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arXiv:quant-ph/0103067 · Physical Review A

Multiparticle entanglement with quantum logic networks: Application to cold trapped ions

Marek Šašura, Vladimír Bužek

Published Jun 4, 2001• 65 citations
arXivHTMLPDF

Abstract

We show how to construct a multiqubit control gate on a quantum register of an arbitrary size N. This gate performs a single-qubit operation on a specific qubit conditioned by the state of other $N\ensuremath{-}1$ qubits. We provide an algorithm how to build up an array of networks consisting of single-qubit rotations and multiqubit control-NOT (CNOT) gates for the synthesis of an arbitrary entangled quantum state of N qubits. We illustrate the algorithm on a system of cold trapped ions. This example illuminates the efficiency of the direct implementation of the multiqubit CNOT gate compared to its decomposition into a network of two-qubit CNOT gates.

DOI
10.1103/physreva.64.012305

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The prevalent approach to executing quantum algorithms on quantum computers is to break down the algorithms to a concatenation of universal gates, typically single and two-qubit gates. However such a decomposition results in long gate sequences which are exponential in the qubit register size. Furthermore, gate fidelities tend to decrease when acting in larger qubit registers. Thus high-fidelity implementations in large qubit registers are still a prominent challenge. Here we propose and investigate multiqubit entangling gates for trapped ions. Our gates couple many qubits at once, allowing us to decrease the total number of gates used while retaining a high gate fidelity. Our method employs all of the normal modes of motion of the ion chain, which allows us to operate outside of the adiabatic regime and at rates comparable to the secular ion-trapping frequency. Furthermore we extend our method for generating Hamiltonians which are suitable for quantum analog simulations, such as a nearest-neighbor spin Hamiltonian or the Su-Schrieffer-Heeger Hamiltonian.
In quantum computation every unitary operation can be decomposed into quantum circuits---a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-not(cnot) gates. Two measures are important when judging the complexity of the circuit: the total number of cnot gates needed to implement it and the depth of the circuit, measured by the minimal number of computation steps needed to perform it. Here we give an explicit and simple quantum circuit scheme for preparation of arbitrary quantum states, which can directly utilize any decomposition scheme for arbitrary full quantum gates, thus connecting the two problems. Our circuit reduces the depth of the best currently known circuit by a factor of 222. It also reduces the total number of cnot gates from 2n{2}^{n}2n to 23242n\frac{23}{24}{2}^{n}2423​2n in the leading order for even number of qubits. Specifically, the scheme allows us to decrease the upper bound from 111111 cnot gates to 999 and the depth from 111111 to 555 steps for four qubits. Our results are expected to help in designing and building small-scale quantum circuits using present technologies.
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We propose the efficient combinations of laser pulses for constructing a multiqubit gate with cold trapped ions in order to implement maximally entangled states with quantum logic. Within the ion-trap quantum computation using the center of mass as the data bus, we can minimize the number of laser pulses as well as their operation time, which can improve the fidelity. We also present some numerical results of the operation time for different numbers of qubits and values of the Lamb-Dicke parameter.
Large-scale quantum computers will require quantum gate operations between widely separated qubits. A method for implementing such operations, known as quantum gate teleportation (QGT), requires only local operations, classical communication, and shared entanglement. We demonstrate QGT in a scalable architecture by deterministically teleporting a controlled-NOT (CNOT) gate between two qubits in spatially separated locations in an ion trap. The entanglement fidelity of our teleported CNOT is in the interval (0.845, 0.872) at the 95% confidence level. The implementation combines ion shuttling with individually addressed single-qubit rotations and detections, same- and mixed-species two-qubit gates, and real-time conditional operations, thereby demonstrating essential tools for scaling trapped-ion quantum computers combined in a single device.