Related papers: The mixed Schur transform: efficient quantum circu…
Quantum mechanics requires the operation of quantum computers to be unitary, and thus makes it important to have general techniques for developing fast quantum algorithms for computing unitary transforms. A quantum routine for computing a…
In classical computational chemistry, the coupled-cluster ansatz is one of the most commonly used $ab~initio$ methods, which is critically limited by its non-unitary nature. The unitary modification as an ideal solution to the problem is,…
Classical simulation of quantum physics is a central approach to investigating physical phenomena. Quantum computers enhance computational capabilities beyond those of classical resources, but it remains unclear to what extent existing…
Birkhoff's Theorem states that doubly stochastic matrices are convex combinations of permutation matrices. Quantum mechanically these matrices are doubly stochastic channels, i.e. they are completely positive maps preserving both the trace…
The design of efficient quantum circuits is an important issue in quantum computing. It is in general a formidable task to find a highly optimized quantum circuit for a given unitary matrix. We propose a quantum circuit design method that…
Schur-Weyl duality is a ubiquitous tool in quantum information. At its heart is the statement that the space of operators that commute with the tensor powers of all unitaries is spanned by the permutations of the tensor factors. In this…
Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics.…
In this manuscript we analyse generalised port-based teleportation (PBT) schemes, allowing for transmitting more than one unknown quantum state (or a composite quantum state) in one go, where the state ends up in several ports at Bob's…
The notion of shifted quantum groups has recently played an important role in algebraic geometry. This subtle modification of the original definition brings more flexibility in the representation theory of quantum groups. The first part of…
The quantum Fourier transform (QFT) is a powerful tool in quantum computing. The main ingredients of QFT are formed by the Walsh-Hadamard transform H and phase shifts P(.), both of which are 2x2 unitary matrices as operators on the…
The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and…
We present a new application of harmonic analysis to quantum information by constructing intriguing classes of quantum channels stemming from specific representations of multiplier algebras over locally compact groups $G$. Beginning with a…
Quantum circuit model is the most popular paradigm for implementing complex quantum computation. Based on Cartan decomposition, we show that $2(N-1)$ generalized controlled-$X$ (GCX) gates, $6$ single-qubit rotations about the $y$- and…
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…
We address the question of efficient implementation of quantum protocols, with small communication and entanglement, and short depth circuit for encoding or decoding. We introduce two new methods to achieve this, the first method involving…
We propose a quantum-classical hybrid scheme for implementing the nonunitary Gutzwiller factor using a discrete Hubbard-Stratonovich transformation, which allows us to express the Gutzwiller factor as a linear combination of unitary…
Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks…
Using the tensor product representation in the density matrix renormalization group, we show that a quantum circuit of Grover's algorithm, which has one-qubit unitary gates, generalized Toffoli gates, and projective measurements, can be…
A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability…
This article focuses on those aspects about partial actions of groups which are related to Schur's theory on projective representations. It provides an exhaustive description of the partial Schur multiplier, and this result is achieved by…