Related papers: Low Depth Quantum Simulation of Electronic Structu…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the…
As physical implementations of quantum architectures emerge, it is increasingly important to consider the cost of algorithms for practical connectivities between qubits. We show that by using an arrangement of gates that we term the…
We present a quantum algorithm for simulating quantum chemistry with gate complexity $\tilde{O}(N^{1/3} \eta^{8/3})$ where $\eta$ is the number of electrons and $N$ is the number of plane wave orbitals. In comparison, the most efficient…
The quantum simulation of quantum chemistry is a promising application of quantum computers. However, for N molecular orbitals, the $\mathcal{O}(N^4)$ gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes…
Achieving an accurate description of fermionic systems typically requires considerably many more orbitals than fermions. Previous resource analyses of quantum chemistry simulation often failed to exploit this low fermionic number…
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…
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…
Here we describe an approach for simulating electronic structure on quantum computers with significantly lower asymptotic complexity than prior work. The approach uses a real-space first-quantised representation of the molecular Hamiltonian…
Simulation of materials is one of the most promising applications of quantum computers. On near-term hardware the crucial constraint on these simulations is circuit depth. Many quantum simulation algorithms rely on a layer of unitary…
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…
One limitation of the variational quantum eigensolver algorithm is the large number of measurement steps required to estimate different terms in the Hamiltonian of interest. Unitary partitioning reduces this overhead by transforming the…
We design and implement quantum circuits for the simulation of the one-dimensional wave equation on the Quantinuum H1-1 quantum computer. The circuit depth of our approach scales as $O(n^{2})$ for $n$ qubits representing the solution on…
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…
We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use…
We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting commutativity of the target Hamiltonian, sparsity of interactions, and…
Digital quantum simulation has broad applications in approximating unitary evolution of Hamiltonians. In practice, many simulation tasks for quantum systems focus on quantum states in the low-energy subspace instead of the entire Hilbert…
Quantum simulation is a promising way toward practical quantum advantage, but noise in current quantum hardware poses a significant obstacle. We prove that not only the physical error but also the algorithmic error in a single Trotter step…
Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep…
Digital quantum simulators are among the most appealing applications of a quantum computer. Here we propose a universal, scalable, and integrated quantum computing platform based on tunable nonlinear electromechanical nano-oscillators. It…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…