Parallel Entangling Operations on a Universal Ion Trap Quantum Computer (1810.11948v1)

Abstract: The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear efficiency gains in numerous quantum circuits as well as for entire algorithms such as Shor's factoring algorithm and quantum simulations. In cases such as full adders and multiple-control Toffoli gates, parallelism can provide an exponential improvement in overall execution time. More importantly, quantum gate parallelism is essential for the practical fault-tolerant error correction of qubits that suffer from idle errors. The implementation of parallel quantum gates is complicated by potential crosstalk, especially between qubits fully connected by a common-mode bus, such as in Coulomb-coupled trapped atomic ions or cavity-coupled superconducting transmons. Here, we present the first experimental results for parallel 2-qubit entangling gates in an array of fully-connected trapped ion qubits. We demonstrate an application of this capability by performing a 1-bit full addition operation on a quantum computer using a depth-4 quantum circuit. These results exploit the power of highly connected qubit systems through classical control techniques, and provide an advance toward speeding up quantum circuits and achieving fault tolerance with trapped ion quantum computers.

• The paper demonstrates the experimental implementation of parallel entangling operations using shaped Raman pulses to achieve two-qubit gate fidelities of 96-99%.
• The methodology employs a linear chain of trapped 171Yb+ ions and nonlinear optimization techniques to selectively entangle target qubit pairs with minimal crosstalk.
• The results imply significant gains in computational speed and fault tolerance, paving the way for more efficient quantum error correction and algorithmic advancements.

Overview of Parallel Entangling Operations on a Universal Ion Trap Quantum Computer

The paper outlined in "Parallel Entangling Operations on a Universal Ion Trap Quantum Computer" explores an innovative approach to executing parallel entangling operations within a fully connected ion trap quantum computer, offering significant improvements in computational efficiency and fault tolerance. The research explores the experimental implementation of parallel two-qubit gates, demonstrating their application in creating a 1-bit quantum full adder circuit.

Trapped atomic ions are utilized as qubits in this quantum computing model due to their high connectivity and precise control over gate operations. The experiment leverages the excellent characteristics of atomic ions, such as their inherent atomic clock precision and reconfigurable network capability, allowing for the execution of parallel entangling operations that are essential for optimizing complex quantum circuits and algorithms.

Methodology and Results

In the quantum computer model employed, ions are arranged in a linear chain with coherent quantum gate operations performed via Raman beams from a mode-locked laser. The researchers implemented parallel gates using nonlinear optimization techniques to shape the laser pulses, allowing them to entangle only the intended qubit pairs in the presence of potential crosstalk from other qubits in close proximity.

The experimental setup featured a chain of five atomic $^{171}$Yb$^+$ ions. The paper measured gate fidelities typically between 96-99% for pairs such as (1,4) and (2,5), with crosstalk errors at a few percent, demonstrating high-fidelity parallel operations. These results indicate that, by executing multiple gates in parallel, one can significantly enhance computational speed while maintaining precision, a necessity for practical error correction and achieving fault tolerance in quantum computing.

Implications and Speculative Futures

The practical implications of parallel gate operations extend into several key areas:

1. Efficiency Gains: The execution of parallel entangling operations reduces the overall execution time for critical operations in quantum circuits, such as adders and multiply-controlled gates, providing exponential improvements.
2. Error Correction Enhancement: By mitigating idle errors through parallelism, this approach plays a significant role in promoting substantial fault-tolerant quantum error correction.
3. Algorithmic Development: Algorithms like Shor’s factoring and quantum simulations can be significantly expedited through parallel entangling gates, facilitating real-world applications of quantum computing.

Looking forward, further optimization of nonlinear control signals and exploration of different numerical techniques may yield even more efficient gate implementations. This research paves the way towards constructing multi-qubit GHZ states in single operations, which would drastically reduce the depth of key algorithms like the quantum Fourier transform.

Overall, this paper marks a promising step towards unlocking the full potential of trapped ion quantum computing by harnessing parallel entangling operations to overcome practical challenges and accelerate computational power. The ongoing advancement in this domain could result in breakthroughs in computational capabilities and error mitigation strategies, propelling AI and quantum computing fusion towards practical and scalable solutions.