Related papers: Quantum oracles for the finite element method
An algorithm for structured database searching is presented and used to solve the set partition problem. O(n) oracle calls are required in order to obtain a solution, but the probability that this solution is optimal decreases exponentially…
Quantum algorithms for computational linear algebra promise up to exponential speedups for applications such as simulation and regression, making them prime candidates for hardware realization. But these algorithms execute in a model that…
A quantum algorithm for computing the determinant of a unitary matrix $U\in U(N)$ is given. The algorithm requires no preparation of eigenstates of $U$ and estimates the phase of the determinant to $t$ binary digits accuracy with…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the…
We propose a couple of oracle construction methods for quantum pattern matching. We in turn show that one of the construct can be used with the Grover's search algorithm for exact and partial pattern matching, deterministically. The other…
Many quantum algorithms make use of ancilla, additional qubits used to store temporary information during computation, to reduce the total execution time. Quantum computers will be resource-constrained for years to come so reducing ancilla…
In existing general-purpose architectures for surface-code-based fault-tolerant quantum computers, the cost of a quantum computation is determined by the circuit volume, i.e., the number of qubits multiplied by the number of non-Clifford…
Quantum signal processing and quantum singular value transformation are powerful tools to implement polynomial transformations of block-encoded matrices on quantum computers, and has achieved asymptotically optimal complexity in many…
We describe a quantum algorithm for finding the smallest eigenvalue of a Hermitian matrix. This algorithm combines Quantum Phase Estimation and Quantum Amplitude Estimation to achieve a quadratic speedup with respect to the best classical…
The Quantum Approximate Optimization Algorithm (QAOA) was originally developed to solve combinatorial optimization problems, but has become a standard for assessing the performance of quantum computers. Fully descriptive benchmarking…
In the oracle identification problem, we are given oracle access to an unknown N-bit string x promised to belong to a known set C of size M and our task is to identify x. We present a quantum algorithm for the problem that is optimal in its…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
Random unitaries are a central object of study in quantum information, with applications to quantum computation, quantum many-body physics, and quantum cryptography. Recent work has constructed unitary designs and pseudorandom unitaries…
We show that $n$-bit integers can be factorized by independently running a quantum circuit with $\tilde{O}(n^{3/2})$ gates for $\sqrt{n}+4$ times, and then using polynomial-time classical post-processing. The correctness of the algorithm…
Numerous scientific developments in this NISQ-era (Noisy Intermediate Scale Quantum) have raised the importance for quantum algorithms relative to their conventional counterparts due to its asymptotic advantage. For resource estimates in…
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…
We propose a universal quantum circuit design that can estimate any arbitrary one-dimensional periodic functions based on the corresponding Fourier expansion. The quantum circuit contains N-qubits to store the information on the different…
Quantum annealing may provide advantages over simulated annealing on solving some problems such as Kth order binary optimization problem. No feasible architecture exists to implement the high-order optimization problem (K > 2) on current…
We consider a generic framework of optimization algorithms based on gradient descent. We develop a quantum algorithm that computes the gradient of a multi-variate real-valued function $f:\mathbb{R}^d\rightarrow \mathbb{R}$ by evaluating it…