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Physical Review A

Qutrit quantum computer with trapped ions

A. B. Klimov, Robert Guzman, J. C. Retamal, C. Saavedra

Published Jun 26, 2003• 224 citations
Publisher

Abstract

We study the physical implementation of a qutrit quantum computer in the context of trapped ions. Qutrits are defined in terms of electronic levels of trapped ions. We concentrate our attention on a universal two-qutrit gate, which corresponds to a controlled-NOT gate between qutrits. Using this gate and a general gate of an individual qutrit, any gate can be decomposed into a sequence of these gates. In particular, we show how this works for performing the quantum Fourier transform for n qutrits.

DOI
10.1103/physreva.67.062313

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We study the physical implementation of a qutrit quantum computer in the context of trapped ions. Qutrits are defined in terms of electronic levels of trapped ions. We concentrate our attention on a universal two-qutrit gate, which corresponds to a controlled-NOT gate between qutrits. Using this gate and a general gate of an individual qutrit, any gate can be decomposed into a sequence of these gates. In particular, we show how this works for performing the quantum Fourier transform for n qutrits.
Quantum computers can solve certain problems more efficiently compared to conventional classical methods. In the endeavor to build a quantum computer, several competing platforms have emerged that can implement certain quantum algorithms using a few qubits. However, the demonstrations so far have been done usually by tailoring the hardware to meet the requirements of a particular algorithm implemented for a limited number of instances. Although such proof of principal implementations are important to verify the working of algorithms on a physical system, they further need to have the potential to serve as a general purpose quantum computer allowing the flexibility required for running multiple algorithms and be scaled up to host more qubits. Here we demonstrate a small programmable quantum computer based on five trapped atomic ions each of which serves as a qubit. By optically resolving each ion we can individually address them in order to perform a complete set of single-qubit and fully connected two-qubit quantum gates and alsoperform efficient individual qubit measurements. We implement a computation architecture that accepts an algorithm from a user interface in the form of a standard logic gate sequence and decomposes it into fundamental quantum operations that are native to the hardware using a set of compilation instructions that are defined within the software. These operations are then effected through a pattern of laser pulses that perform coherent rotations on targeted qubits in the chain. The architecture implemented in the experiment therefore gives us unprecedented flexibility in the programming of any quantum algorithm while staying blind to the underlying hardware. As a demonstration we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms on the five-qubit processor and achieve average success rates of 95 and 90 percent, respectively. We also implement a five-qubit coherent quantum Fourier transform and examine its performance in the period finding and phase estimation protocol. We find fidelities of 84 and 62 percent, respectively. While maintaining the same computation architecture the system can be scaled to more ions using resources that scale favorably (O(N^2)) with the number of qubits N.
We discuss possibilities of quantum manipulations of trapped ions from the perspective of quantum information processing. We show how from a restricted set of feasible microscopic interactions a physical implementation of an arbitrary unitary operator can be realized. An example is given for the discrete Fourier transform. The synthesis of operators enables to realize universal quantum gates to process unknown input qubits which can be encoded into vibrational levels of trapped ions. We discuss also problem of an arbitrary measurement which can be performed using quantum gates.
Trapped ions are one of the most promising systems to implement quantum computations. In fact, there seems to be no fundamental obstacle to scale-up existing set-ups [1,2]. This is achieved by moving the ions without affecting their internal state, something that has been successfully demonstrated. The current limitations of trapped ions lie in the performance of the two--qubit quantum gates which are required for universal quantum computations. In particular, the time required to perform a gate is limited by the frequency of the trap holding the ions, something which cannot be increased arbitrarily. In this work [3] we show that such a time limitation is by no means fundamental. In fact, we propose a new concept of quantum gate which is not limited by the trap frequency, is completely independent of the temperature (even beyond the Lamb-Dicke limit), and requires no addressability. We also analyze the performance of quantum gates based on this new scheme.
We report on the implementation of arbitrary circuits on a universal two-qubit register that can act as the computational module in a trapped-ion quantum computer based on the quantum charge-coupled device architecture. A universal set of quantum gates is implemented on a two-ion Coulomb crystal of Be + 9 ions using only chip-integrated microwave addressing. Individual-ion addressing is implemented using microwave micromotion sideband transitions; we obtain upper limits on addressing crosstalk in the register. Arbitrary two-qubit operations are characterized using the cycle benchmarking protocol. Published by the American Physical Society 2024