Related papers: Quantum simulation with sum-of-squares spectral am…
Many machine learning and optimization algorithms can be cast as instances of stochastic approximation (SA). The convergence rate of these algorithms is known to be slow, with the optimal mean squared error (MSE) of order $O(n^{-1})$. In…
The Sum-of-Squares (SoS) hierarchy of semidefinite programs is a powerful algorithmic paradigm which captures state-of-the-art algorithmic guarantees for a wide array of problems. In the average case setting, SoS lower bounds provide strong…
Two-dimensional electronic spectroscopy (2DES) is a powerful tool for exploring quantum effects in energy transport within photosynthetic systems and investigating novel material properties. However, simulating the dynamics of these…
Quantum simulation is one of the central discipline to demonstrate the power of quantum computing. In recent years, the theoretical framework of quantum superchannels has been developed and applied widely as the extension of quantum…
Integrating quantum computing into deep learning architectures is a promising but poorly understood endeavor: when does a quantum layer actually help, and how much quantum is enough? We address both questions through Quantum Adaptive…
Establishing quantum advantage for variational quantum algorithms is an important direction in quantum computing. In this work, we apply the Quantum Approximate Optimisation Algorithm (QAOA) -- a popular variational quantum algorithm for…
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault…
Simulations of quantum chemistry and quantum materials are believed to be among the most important potential applications of quantum information processors, but realizing practical quantum advantage for such problems is challenging. Here,…
The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The general problem of quantum compiling is to approximate any unitary…
Quantum simulation algorithms often require numerous ancilla qubits and deep circuits, prohibitive for near-term hardware. We introduce a framework for simulating quantum channels using ensembles of low-depth circuits in place of many-qubit…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
Quantum simulation provides quantum systems under study with analogous controllable quantum systems and has wide applications from condensed-matter physics to high energy physics and to cosmology. The quantum system of a homogeneous and…
Quantum simulation is a leading candidate for demonstrating practical quantum advantage over classical computation, as it is believed to provide exponentially more compute power than any classical system. It offers new means of studying the…
Quantum Signal Processing (QSP) is a technique that can be used to implement a polynomial transformation $P(x)$ applied to the eigenvalues of a unitary $U$, essentially implementing the operation $P(U)$, provided that $P$ satisfies some…
We show that one can quantum simulate the dynamics of a Sachdev-Ye-Kitaev model with $N$ Majorana modes for time $t$ to precision $\epsilon$ with gate complexity $O(N^{7/2} t + N^{5/2} t \,{\rm polylog}(N/ \epsilon))$. In addition to…
Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in…
Quantum phase estimation (QPE) is one of the core algorithms for quantum computing. It has been extensively studied and applied in a variety of quantum applications such as the Shor's factoring algorithm, quantum sampling algorithms and the…
The Boolean satisfiability problem (SAT), in particular 3SAT with its bounded clause size, is a well-studied problem since a wide range of decision problems can be reduced to it. Due to its high complexity, examining potentials of quantum…
Quasi-equilibrium approximation is a widely used closure approximation approach for model reduction with applications in complex fluids, materials science, etc. It is based on the maximum entropy principle and leads to thermodynamically…
In this paper, we present an algorithm for preparing quantum states of the form $\sum_{i=0}^{n-1} \alpha_i |i\rangle$, where the coefficients $\alpha_i$ are specified by a quantum oracle. Our method achieves this task twice as fast as the…