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Mean Centering (MC) is an important data preprocessing technique, which has a wide range of applications in data mining, machine learning, and multivariate statistical analysis. When the data set is large, this process will be…

Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we…

Transversal gates on quantum error correction codes have been a promising approach for fault-tolerant quantum computing, but are limited by the Eastin-Knill no-go theorem. Existing solutions like gate teleportation and magic state…

Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…

Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit…

In this work we study the encoding of smooth, differentiable multivariate functions in quantum registers, using quantum computers or tensor-network representations. We show that a large family of distributions can be encoded as…

We develop new algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework that encapsulates most known quantum algorithms and serves as the foundation for new ones. Existing implementations of QSVT rely on block…

In many practical applications, quantum algorithms require several qubits, significantly more than those available with current noisy intermediate-scale quantum processors. Distributed quantum computing (DQC) is considered a scalable…

Code switching is an established technique that facilitates a universal set of FT quantum gate operations by combining two QEC codes with complementary sets of gates, which each by themselves are easy to implement fault-tolerantly. In this…

We provide modular circuit-level implementations and resource estimates for several methods of block-encoding a dense $N\times N$ matrix of classical data to precision $\epsilon$; the minimal-depth method achieves a $T$-depth of…

Error correcting codes protect quantum information and form the basis of fault tolerant quantum computing. Leading proposals for fault-tolerant quantum computation require codes with an exceedingly rare property, a transverse non-Clifford…

Variational Quantum algorithms, especially Quantum Approximate Optimization and Variational Quantum Eigensolver (VQE) have established their potential to provide computational advantage in the realm of combinatorial optimization. However,…

We develop novel protocols for generating loss-tolerant quantum codes; these are central for safeguarding information against qubit losses, with most crucial applications in quantum communications. Contrary to current proposals, our method…

Fault-tolerant quantum computation requires minimizing non-Clifford gates, whose implementation via magic state distillation dominates the resource costs. While $T$-count minimization is well-studied, dedicated $CCZ$ factories shift the…

Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting…

Matrices with the displacement structures of circulant, Toeplitz, and Hankel types as well as matrices with structures generalizing these types are omnipresent in computations of sciences and engineering. In this paper, we present efficient…

Block encodings are a fundamental primitive in quantum algorithms, but can often have large ancilla overhead. In this work, we introduce novel techniques for reducing this overhead in two distinct ways. In Part I, we prove the existence of…

Dynamic quantum circuits (DQCs) incorporate mid-circuit measurements and gates conditioned on these measurement outcomes. DQCs can prepare certain long-range entangled states in constant depth, making them a promising route to preparing…

Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. In deep-space optical communications, current receivers for the…

Efficient block encoding of many-body Hamiltonians is a central requirement for quantum algorithms in scientific computing, particularly in the early fault-tolerant era. In this work, we introduce new explicit constructions for block…