Related papers: Hamiltonian quantum computer in one dimension

We describe a method to simulate Hamiltonian evolution on a quantum computer by repeatedly using a superposition of steps of a quantum walk, then applying a correction to the weightings for the numbers of steps of the quantum walk. This…

The concept of qudit (a d-level system) cluster state is proposed by generalizing the qubit cluster state (Phys. Rev. Lett. \textbf{86}, 910 (2001)) according to the finite dimensional representations of quantum plane algebra. We…

We introduce a scheme to perform universal quantum computation in quantum cellular automata (QCA) fashion in arbitrary subsystem dimension (not necessarily finite). The scheme is developed over a one spatial dimension $N$-element array,…

The author analyzes quantum computation with the hybrid qubit (HQ) that is encoded using the three-electron configuration of a double quantum dot. All gate operations are controlled with electric signals, while the qubit remains at an…

In some of the earliest work on quantum mechanical computers, Feynman showed how to implement universal quantum computation by the dynamics of a time-independent Hamiltonian. I show that this remains possible even if the Hamiltonian is…

Quantum computing opens up new possibilities for the simulation of many-body nuclear systems. As the number of particles in a many-body system increases, the size of the space if the associated Hamiltonian increases exponentially. This…

We derive an explicit Hamiltonian for copying the basis up and down states of a quantum two-state system - a qubit - onto n "copy" qubits initially all prepared in the down state. In terms of spin components, for spin-1/2 particle spin…

The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…

Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…

Efficiently characterising quantum systems, verifying operations of quantum devices and validating underpinning physical models, are central challenges for the development of quantum technologies and for our continued understanding of…

We prove that estimating the ground state energy of a translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is QMAEXP-complete, even for systems of low local dimension (roughly 40). This is an improvement over the best…

We classify two-qubit commuting Hamiltonians in terms of their computational complexity. Suppose one has a two-qubit commuting Hamiltonian H which one can apply to any pair of qubits, starting in a computational basis state. We prove a…

By encoding a qudit in a harmonic oscillator and investigating the infinite limit, we give an entirely new realization of continuous-variable quantum computation. The generalized Pauli group is generated by number and phase operators for…

Classical simulation of real-space quantum dynamics is challenging due to the exponential scaling of computational cost with system dimensions. Quantum computer offers the potential to simulate quantum dynamics with polynomial complexity;…

We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…

Quantum chemistry simulations on a quantum computer suffer from the overhead needed for encoding the fermionic problem in a bosonic system of qubits. By exploiting the block diagonality of a fermionic Hamiltonian, we show that the number of…

Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…

We introduce an algorithm to compute Hamiltonian dynamics on digital quantum computers that requires only a finite circuit depth to reach an arbitrary precision, i.e. achieves zero discretization error with finite depth. This finite number…

Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…

Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks. However, many studies rely on toy datasets or heavy feature reduction, raising concerns about their scalability.…