Related papers: Approximate encoded permutations and piecewise qua…
An $n$-qubit quantum circuit is said to be peaked if it has an output probability that is at least inverse-polynomially large as a function of $n$. We describe a classical algorithm with quasipolynomial runtime $n^{O(\log{n})}$ that…
We study a method of producing approximately diagonal 1-qubit gates. For each positive integer, the method provides a sequence of gates that are defined iteratively from a fixed diagonal gate and an arbitrary gate. These sequences are…
The Advanced Encryption Standard (AES) is widely used and well-studied for its efficiency and strong security. This paper presents quantum circuit designs for the AES S-box by introducing the composite field \( F((2^4)^2) \) to replace the…
In this study, we propose a new method for constrained combinatorial optimization using variational quantum circuits. Quantum computers are considered to have the potential to solve large combinatorial optimization problems faster than…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
Decoherence of quantum hardware is currently limiting its practical applications. At the same time, classical algorithms for simulating quantum circuits have progressed substantially. Here, we demonstrate a hybrid framework that integrates…
We demonstrate the applicability of a universal gate set in the parity encoding, which is a dual to the standard gate model, by exploring several quantum gate algorithms such as the quantum Fourier transform and quantum addition. Embedding…
Quantum computers require quantum processors. An important part of the processor of any computer is the arithmetic unit, which performs binary addition, subtraction, division and multiplication, however multiplication can be performed using…
Probabilistic graphical models such as Bayesian networks are widely used to model stochastic systems to perform various types of analysis such as probabilistic prediction, risk analysis, and system health monitoring, which can become…
Compressed inverted indices in use today are based on the idea of gap compression: documents pointers are stored in increasing order, and the gaps between successive document pointers are stored using suitable codes which represent smaller…
Progress in quantum hardware design is progressing toward machines of sufficient size to begin realizing quantum algorithms in disciplines such as encryption and physics. Quantum circuits for addition are crucial to realize many quantum…
When considering a sequent-style proof system for quantum programs, there are certain elements of quantum mechanics that we may wish to capture, such as phase, dynamics of unitary transformations, and measurement probabilities. Traditional…
We present a method for classically simulating quantum circuits based on the tensor contraction model of Markov and Shi (quant-ph/0511069). Using this method we are able to classically simulate the approximate quantum Fourier transform in…
In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…
We introduce the novel class $(E_\alpha)_{\alpha \in [-\infty,1)}$ of reverse map projection embeddings, each one defining a unique new method of encoding classical data into quantum states. Inspired by well-known map projections from the…
Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic…
Quantum error correction (QEC) codes are traditionally defined and searched for without specifying the manner in which its syndrome extraction circuits are executed using elementary gates and measurements. We show how morphing circuits…
We present near-term quantum algorithms for auxiliary-field quantum Monte Carlo (AFQMC), viewed as imaginary-time projection for ground-state calculation as an ensemble of one-body propagators driven by stochastic fields $\Omega$. Starting…
The quantum Fourier transform (QFT) is a ubiquitous quantum operation that is used in numerous quantum computing applications. The major obstacle to constructing a QFT circuit is that numerous elementary gates are required. Among the…
Recently it has been shown that Repeat-Until-Success (RUS) circuits can approximate a given single-qubit unitary with an expected number of $T$ gates of about $1/3$ of what is required by optimal, deterministic, ancilla-free decompositions…