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arXiv:quant-ph/0304168 · Physical Review A

Ion-trap quantum computing in the presence of cooling

Almut Beige

Published Jan 9, 2004• 26 citations
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Abstract

This paper discusses ways to implement two-qubit gate operations for quantum computing with cold trapped ions within one step. The proposed scheme is widely robust against parameter fluctuations and its simplicity might help to increase the number of qubits in present experiments. The basic idea is to use the quantum Zeno effect originating from continuous measurements on a common vibrational mode to realize gate operations with very high fidelities. The gate success rate can, in principle, be arbitrarily high but operation times comparable to other schemes can only be obtained by accepting success rates below 80%.

DOI
10.1103/physreva.69.012303

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This paper discusses ways to implement two-qubit gate operations for quantum computing with cold trapped ions within one step. The proposed scheme is widely robust against parameter fluctuations and its simplicity might help to increase the number of qubits in present experiments. The basic idea is to use the quantum Zeno effect originating from continuous measurements on a common vibrational mode to realize gate operations with very high fidelities. The gate success rate can, in principle, be arbitrarily high but operation times comparable to other schemes can only be obtained by accepting success rates below 80%.
The principal obstacle to quantum information processing with many qubits is decoherence. One source of decoherence is spontaneous emission which causes loss of energy and information. Inability to control system parameters with high precision is another possible source of error. As a solution we propose quantum computing experiments using dissipation based on an environment-induced quantum Zeno effect. As an example we present a simple scheme for quantum gate implementations with cold trapped ions in the presence of cooling.
This thesis describes schemes for both a fast two-qubit gate operation and the steady-state preparation of a Bell state with trapped ions. A critical figure of merit for quantum computing with trapped ions is the gate duration relative to the decoherence timescale. We propose a fast gate scheme that off ers improvements in time, fidelity and simplicity of implementation over existing fast gate proposals. Our scheme can operate on both neighbouring and non-neighbouring ions in a long ion crystal. This provides a simpler and faster mechanism than traditional gates for complex quantum computing operations on large numbers of ions. The scheme achieves fidelities well above quantum error correction thresholds around 0.0001, and operates arbitrarily fast given arbitrary laser repetition rates. The production of these ultra-fast pulses is an experimental challenge, and fast gates have not yet been implemented; we present an implementation scheme using pulse splitting to provide a higher repetition rate and the pulse timing freedoms required for the gate scheme. We also analyse the effects of errors in the pulses on the gate operation. We analyse another strategy to generate entanglement using a driven dissipative process. Typically, environmental couplings cause decoherence. However, by combining dissipative dynamics with suitably chosen Hamiltonian evolution, the system can be steered to the desired steady states. Our steady-state scheme prepares a maximally-entangled Bell state with fidelity above 0.99, much higher than for schemes implemented with trapped ions. The driven dissipation continuously pumps the system towards the antisymmetric Bell steady-state, which is dark to the system dynamics and robust to parameter variations. The dominant loss mechanism is anomalous heating of the motional modes, reducing our fidelity by less than 0.01 for current experimental rates. Our scheme jointly addresses the ions and does not use sympathetic cooling. We enhance our scheme by combining the dissipative state preparation with the detection of photons, and obtain a significant fidelity enhancement.
Realising large-scale quantum computation in the near future will require increasing the number of low-error two-qubit gates that can be implemented on a quantum computer before decoherence. One of the biggest challenges facing current trapped ion quantum computers is implementing high-speed two-qubit operations, whilst increasing the number of qubits. One of the most promising proposals for overcoming current limitations is the use of ultra-fast pulses to implement fast two-qubit gates between nearest-neighbour pairs of ions. In this thesis, I investigate these ‘fast gates’ in two-dimensional arrays of microtraps, each containing a single ion. I argue that two-dimensional architectures allow for a significant reduction in the number of two-qubit gates required for a particular computation, as compared to one-dimensional ion chains. I demonstrate this reduction for a quantum simulation of a 40-mode Fermi-Hubbard Hamiltonian. I develop an efficient scheme that allows fast gates to be numerically optimised for two-dimensional geometries. I find that this optimisation scheme is capable of designing gates that are faster, higher fidelity, and require lower laser repetition rates. Using this scheme, I find that high-speed two-qubit gates can be optimised for two-dimensional architectures, with fidelities well above thresholds required for fault tolerant error correction, around 99.99%. Furthermore, I find that fast gates in these architectures are robust to the presence of large numbers of surrounding ions. Following previous studies [1, 2] which have identified pulse imperfections as a dominant source of error in fast gates, I perform a worst-case error analysis. I find the fast gates presented in this thesis to require very small errors in single-qubit rotations, and I present recommendations for achieving those requirements. I also investigate other experimental considerations, and make recommendations for overcoming other technical challenges in realising fast gates.
In the system with a two-level ion confined both in a linear trap and in a high-Q single-mode cavity, we present a simple scheme to realize the basic two-qubit logic gates such as the quantum phase gate (QPG), the SWAP gate and the controlled-NOT (CNOT) gate beyond the Lamb–Dicke (LD) limit. We realize the three kinds of two-qubit quantum phase gates, i.e. QPG operation involving the cavity mode as well as the vibrational mode of the trapped ion, QPG operation involving the internal states as well as the vibrational mode of the trapped ion and QPG operation involving the internal states of the trapped ion as well as the cavity mode. The controlled-NOT gate can be implemented from a QPG operation through a rotation of the second qubit before and after the QPG operation. We can also perform the SWAP gate operation involving the ionic internal states of the trapped ion and the two-mode bosonic basis. The logic gates involving the cavity mode as well as the vibrational mode of the trapped ion are insensitive to spontaneous emission, and the logic gates involving the internal states as well as the vibrational mode of the trapped ion are insensitive to the decay of the cavity, which is an important feature for the practical implementation of quantum computing. Neither the LD approximation nor the auxiliary atomic level is needed in our scheme. Experimental feasibility for achieving our scheme is also discussed.
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.