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Scalable modular architecture for universal quantum computation

Fernando Gago-Encinas, Christiane P. Koch

TL;DR

The paper addresses how to achieve universal quantum computation with resource-efficient hardware by adopting a modular architecture. It proves that connecting two evolution operator controllable modules with a single entangling two-qubit gate suffices to make the composite system controllable, enabling scalable QPUs with reduced local controls and couplings. The main contribution is a formal theorem showing that the dynamical Lie algebra of the combined system becomes $\mathfrak{su}(2^{M+N})$, plus a concrete design template and examples (including a 10- and a 127-qubit layout inspired by IBM processors) that realize significant resource reductions. This work provides a principled pathway to scalable, universal quantum computation using modular, tunable-coupler hardware while highlighting trade-offs with operation times and error propagation.

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.

Scalable modular architecture for universal quantum computation

TL;DR

The paper addresses how to achieve universal quantum computation with resource-efficient hardware by adopting a modular architecture. It proves that connecting two evolution operator controllable modules with a single entangling two-qubit gate suffices to make the composite system controllable, enabling scalable QPUs with reduced local controls and couplings. The main contribution is a formal theorem showing that the dynamical Lie algebra of the combined system becomes , plus a concrete design template and examples (including a 10- and a 127-qubit layout inspired by IBM processors) that realize significant resource reductions. This work provides a principled pathway to scalable, universal quantum computation using modular, tunable-coupler hardware while highlighting trade-offs with operation times and error propagation.

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.

Paper Structure

This paper contains 9 sections, 4 theorems, 34 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Controllability of bipartite systems with an entangling control
  3. Design of large qubit arrays
  4. Summary and Perspectives
  5. Proof of the theorem
  6. Notation and problem statement
  7. Operations with tensor products of Pauli matrices
  8. Preliminaries
  9. Controllability of two controllable qubit arrays coupled via a two-qubit control

Key Result

Theorem 1

Let $\mathcal{A}$ and $\mathcal{B}$ be two evolution operator controllable qubit arrays with $M$ and $N$ qubits. Let $\hat{H}^{\mu, n}_c$ be a two-qubit operator given by eqn:2qubit. Then, the extended bipartite system with a tunable two-qubit coupling with control operator $\hat{H}^{\mu, n}_c$ is o

Figures (2)

  • Figure 1: (a): Controllable five-qubit system using just two controls gago2023graph. Qubits with (without) local controls are shaded (blank) and static couplings are drawn as straight black lines. (b): Controllable system built up from two copies of the system in (a) with a tunable coupling (blue zig-zag connection).
  • Figure 2: Controllable qubit array starting from the connectivity of IBM's Eagle processor (cf. https://quantum.cloud.ibm.com/docs/en/guides/processor-types) but with a reduced number of controls and couplings, based on a decomposition into three different modules consisting of four, resp. five qubits (indicated by the yellow, green and red background color). Shaded qubits are equipped with local controls, while the blank ones are not. Blue zigzag lines are required tunable couplings, whereas coiled lines represent tunable couplings that are present in Eagle but can be removed without hampering controllability. The couplings within each module are static, as opposed to the other tunable ones. The Hamiltonians for the three modules are given in \ref{['eqn:127q']}.

Theorems & Definitions (8)

  • Theorem 1
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • proof : Proof of Theorem \ref{['thm:modular']}