Related papers: The limits of quantum circuit simulation with low …
Digital quantum simulation is a promising application for quantum computers. Their free programmability provides the potential to simulate the unitary evolution of any many-body Hamiltonian with bounded spectrum by discretizing the time…
As the field of quantum computing grows, novel algorithms which take advantage of quantum phenomena need to be developed. As we are currently in the NISQ (noisy intermediate scale quantum) era, quantum algorithm researchers cannot reliably…
Efficient methods for the simulation of quantum circuits on classic computers are crucial for their analysis due to the exponential growth of the problem size with the number of qubits. Here we study lumping methods based on bisimulation,…
We consider recent works on the simulation of quantum circuits using the formalism of matrix product states and the formalism of contracting tensor networks. We provide simplified direct proofs of many of these results, extending an…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
We present an algorithm, along with its implementation that finds T-optimal approximations of single-qubit Z-rotations using quantum circuits consisting of Clifford and T gates. Our algorithm is capable of handling errors in approximation…
The Schwinger model (quantum electrodynamics in 1+1 dimensions) is a testbed for the study of quantum gauge field theories. We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and…
The quantum circuit model is the de-facto way of designing quantum algorithms. Yet any level of abstraction away from the underlying hardware incurs overhead. In the era of near-term, noisy, intermediate-scale quantum (NISQ) hardware with…
Although near-term quantum computing devices are still limited by the quantity and quality of qubits in the so-called NISQ era, quantum computational advantage has been experimentally demonstrated. Moreover, hybrid architectures of quantum…
Quantum circuit simulation provides the foundation for the development of quantum algorithms and the verification of quantum supremacy. Among the various methods for quantum circuit simulation, tensor network contraction has been increasing…
Quantum circuit simulation is paramount to the verification and optimization of quantum algorithms, and considerable research efforts have been made towards efficient simulators. While circuits often contain high-level gates such as oracles…
We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm…
Today's experimental noisy quantum processors can compete with and surpass all known algorithms on state-of-the-art supercomputers for the computational benchmark task of Random Circuit Sampling [1-5]. Additionally, a circuit-based quantum…
Probabilistic graphical models such as Bayesian networks are widely used to model stochastic systems to perform various types of analysis such as probabilistic prediction, risk analysis, and system health monitoring, which can become…
We show that the cost of strong simulation of quantum circuits using $t$ $T$ gate magic states exhibits non-trivial reductions on its upper bound for $t=1$, $t=2$, $t=3$, and $t=6$ with odd-prime-qudits. This agrees with previous numerical…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
In recent investigations, it has been found that conservation laws generally lead to precision limits on quantum computing. Lower bounds of the error probability have been obtained for various logic operations from the commutation relation…
Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics.…
Randomized algorithms such as qDRIFT provide an efficient framework for quantum simulation by sampling terms from a decomposition of the system's generator. However, existing error bounds for qDRIFT scale quadratically with the norm of the…
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce…