Related papers: Accelerated Quantum Amplitude Estimation without Q…
We describe a method to upper bound the quantum query complexity of Boolean formula evaluation problems, using fundamental theorems about the general adversary bound. This nonconstructive method can give an upper bound on query complexity…
We propose a new finding $k$-minima algorithm and prove that its query complexity is $\mathcal{O}(\sqrt{kN})$, where $N$ is the number of data indices. Though the complexity is equivalent to that of an existing method, the proposed is…
Composition is something we take for granted in classical algorithms design, and in particular, we take it as a basic axiom that composing ``efficient'' algorithms should result in an ``efficient'' algorithm -- even using this intuition to…
The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…
Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find…
Quantum query complexity has several nice properties with respect to composition. First, bounded-error quantum query algorithms can be composed without incurring log factors through error reduction (exactness). Second, through careful…
The accurate estimation of quantum observables is a critical task in science. With progress on the hardware, measuring a quantum system will become increasingly demanding, particularly for variational protocols that require extensive…
Quantum computing hardware has grown sufficiently complex that it often can no longer be simulated by classical computers, but its computational power remains limited by errors. These errors corrupt the results of quantum algorithms, and it…
Demonstrating quantum supremacy, a complexity-guaranteed quantum advantage against over the best classical algorithms by using less universal quantum devices, is an important near-term milestone for quantum information processing. Here we…
In this note, we develop a bounded-error quantum algorithm that makes $\tilde O(n^{1/4}\varepsilon^{-1/2})$ queries to a Boolean function $f$, accepts a monotone function, and rejects a function that is $\varepsilon$-far from being…
This paper generalizes the quantum amplitude amplification and amplitude estimation algorithms to work with non-boolean oracles. The action of a non-boolean oracle $U_\varphi$ on an eigenstate $|x\rangle$ is to apply a state-dependent…
Quantum phase estimation is one of the most important tools in quantum algorithms. It can be made non-adaptive (meaning all applications of the unitary $U_\phi$ happen simultaneously) without using more applications of $U_\phi$, albeit at…
Modelling non-linear activation functions on quantum computers is vital for quantum neurons employed in fully quantum neural networks, however, remains a challenging task. We introduce an amplitude-based implementation for approximating…
We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n + log log (1/epsilon)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2^n…
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
The Heisenberg time-energy relation prevents determination of an atomic transition to better than the inverse of the measurement time. The relation generally applies to frequency estimation of a near-resonant field [1-3], since information…
Quantum computational approaches to some classic target identification and localization algorithms, especially for radar images, are investigated, and are found to raise a number of quantum statistics and quantum measurement issues with…
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian…
We present an improved version of a quantum amplitude encoding scheme that encodes the $N$ entries of a unit classical vector $\vec{v}=(v_1,..,v_N)$ into the amplitudes of a quantum state. Our approach has a quadratic speed-up with respect…