themselves). Most notably, we factor $n$-bit integers…

This study presents a roadmap towards utilizing a single arbitrary gate for universal quantum computing. Since two decades ago, it has been widely accepted that almost any single arbitrary gate with qubit number $>2$ is universal. Utilizing…

We introduce a novel software-oriented model of quantum computation motivated by the practical constraints of near-term quantum hardware. In this model, gates are specified by constraints expressed in terms of Pauli observables, with each…

It is widely accepted that noisy quantum devices are limited to logarithmic depth circuits unless mid-circuit measurements and error correction are employed. However, this conclusion holds only for unital error channels, such as…

Fault-tolerant quantum computation traditionally incurs substantial resource overhead, with both qubit and time overheads scaling polylogarithmically with the size of the computation. While prior work by Gottesman showed that constant qubit…

Diagonal quantum circuits are quantum circuits comprising only diagonal gates in the computational basis. In spite of a classical feature of diagonal quantum circuits in the sense of commutativity of all gates, their computational power is…

Quantum Neuromorphic Computing (QNC) merges quantum computation with neural computation to create scalable, noise-resilient algorithms for quantum machine learning (QML). At the core of QNC is the quantum perceptron (QP), which leverages…

Permutational Quantum Computing (PQC) [\emph{Quantum~Info.~Comput.}, \textbf{10}, 470--497, (2010)] is a natural quantum computational model conjectured to capture non-classical aspects of quantum computation. An argument backing this…

Quantum computation based on geometric phase is generally believed to be more robust against certain errors or noises than the conventional dynamical strategy. However, the gate error caused by the decoherence effect is inevitable, and thus…

The relationship between BQP and PH has been an open problem since the earliest days of quantum computing. We present evidence that quantum computers can solve problems outside the entire polynomial hierarchy, by relating this question to…

We give a fault tolerant construction for error correction and computation using two punctured quantum Reed-Muller (PQRM) codes. In particular, we consider the $[[127,1,15]]$ self-dual doubly-even code that has transversal Clifford gates…

We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with the $p$-faces of the $n$-cube (for $n>p$) and stabilizer constraints with faces of dimension $(p\pm1)$. The quantum code obtained by identifying…

Descriptions of quantum algorithms, communication etc. protocols assume the existence of closed quantum system. However, real life quantum systems are open and are highly sensitive to errors. Hence error correction is of utmost importance…

Quantum Phase Estimation (QPE) stands as a pivotal quantum computing subroutine that necessitates an inverse Quantum Fourier Transform (QFT). However, it is imperative to recognize that enhancing the precision of the estimation inevitably…

We study a quantum analogue of locally decodable error-correcting codes. A q-query locally decodable quantum code encodes n classical bits in an m-qubit state, in such a way that each of the encoded bits can be recovered with high…

Classical simulations of quantum circuits are essential for verifying and benchmarking quantum algorithms, particularly for large circuits, where computational demands increase exponentially with the number of qubits. Among available…

We present characterisations of "exact" gap-definable classes, in terms of indeterministic models of computation which slightly modify the standard model of quantum computation. This follows on work of Aaronson [arXiv:quant-ph/0412187], who…

Fault-tolerant quantum computing demands decoders that are fast, accurate, and adaptable to circuit structure and realistic noise. While machine learning (ML) decoders have demonstrated impressive performance for quantum memory, their use…