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arXiv:2507.14691 · SciPost Physics

Scalable modular architecture for universal quantum computation

Fernando Gago-Encinas, Christiane P. Koch

Published Feb 17, 2026• 1 citation
arXivHTMLPDF

Abstract

Universal quantum computing requires the ability to perform every unitary operation, i.e., evolution operator controllability. In view of developing resource-efficient quantum processing units (QPUs), it is important to determine how many local controls and qubit-qubit couplings are required for controllability. Unfortunately, assessing the controllability of large qubit arrays is a difficult task, due to the exponential scaling of Hilbert space dimension. Here we show that it is sufficient to connect two qubit arrays that are evolution operator controllable by a single entangling two-qubit gate in order to obtain a composite qubit array that is evolution operator controllable. The proof provides a template to build up modular QPUs from smaller building blocks with reduced numbers of local controls and couplings. We illustrate the approach with two examples, consisting of 10, respectively 127 qubits, inspired by IBM quantum processors.

DOI
10.21468/scipostphys.20.2.046

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•Oct 14, 2021•0 citations
Universal quantum computing requires the ability to perform every unitary operation, i.e., evolution operator controllability. In view of developing resource-efficient quantum processing units (QPUs), it is important to determine how many local controls and qubit-qubit couplings are required for controllability. Unfortunately, assessing the controllability of large qubit arrays is a difficult task, due to the exponential scaling of Hilbert space dimension. Here we show that it is sufficient to connect two qubit arrays that are evolution operator controllable by a single entangling two-qubit gate in order to obtain a composite qubit array that is evolution operator controllable. The proof provides a template to build up modular QPUs from smaller building blocks with reduced numbers of local controls and couplings. We illustrate the approach with two examples, consisting of 10, respectively 127 qubits, inspired by IBM quantum processors.
Abstract The ability to implement any desired quantum logic gate on a quantum processing unit is equivalent to evolution-operator controllability of the qubits. Conversely, controllability analysis can be used to minimize the resources, i.e. the number of external controls and qubit–qubit couplings, required for universal quantum computing. Standard controllability analysis, consisting in the construction of the dynamical Lie algebra, is, however, impractical already for a comparatively small number of qubits. Here, we show how to leverage an alternative approach, based on a graph representation of the Hamiltonian, to determine controllability of arrays of coupled qubits. We provide a complete computational framework and exemplify it for arrays of five qubits, inspired by the ibmq_quito architecture. We find that the number of controls can be reduced from five to one for complex qubit–qubit couplings and to two for standard qubit–qubit couplings.
Operator controllability refers to the ability to implement an arbitrary unitary in SU(N) and is a prerequisite for universal quantum computing. Controllability tests can be used in the design of quantum devices to reduce the number of external controls. Their practical use is hampered, however, by the exponential scaling of their numerical effort with the number of qubits. Here, we devise a hybrid quantum-classical algorithm based on a parametrized quantum circuit. We show that controllability is linked to the number of independent parameters, which can be obtained by dimensional expressivity analysis. We exemplify the application of the algorithm to qubit arrays with nearest-neighbour couplings and local controls. Our work provides a systematic approach to the resource-efficient design of quantum chips.
Operator controllability refers to the ability to implement an arbitrary unitary in SU(N) and is a prerequisite for universal quantum computing. Controllability tests can be used in the design of quantum devices to reduce the number of external controls. Their practical use is hampered, however, by the exponential scaling of their numerical effort with the number of qubits. Here, we devise a hybrid quantum-classical algorithm based on a parametrized quantum circuit. We show that controllability is linked to the number of independent parameters, which can be obtained by dimensional expressivity analysis. We exemplify the application of the algorithm to qubit arrays with nearest-neighbour couplings and local controls. Our work provides a systematic approach to the resource-efficient design of quantum chips.
Abstract Scalable quantum information processing with limited physical resources is a key challenge in the pursuit of practical quantum advantage. Here, we introduce an approach that encodes two qubits per ion, enabling an n -ion–2 n -qubit quantum processor by harnessing four internal levels of trapped ions. As a proof of principle, we demonstrate a universal 1-ion–2-qubit processor using the valence electron spin and nuclear spin of a single 171 Yb + ion, achieving gate fidelities exceeding 98% for both single- and two-qubit operations via quantum process tomography. Furthermore, we implement Grover’s algorithm with a success rate surpassing 99%, showing the system’s computational capability. Through robust optimal quantum control, we enhance gate robustness against amplitude and frequency fluctuations, critical for large-scale operation. We present scalable architectures leveraging both laser-free and laser-based entangling gates, revealing that intra-atomic electron–nuclear spin interactions can reduce the complexity of inter-atomic operations. By substituting inter-atomic gates with high-fidelity intra-atomic ones, our scheme significantly improves circuit performance. This work establishes a pathway to exponentially expand the Hilbert space of quantum processors, and represents an important advance toward scalable, high-capacity quantum computing.
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.