Related papers: On the representation of Boolean and real function…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
The exponential speedups promised by Hamiltonian simulation on a quantum computer depends crucially on structure in both the Hamiltonian $\hat{H}$, and the quantum circuit $\hat{U}$ that encodes its description. In the quest to better…
Exactly solvable Hamiltonians are useful in the study of quantum many-body systems using quantum computers. In the variational quantum eigensolver, a decomposition of the target Hamiltonian into exactly solvable fragments can be used for…
In this paper we consider an application of the recently proposed quantum hashing technique for computing Boolean functions in the quantum communication model. The combination of binary functions on non-binary quantum hash function is done…
We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,'…
This paper develops practical summation techniques in ZXW calculus to reason about quantum dynamics, such as unitary time evolution. First we give a direct representation of a wide class of sums of linear operators, including arbitrary…
Compilation optimizes quantum algorithms performances on real-world quantum computers. To date, it is performed via classical optimization strategies. We introduce a class of quantum algorithms to perform compilation via quantum computers,…
We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation…
In this report, we explore the use of a quantum optimization algorithm for obtaining low energy conformations of protein models. We discuss mappings between protein models and optimization variables, which are in turn mapped to a system of…
Simulations of quantum chemistry and quantum materials are believed to be among the most important potential applications of quantum information processors, but realizing practical quantum advantage for such problems is challenging. Here,…
Simulating quantum systems is one of the most important potential applications of quantum computers. The high-level circuit defining the simulation needs to be compiled into one that complies with hardware limitations such as qubit…
The query model (or black-box model) has attracted much attention from the communities of both classical and quantum computing. Usually, quantum advantages are revealed by presenting a quantum algorithm that has a better query complexity…
Quantum computing has the potential to significantly speed up complex computational tasks, and arguably the most promising application area for near-term quantum computers is the simulation of quantum mechanics. To make the most of our…
We present a framework for computing the solution to Hamiltonian eigenproblems in a subspace defined by bit-strings sampled from a quantum computer. Hamiltonians are represented using an extended alphabet that includes projection and ladder…
Many computer vision applications need to recover structure from imperfect measurements of the real world. The task is often solved by robustly fitting a geometric model onto noisy and outlier-contaminated data. However, recent theoretical…
Analogue Hamiltonian simulation is a promising near-term application of quantum computing and has recently been put on a theoretical footing. In Hamiltonian simulation, a physical Hamiltonian is engineered to have identical physics to…
We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in previous work [Babbush et al., New…
Quantum annealing aims at solving optimization problems of practical relevance using quantum-computing hardware. Problems of interest are typically formulated in terms of quadratic unconstrained binary optimization (QUBO) Hamiltonians.…
Exponentiation of Hamiltonians refers to a mathematical operation to a Hamiltonian operator, typically in the form e^(-i.t.H), where H is the Hamiltonian and t is a time parameter. This operation is fundamental in quantum mechanics,…
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…