Related papers: Local Hamiltonian decomposition and classical simu…
We consider the task of approximating the ground state energy of two-local quantum Hamiltonians on bounded-degree graphs. Most existing algorithms optimize the energy over the set of product states. Here we describe a family of shallow…
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-local qubit Hamiltonians with a small set of physically…
We study the problem of simulating the time evolution of a lattice Hamiltonian, where the qubits are laid out on a lattice and the Hamiltonian only includes geometrically local interactions (i.e., a qubit may only interact with qubits in…
We show a certain kind of non-local operations can be simulated by sampling a set of local operations with a quasi-probability distribution when the task of a quantum circuit is to evaluate an expectation value of observables. Utilizing the…
The local Hamiltonian (LH) problem, the quantum analog of the classical constraint satisfaction problem, is a cornerstone of quantum computation and complexity theory. It is known to be QMA-complete, indicating that it is challenging even…
While advances in quantum hardware occur in modest steps, simulators running on classical computers provide a valuable test bed for the construction of quantum algorithms. Given a unitary matrix that performs certain operation, obtaining…
Any unitary transformation of quantum computational networks is explicitly decomposed, in an exact and unified form, into a sequence of a limited number of one-qubit quantum gates and the two-qubit diagonal gates that have diagonal unitary…
A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group B n for every $n \ge 2$. If we view such an operator as a quantum-computational gate, then topological…
In computer simulations, quantum delocalization of atomic nuclei can be modeled making use of the Path Integral (PI) formulation of quantum statistical mechanics. This approach, however, comes with a large computational cost. By restricting…
All known examples confirming the possibility of an exponential separation between classical simulation algorithms and stoquastic adiabatic quantum computing (AQC) exploit symmetries that constrain adiabatic dynamics to effective, symmetric…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
A general scheme is presented to decompose a $d$-by-$d$ unitary matrix as the product of two-level unitary matrices with additional structure and prescribed determinants. In particular, the decomposition can be done by using two-level…
We introduce a distributed classical simulation algorithm for general quantum circuits, and present numerical results for calculating the output probabilities of universal random circuits. We find that we can simulate more qubits to greater…
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…
In many practical applications, quantum algorithms require several qubits, significantly more than those available with current noisy intermediate-scale quantum processors. Distributed quantum computing (DQC) is considered a scalable…
Noisy intermediate scale quantum computers are useful for various tasks such as state preparation and variational quantum algorithms. However, the non-Euclidean quantum geometry of parameterized quantum circuits is detrimental for these…
Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy…
We examine the problem of determining whether a multi-qubit two-local Hamiltonian can be made stoquastic by single-qubit unitary transformations. We prove that when such a Hamiltonian contains one-local terms, then this task can be NP-hard.…
Estimating the eigenstate properties of quantum systems is a long-standing, challenging problem for both classical and quantum computing. Existing universal quantum algorithms typically rely on ideal and efficient query models (e.g. time…
Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential…