Related papers: Efficient classical algorithms for simulating symm…
Using the tensor product representation in the density matrix renormalization group, we show that a quantum circuit of Grover's algorithm, which has one-qubit unitary gates, generalized Toffoli gates, and projective measurements, can be…
Permutational Quantum Computing (PQC) [\emph{Quantum~Info.~Comput.}, \textbf{10}, 470--497, (2010)] is a natural quantum computational model conjectured to capture non-classical aspects of quantum computation. An argument backing this…
The efficient simulation of complex quantum systems remains a central challenge due to the exponential growth of Hilbert space with system size. Tensor network methods have long been established as powerful approximation schemes, and their…
We introduce a systematic study of "symmetric quantum circuits", a new restricted model of quantum computation that preserves the symmetries of the problems it solves. This model is well-adapted for studying the role of symmetry in quantum…
We introduce a hybrid classical-quantum algorithm to compute dynamical correlation functions and excitation spectra in many-body quantum systems, with a focus on molecular systems. The method combines classical preparation of a perturbed…
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
We present a hybrid quantum-classical algorithm to simulate thermal states of a classical Hamiltonians on a quantum computer. Our scheme employs a sequence of locally controlled rotations, building up the desired state by adding qubits one…
Simulating the dynamics of complex quantum systems is a central application of quantum devices. Here, we propose leveraging the power of measurements to simulate short-time quantum dynamics of physically prepared quantum states in classical…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
We propose examples of a hybrid quantum-classical simulation where a classical computer assisted by a small quantum processor can efficiently simulate a larger quantum system. First we consider sparse quantum circuits such that each qubit…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the…
In optimization, one of the well-known classical algorithms is power iterations. Simply stated, the algorithm recovers the dominant eigenvector of some diagonalizable matrix. Since numerous optimization problems can be formulated as an…
Estimating expectation values is a key subroutine in quantum algorithms. Near-term implementations face two major challenges: a limited number of samples required to learn a large collection of observables, and the accumulation of errors in…
Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
We present a quantum algorithm for simulating the classical dynamics of $2^n$ coupled oscillators (e.g., $2^n$ masses coupled by springs). Our approach leverages a mapping between the Schr\"odinger equation and Newton's equation for…
We present quantum algorithms for simulating the dynamics of a broad class of classical oscillator systems containing $2^n$ coupled oscillators (Eg: $2^n$ masses coupled by springs), including those with time-dependent forces, time-varying…