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Quantum processors are now able to run quantum circuits that are infeasible to simulate classically, creating a need for benchmarks that assess a quantum processor's rate of errors when running these circuits. Here, we introduce a general…
Simulations of collisions of fundamental particles on a quantum computer are expected to have an exponential advantage over classical methods and promise to enhance searches for new physics. Furthermore, scattering in scalar field theory…
Quantum walk is a useful model to simulate complex quantum systems and to build quantum algorithms; in particular, to develop spatial search algorithms on graphs, which aim to find a marked vertex as quickly as possible. Quantum walks are…
Motivated by far-reaching applications ranging from quantum simulations of complex processes in physics and chemistry to quantum information processing, a broad effort is currently underway to build large-scale programmable quantum systems.…
Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum…
Arbitrary exponentially large unitaries cannot be implemented efficiently by quantum circuits. However, we show that quantum circuits can efficiently implement any unitary provided it has at most polynomially many nonzero entries in any row…
Photonic circuits are central to classical and quantum information processing. While integrated technologies dominate, free-space architectures are emerging as attractive alternatives, offering broad bandwidth and direct manipulation of…
Quantum signal processing (QSP), which enables systematic polynomial transformations on quantum data through sequences of qubit rotations, has emerged as a fundamental building block for quantum algorithms and data re-uploading quantum…
Simulation of quantum systems is notoriously challenging for classical computers, while quantum hardware is naturally well-suited for this task. However, the imperfections of contemporary quantum systems poses a considerable challenge in…
In recent years, strong expectations have been raised for the possible power of quantum computing for solving difficult optimization problems, based on theoretical, asymptotic worst-case bounds. Can we expect this to have consequences for…
The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk, which allows for incoherent…
Quantum chemistry provides a target for quantum simulation of considerable scientific interest and industrial importance. The majority of algorithms to date have been based on a second-quantized representation of the electronic structure…
Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected ``logical'' qubits, where information is…
Large-scale classical simulation of quantum computers is crucial for benchmarking quantum algorithms, establishing boundaries of quantum advantage and exploring heuristic quantum algorithms. We present a full-state vector simulation…
Traditional algorithms for simulating quantum computers on classical ones require an exponentially large amount of memory, and so typically cannot simulate general quantum circuits with more than about 30 or so qubits on a typical PC-scale…
We present an efficient tensor-network-based approach for simulating large-scale quantum circuits, demonstrated using Quantum Support Vector Machines (QSVMs). Our method effectively reduces exponential runtime growth to near-quadratic…
Quantum circuit simulation is crucial for the development of quantum algorithms, particularly given the high cost and noise limitations of physical quantum hardware. While full-state quantum circuit simulation is commonly employed for…
The quantum random walk is a possible approach to construct new quantum algorithms. Several groups have investigated the quantum random walk and experimental schemes were proposed. In this paper we present the experimental implementation of…
Classical random walk formalism shows a significant role across a wide range of applications. As its quantum counterpart, the quantum walk is proposed as an important theoretical model for quantum computing. By exploiting the quantum…
Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…