Related papers: Quantum singular value transformation without bloc…
Simulating the time evolution of quantum field theories given some Hamiltonian $H$ requires developing algorithms for implementing the unitary operator e^{-iHt}. A variety of techniques exist that accomplish this task, with the most common…
For the solution of partial differential equations (PDEs), we show that the quantum Fourier transform (QFT) can enable the design of quantum circuits that are particularly simple, both conceptually and with regard to hardware requirements.…
The polar decomposition of a matrix is a key element in the quantum linear algebra toolbox. We show that the problem of quantum polar decomposition, recently studied in Lloyd et al. [LBP+20], has a simple and concise implementation via the…
We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve…
We introduce Unitaria, a Python library that brings the simplicity of classical linear algebra toolkits such as NumPy and SciPy to the implementation of quantum algorithms based on block encodings, a general-purpose abstraction in which a…
Quantum machine learning is an approach that aims to improve the performance of machine learning methods by leveraging the properties of quantum computers. In quantum circuit learning (QCL), a supervised learning method that can be…
Quantum computers can efficiently simulate Lindbladian dynamics, enabling powerful applications in open system simulation, thermal and ground-state preparation, autonomous quantum error correction, dissipative engineering, and more. Despite…
We propose a computational protocol for quantum simulations of Fermionic Hamiltonians on a quantum computer, enabling calculations which were previously not feasible with conventional encoding and ansatses of variational quantum…
Gate-based universal quantum computation is formulated in terms of two types of operations: local single-qubit gates, which are typically easily implementable, and two-qubit entangling gates, whose faithful implementation remains one of the…
Quantum linear system solvers like the Quantum Singular Value Transformation (QSVT) require a block encoding of the system matrix $A$ within a unitary operator $U_A$. Unfortunately, block encoding often results in significant…
The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The…
In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework…
Hamiltonian simulation is known to be one of the fundamental building blocks of a variety of quantum algorithms such as its most immediate application, that of simulating many-body systems to extract their physical properties. In this work,…
Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, $PT$ symmetry, and resonances. However, the quantum simulation of these models has been limited by the…
Real-valued transforms such as the discrete cosine, sine, and Hartley transforms play a central role in classical computing, complementing the Fourier transform in applications from signal and image processing to data compression. However,…
In Noisy Intermediate-Scale Quantum (NISQ) era, quantum processing units (QPUs) suffer from, among others, highly limited connectivity between physical qubits. To make a quantum circuit effectively executable, a circuit transformation…
We introduce a framework for simulating hybrid oscillator-qubit quantum processors on qubit-only systems through position encoding. By encoding continuous-variable position and momentum wave functions into qubit amplitudes, our method…
We present an encoding and hardware-independent formulation of optimization problems for quantum computing. Using this generalized approach, we present an extensive library of optimization problems and their various derived spin encodings.…
One strategy to fit larger problems on NISQ devices is to exploit a tradeoff between circuit width and circuit depth. Unfortunately, this tradeoff still limits the size of tractable problems since the increased depth is often not realizable…
Simulating quantum dynamics is one of the central applications of quantum computing. For Hamiltonians written as a sum of many terms, deterministic Trotter--Suzuki product formulas can require applying a large number of term-wise evolutions…