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arXiv:2110.07737 · npj Quantum Information

Scalable and robust quantum computing on qubit arrays with fixed coupling

Nguyen H. Le, Max Cykiert, Eran Ginossar

Published Jan 5, 2023• 31 citations
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Abstract

Abstract We propose a scheme for scalable and robust quantum computing on two-dimensional arrays of qubits with fixed longitudinal coupling. This opens the possibility for bypassing the device complexity associated with tunable couplers required in conventional quantum computing hardware. Our approach is based on driving a subarray of qubits such that the total multi-qubit Hamiltonian can be decomposed into a sum of commuting few-qubit blocks, and efficient optimisation of the unitary evolution within each block. The driving pulses are optimised to implement a target gate on the driven qubits, and at the same time identity gates on the neighbouring undriven qubits, cancelling any unwanted evolution due to the constant qubit-qubit interaction. We show that it is possible to realise a universal set of quantum gates with high fidelity on the basis blocks, and by shifting the driving pattern one can realise an arbitrary quantum circuit on the array. Allowing for imperfect Hamiltonian characterisation, we use robust optimal control to obtain fidelities around 99.99% despite 1% uncertainty in the qubit-qubit and drive-qubit couplings, and a detuning uncertainty at 0.1% of the qubit-qubit coupling strength. This robust feature is crucial for scaling up as parameter uncertainty is significant in large devices.

DOI
10.1038/s41534-022-00668-3

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Abstract We propose a scheme for scalable and robust quantum computing on two-dimensional arrays of qubits with fixed longitudinal coupling. This opens the possibility for bypassing the device complexity associated with tunable couplers required in conventional quantum computing hardware. Our approach is based on driving a subarray of qubits such that the total multi-qubit Hamiltonian can be decomposed into a sum of commuting few-qubit blocks, and efficient optimisation of the unitary evolution within each block. The driving pulses are optimised to implement a target gate on the driven qubits, and at the same time identity gates on the neighbouring undriven qubits, cancelling any unwanted evolution due to the constant qubit-qubit interaction. We show that it is possible to realise a universal set of quantum gates with high fidelity on the basis blocks, and by shifting the driving pattern one can realise an arbitrary quantum circuit on the array. Allowing for imperfect Hamiltonian characterisation, we use robust optimal control to obtain fidelities around 99.99% despite 1% uncertainty in the qubit-qubit and drive-qubit couplings, and a detuning uncertainty at 0.1% of the qubit-qubit coupling strength. This robust feature is crucial for scaling up as parameter uncertainty is significant in large devices.
We show how robust and scalable quantum computing can be realized on an arbitrarily large two dimensional arrays of qubits with fixed longitudinal couplings despite significant uncertainty in all the qubit-qubit and drive-qubit coupling strengths. This opens the possibility for bypassing the fabrication complexity associated with tunable couplers required in conventional quantum computing hardware. Our approach is based on driving a chosen subarray of qubits such that the total multi-qubit Hamiltonian can be decomposed into a sum of commuting few-qubit blocks and on efficient optimization of the unitary evolution within each block. Robust optimal control is then employed to implement a universal set of quantum gates with fidelities around 99.99% despite 1% uncertainty in the Hamiltonian's parameters. This robust feature is crucial for scaling up as uncertainty in the properties of qubits is substantial in large devices.
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.
Accurate and efficient implementation of parallel quantum gates is crucial for scalable quantum information processing. However, the unavoidable crosstalk between qubits in current noisy processors impedes the achievement of high gate fidelities and renders full Hilbert-space control optimization prohibitively difficult. Here, we overcome this challenge by reducing the full-system optimization to crosstalk-robust control over constant-sized subsystems, which dramatically reduces the computational cost. Our method effectively eliminates the leading-order gate operation deviations induced by crosstalk, thereby suppressing error rates. Within this framework, we construct analytical pulse solutions for parallel single-qubit gates and numerical pulses for parallel multi-qubit operations. We validate the proposed approach numerically across multiple platforms, including coupled nitrogen-vacancy centers, a nuclear-spin processor, and superconducting-qubit arrays with up to 200 qubits. As a result, the noise scaling is reduced from exponential to linear for parallel single-qubit gates, and an order-of-magnitude reduction is achieved for parallel multi-qubit gates. Moreover, our method does not require precise knowledge of crosstalk strengths and makes no assumption about the underlying qubit connectivity or lattice geometry, thereby establishing a scalable framework for parallel quantum control in large-scale quantum architectures.
Fault-tolerant quantum computing requires high-fidelity quantum gates that are resilient to control errors and device imperfections. Here, we develop energy-optimal control pulses for single-qubit gates that are simultaneously robust against frequency detuning and waveform inhomogeneities while also suppressing leakage outside the computational subspace. Combining the optimized pulse envelopes with an adaptive control scheme, we experimentally demonstrate optimal robust gates on a superconducting quantum processor. For a gate duration of 90ns, we achieve fidelities above 99.9% for the X gate and 99.6% for Hadamard-type gates. For the X gate, we maintain fidelities above 99.5% for simultaneous drive-amplitude variations up to 20% and qubit detuning up to 4 MHz. This robustness outperforms that of conventional Gaussian pulses by an order of magnitude, without much difference in peak gate fidelity. These results establish a route towards robust single-qubit control in large-scale quantum processors, advancing the development of fault-tolerant quantum computing.
A major current challenge in solid-state quantum computing is to scale qubit arrays to a larger number of qubits. This is hampered by the complexity of the control wiring for the large number of independently tunable interqubit couplings within these arrays. One approach to simplifying the problem is to use a qubit array with fixed Ising (ZZ) interactions. When simultaneously driving a specific subset of qubits in such a system, the dynamics are confined to a set of commuting su(2)\text{su}(2)su(2) subalgebras. Within these su(2)s\text{su}(2)\mathrm{s}su(2)s we describe how to perform X-gates and $\frac{\ensuremath{\pi}}{2}\phantom{\rule{4pt}{0ex}}\text{ZZ}$ rotations robustly against either leakage, which is the main source of error in transmon qubits, or coupling fluctuations, which is the main source of infidelity in flux or semiconductor spin qubits. These gates together with virtual-zzz gates form a universal set of gates for quantum computing. We construct this set of robust gates for two-edge, three-edge, and four-edge vertices, which compose all existing superconducting qubit and semiconductor spin qubit arrays.
Optimal control can be used to significantly improve multi-qubit gates in quantum information processing hardware architectures based on superconducting circuit quantum electrodynamics. We apply this approach not only to dispersive gates of two qubits inside a cavity, but, more generally, to architectures based on two-dimensional (2D) arrays of cavities and qubits. For high-fidelity gate operations, simultaneous evolutions of controls and couplings in the two coupling dimensions of cavity grids are shown to be significantly faster than conventional sequential implementations. Even under experimentally realistic conditions speedups by a factor of three can be gained. The methods immediately scale to large grids and indirect gates between arbitrary pairs of qubits on the grid. They are anticipated to be paradigmatic for 2D arrays and lattices of controllable qubits.