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Previously proposed quantum algorithms for solving linear systems of equations cannot be implemented in the near term due to the required circuit depth. Here, we propose a hybrid quantum-classical algorithm, called Variational Quantum…
A promising approach to useful computational quantum advantage is to use variational quantum algorithms for optimisation problems. Crucial for the performance of these algorithms is to ensure that the algorithm converges with high…
Gottesman, Kitaev and Preskill have formulated a way of encoding a qubit into an oscillator such that the qubit is protected against small shifts (translations) in phase space. The idea underlying this encoding is that error processes of…
The rapid advancement of quantum computing has led to the development of various quantum libraries, empowering compilation, simulation, and hardware backend interfaces. However, ensuring the correctness of these libraries remains a…
Reliable qubits are difficult to engineer, but standard fault-tolerance schemes use seven or more physical qubits to encode each logical qubit, with still more qubits required for error correction. The large overhead makes it hard to…
Quantum error correction codes (QECCs) are critical for realizing reliable quantum computing by protecting fragile quantum states against noise and errors. However, limited research has analyzed the noise resilience of QECCs to help select…
For reliable large-scale quantum computation, quantum error correction (QEC) is essential to protect logical information distributed across multiple physical qubits. Taking advantage of recent advances in deep learning, neural network-based…
Quantum computing holds the promise of solving problems intractable for classical computers, but practical large-scale quantum computation requires error correction to protect against errors. Fault-tolerant quantum computing (FTQC) enables…
This paper introduces the use of tailored variational forms for variational quantum eigensolver that have properties of representing certain constraints on the search domain of a linear constrained quadratic binary optimization problem…
One of the most promising paths towards large scale fault tolerant quantum computation is the use of quantum error correcting stabilizer codes. Just like every other quantum circuit, these codes must be compiled to hardware in a way to…
We present a fast block direct solver for the unified dynamic simulations of power systems. This solver uses a novel Q-learning based method for task scheduling. Unified dynamic simulations of power systems represent a method in which the…
Given a matrix $A$ of dimension $M \times N$ and a vector $\vec{b}$, the quantum linear system (QLS) problem asks for the preparation of a quantum state $|\vec{y}\rangle$ proportional to the solution of $A\vec{y} = \vec{b}$. Existing QLS…
We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear…
Among the new techniques of Versatile Video Coding (VVC), the quadtree with nested multi-type tree (QT+MTT) block structure yields significant coding gains by providing more flexible block partitioning patterns. However, the recursive…
Quantum computing presents a promising avenue for solving complex problems, particularly in quantum chemistry, where it could accelerate the computation of molecular properties and excited states. This work focuses on hybrid…
This paper introduces quantum circuit methodologies for pointwise multiplication and convolution of complex functions, conceptualized as "processing through encoding". Leveraging known techniques, we describe an approach where multiple…
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…
Polynomial based approaches, such as the Mat-Dot and entangled polynomial codes (EPC) have been used extensively within coded matrix computations to obtain schemes with good recovery thresholds. However, these schemes are well-recognized to…
Quantum signal processing (QSP) and quantum singular value transformation (QSVT), have emerged as unifying frameworks in the context of quantum algorithm design. These techniques allow to carry out efficient polynomial transformations of…
While quantum low-density parity check (qLDPC) codes are a low-overhead means of quantum information storage, it is valuable for quantum codes to possess fault-tolerant features beyond this resource efficiency. In this work, we introduce…