Related papers: Quantum Circuit Implementation of Two Matrix Produ…
The accurate evaluation of diagonal unitary operators is often the most resource-intensive element of quantum algorithms such as real-space quantum simulation and Grover search. Efficient circuits have been demonstrated in some cases but…
In quantum computation every unitary operation can be decomposed into quantum circuits-a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-NOT (CNOT) gates. Two measures are important when…
Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and…
We introduce a new approach for quantum linear algebra based on quantum subspace states and present three new quantum machine learning algorithms. The first is a quantum determinant sampling algorithm that samples from the distribution…
How to implement a computation task efficiently is the central problem in quantum computation science. For a quantum circuit, the multi-control unitary operations are the very important components. We present an extremely efficient approach…
One-way measurement based quantum computations (1WQC) may describe unitary transformations, via a composition of CPTP maps which are not all unitary themselves. This motivates the following decision problems: Is it possible to determine…
In quantum computing the decoherence time of the qubits determines the computation time available and this time is very limited when using current hardware. In this paper we minimize the execution time (the depth) for a class of circuits…
Two different algorithms are presented for generating a quantum circuit realization of a matrix representing a permutation on $2^n$ letters. All circuits involve $n$ qubits and only use multi--controlled Toffoli gates. The first algorithm…
Resource-efficient, low-depth implementations of quantum circuits remain a promising strategy for achieving reliable and scalable computation on quantum hardware, as they reduce gate resources and limit the accumulation of noisy operations.…
A critical step in developing circuits for quantum simulation is to synthesize a desired unitary operator using the circuit building blocks. Studying unitaries and their generators from the Lie algebraic perspective has given rise to…
In this work, we develop a novel mathematical framework for universal digital quantum computation using algebraic probability theory. We rigorously define quantum circuits as finite sequences of elementary quantum gates and establish their…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
Quantum computing holds immense promise for simulating quantum systems, a critical task for advancing our understanding of complex quantum phenomena. One of the primary goals in this domain is to accurately approximate the ground state of…
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…
Quantum walks have proven to be a universal model for quantum computation and to provide speed-up in certain quantum algorithms. The discrete-time quantum walk (DTQW) model, among others, is one of the most suitable candidates for circuit…
The quantum Schur transform is a fundamental building block that maps the computational basis to a coupled basis consisting of irreducible representations of the unitary and symmetric groups. Equivalently, it may be regarded as a change of…
Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the…
We describe a quantum computer based upon the coherent manipulation of two-level atoms between discrete one-dimensional momentum states. Combinations of short laser pulses with kinetic energy dependent free phase evolution can perform the…
In the noisy intermediate-scale quantum (NISQ) era, flexible quantum operations are essential for advancing large-scale quantum computing, as they enable shorter circuits that mitigate decoherence and reduce gate errors. However, the…