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arXiv:2004.04372 · Physical Review Research

Fast entangling gates in long ion chains

Zain Mehdi, Alexander K. Ratcliffe, J. J. Hope

Published Jan 11, 2021• 12 citations
arXivHTMLPDF

Abstract

We present a model for implementing fast entangling gates (∼1 μs) with ultrafast pulses in arbitrarily long ion chains, that requires low numbers of pulses and can be implemented with laser repetition rates well within experimental capability.We demonstrate that we are able to optimize pulse sequences that have theoretical fidelities above 99.99% in arbitrarily long ion chains, for laser repetition rates on the order of 100-300 MHz.Notably, we find higher repetition rates are not required for gates in longer ion chains, which is in contrast to scaling analyses with other gate schemes.When pulse imperfections are considered in our calculations, we find that achievable gate fidelity is independent of the number of ions in the chain.We also show that pulse control requirements do not scale up with the number of ions.We find that population transfer efficiencies of above 99.9% from individual ultrafast pulses is the threshold for realizing high-fidelity gates, which may be achievable in near-future experiments.

DOI
10.1103/physrevresearch.3.013026

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One of the major problems in building a quantum computer is the development of scalable and robust methods to entangle many qubits. Quantum computers based on trapped atomic ions are one of the most mature and promising platforms for quantum information processing, exhibiting excellent coherence properties, near-perfect qubit detection efficiency, and high-fidelity entangling gates. Entangling operations between multiple ions in a chain typically rely on qubit state-dependent forces that modulate their Coulomb-coupled normal modes of motion. However, scaling these operations to large qubit numbers in a single chain must account for the increasing complexity of the normal mode spectrum, and can result in a gate time slowdown or added complexity of the control forces. In this thesis, I present an alternative route to the scalability problem using optical interactions faster than any state evolution. The experiments shown here represent a proof of principle for quantum manipulation of atoms in the strong coupling regime. This work relies on spin dependent forces (SDK) with short laser pulses and use it as our fundamental building block for thermometry and non-trivial motional state preparation. Together with a robust stabilization of the ion trap and high light collection efficiency, we demonstrate two-ion entanglement with ten ultrafast pulses. Due to the nature of the interaction, the demonstrated entangling operation can be made arbitrarily fast only limited by laser engineering.

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We present a model for implementing fast entangling gates (∼1 μs) with ultrafast pulses in arbitrarily long ion chains, that requires low numbers of pulses and can be implemented with laser repetition rates well within experimental capability.We demonstrate that we are able to optimize pulse sequences that have theoretical fidelities above 99.99% in arbitrarily long ion chains, for laser repetition rates on the order of 100-300 MHz.Notably, we find higher repetition rates are not required for gates in longer ion chains, which is in contrast to scaling analyses with other gate schemes.When pulse imperfections are considered in our calculations, we find that achievable gate fidelity is independent of the number of ions in the chain.We also show that pulse control requirements do not scale up with the number of ions.We find that population transfer efficiencies of above 99.9% from individual ultrafast pulses is the threshold for realizing high-fidelity gates, which may be achievable in near-future experiments.
Fast entangling gates for trapped ion pairs offer vastly improved gate operation times relative to implemented gates, as well as approaches to trap scaling. Gates on a neighbouring ion pair only involve local ions when performed sufficiently fast, and we find that even a fast gate between a pair of distant ions with few degrees of freedom restores all the motional modes given more stringent gate speed conditions. We compare pulsed fast gate schemes, defined by a timescale faster than the trap period, and find that our proposed scheme has less stringent requirements on laser repetition rate for achieving arbitrary gate time targets and infidelities well below 10 −4 . By extending gate schemes to ion crystals, we explore the effect of ion number on gate fidelity for coupling two neighbouring ions in large crystals. Inter-ion distance determines the gate time, and a factor of five increase in repetition rate, or correspondingly the laser power, reduces the infidelity by almost two orders of magnitude. We also apply our fast gate scheme to entangle the first and last ions in a crystal. As the number of ions in the crystal increases, significant increases in the laser power are required to provide the short gate times corresponding to fidelity above 0.99.
Fast entangling gates have been proposed for trapped ions that are orders of magnitude faster than current implementations. We present here a detailed analysis of the challenges involved in performing a successful fast gate. We show that the rotating wave approximation is stable with respect to pulse numbers: the time scale on which we can neglect terms rotating at the atomic frequency is negligibly affected by the number of pulses in the fast gate. In contrast, we show that the laser pulse instability does give rise to a pulse-number-dependent effect; the fast gate infidelity is compounded with the number of applied imperfect pulses. Using the dimensional reduction method presented here, we find bounds on the pulse stability required to achieve two-qubit gate fidelity thresholds.
We present an efficient approach to optimizing pulse sequences for implementing fast entangling two-qubit gates on trapped ion quantum information processors. We employ a two-phase procedure for optimizing gate fidelity, which we demonstrate for multi-ion systems in linear Paul trap and microtrap architectures. The first phase involves a global optimization over a computationally inexpensive cost function constructed under strong approximations of the gate dynamics. The second phase involves local optimizations that utilize a more precise ordinary differential equation description of the gate dynamics, which captures the nonlinearity of the Coulomb interaction and the effects of finite laser repetition rate. We propose two gate schemes that are compatible with this approach, and we demonstrate that they outperform existing schemes in terms of achievable gate speed and fidelity for feasible laser repetition rates. In optimizing sub-microsecond gates in microtrap architectures, the proposed schemes achieve orders-of-magnitude-higher fidelities than previous proposals. Finally, we investigate the impact of pulse imperfections on gate fidelity and evaluate error bounds for a range of gate speeds.
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.
The conventional approach to perform two-qubit gate operations in trapped ions relies on exciting the ions on motional sidebands with laser light, which is an inherently slow process. One way to implement a fast entangling-gate protocol requires a suitable pulsed laser to increase the gate speed by orders of magnitude. However, the realization of such a fast entangling-gate operation presents a big technical challenge, as such the required laser source is not available off the shelf. For this, we engineer an ultrafast entangling-gate source based on a frequency comb. The source generates bursts of several hundred mode-locked pulses with pulse energy approximately 800 pJ at 5-GHz repetition rate at 393.3 nm and complies with all requirements for implementing a fast two-qubit gate operation. Using a single, chirped ultraviolet pulse, we demonstrate a rapid adiabatic passage in a Ca+{\mathrm{Ca}}^{+}Ca+ ion. To verify the applicability and projected performance of the laser system for inducing entangling gates we run simulations based on our source parameters. The gate time can be faster than a trap period with an error approaching ${10}^{\ensuremath{-}4}$.
One of the major problems in building a quantum computer is the development of scalable and robust methods to entangle many qubits. Quantum computers based on trapped atomic ions are one of the most mature and promising platforms for quantum information processing, exhibiting excellent coherence properties, near-perfect qubit detection efficiency, and high-fidelity entangling gates. Entangling operations between multiple ions in a chain typically rely on qubit state-dependent forces that modulate their Coulomb-coupled normal modes of motion. However, scaling these operations to large qubit numbers in a single chain must account for the increasing complexity of the normal mode spectrum, and can result in a gate time slowdown or added complexity of the control forces. In this thesis, I present an alternative route to the scalability problem using optical interactions faster than any state evolution. The experiments shown here represent a proof of principle for quantum manipulation of atoms in the strong coupling regime. This work relies on spin dependent forces (SDK) with short laser pulses and use it as our fundamental building block for thermometry and non-trivial motional state preparation. Together with a robust stabilization of the ion trap and high light collection efficiency, we demonstrate two-ion entanglement with ten ultrafast pulses. Due to the nature of the interaction, the demonstrated entangling operation can be made arbitrarily fast only limited by laser engineering.