Related papers: End-to-end quantum algorithms for tensor problems
Running quantum algorithms often involves implementing complex quantum circuits with such a large number of multi-qubit gates that the challenge of tackling practical applications appears daunting. To date, no experiments have successfully…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
Spectral methods are a leading approach for tensor PCA with a ``spiked" Gaussian tensor. The methods use the spectrum of a linear operator in a vector space with exponentially high dimension and in Ref. 1 it was shown that quantum…
In this work, we revisit algorithms for Tensor PCA: given an order-$r$ tensor of the form $T = G+\lambda \cdot v^{\otimes r}$ where $G$ is a random symmetric Gaussian tensor with unit variance entries and $v$ is an unknown boolean vector in…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
A key challenge in realizing fault-tolerant quantum computers is circuit optimization. Focusing on the most expensive gates in fault-tolerant quantum computation (namely, the T gates), we address the problem of T-count optimization, i.e.,…
Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA),…
For the tensor PCA (principal component analysis) problem, we propose a new hierarchy of increasingly powerful algorithms with increasing runtime. Our hierarchy is analogous to the sum-of-squares (SOS) hierarchy but is instead inspired by…
A milestone in the field of quantum computing will be solving problems in quantum chemistry and materials faster than state-of-the-art classical methods. The current understanding is that achieving quantum advantage in this area will…
Quantum computers are expected to bring drastic acceleration to several computing tasks against classical computers. Noisy intermediate-scale quantum (NISQ) devices, which have tens to hundreds of noisy physical qubits, are gradually…
We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…
The ability to efficiently simulate random quantum circuits using a classical computer is increasingly important for developing Noisy Intermediate-Scale Quantum devices. Here we present a tensor network states based algorithm specifically…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
We describe a quantum algorithm for the Planted Noisy $k$XOR problem (also known as sparse Learning Parity with Noise) that achieves a nearly quartic ($4$th power) speedup over the best known classical algorithm while also only using…
We propose an efficient algorithm for tensor PCA based on counting a specific family of weighted hypergraphs. For the order-$p$ tensor PCA problem where $p \geq 3$ is a fixed integer, we show that when the signal-to-noise ratio is $\lambda…
The advent of fault-tolerant quantum computing (FTQC) promises to tackle classically intractable problems. A key milestone is solving the Navier-Stokes equations (NSE), which has remained formidable for quantum algorithms due to their high…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
The recent advent of commercially available quantum annealing hardware (QAH) has expanded opportunities for research into quantum annealing-based algorithms. In the domain of power systems, this advancement has driven increased interest in…
In this paper, we present two tensor network quantum-inspired algorithms to solve the knapsack and the shortest path problems, and enables to solve some of its variations. These methods provide an exact equation which returns the optimal…
Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practical quantum advantage can be said to exist for such problems when the end-to-end time for…