Building globally controlled quantum processors with ZZ interactions

TL;DR

This work develops a framework for globally controlled quantum processors using superconducting qubits with always-on ZZ interactions, introducing static Rabi-frequency inhomogeneities via the crossed-qubit method to achieve local operations under a single global drive. It proves that, by exploiting blockade effects in the strong-coupling regime and carefully partitioning qubits into regular and crossed subgroups, one can realize independent SU(2) rotations on targeted subsystems, enabling universal computation with reduced wiring. The authors instantiate two architectures—the two-species ladder and the two-species conveyor-belt—demonstrating universal gate sets while achieving favorable scaling: the ladder maintains universality with 2 species and crossed elements, whereas the conveyor-belt attains linear scaling in physical qubits for $n$ computational qubits. Collectively, the results offer a concrete pathway toward scalable, hardware-efficient quantum processors that leverage global control, with implications for integrating error-correction strategies in low-dimensional architectures.

Abstract

We present a comprehensive framework for constructing various architectures of globally driven quantum computers, with a focus on superconducting qubits. Our approach leverages static inhomogeneities in the Rabi frequencies of qubits controlled by a common classical pulse -- a technique we refer to as the "crossed-qubit" method. We detail the essential components and design principles required to realize such systems, highlighting how global control can be harnessed to perform local operations, enabling universal quantum computation. This framework offers a scalable pathway toward quantum processors by striking a balance between wiring complexity and computational efficiency, with potential applications in addressing current challenges to scalability.

Figures (5)

• Figure 1: Example of the Hamiltonian model studied in this paper which involves a set of three different species of superconducting qubits, ${\cal S} =\{ A, B,C\}$, represented by the red, blue and green squares, respectively. These qubits are arranged on a graph in the form of a ladder, consisting of two rows connected by an edge. Black springs between pairs of qubits indicate always-on ZZ interactions. Each species is globally controlled by independent classical electrical pulses delivered through dedicated wiring, shown as continuous red, blue, and green lines connecting all qubits of the corresponding group. Elements with crosses correspond to crossed-qubits.
• Figure 2: Pictorial illustration of the equivalence between local control (left) and global control (right) for $N$ qubits in two scenarios: non-interacting qubits [(a)] and qubits with ZZ interactions [(b)]. Here, $\Omega_j$ (with $j = 1, \ldots, N$) denotes the Rabi frequency -- the coupling strength between the drive source and the $j$-th qubit -- associated with the control line addressing that qubit. The Rabi frequency depends on the physical properties of each qubit; thus, as shown on the left, a single drive line can induce different Rabi frequencies across the qubits. The equivalences illustrated in the figure hold under the condition specified in \ref{['eq:rabi']} (see Theorem \ref{['theorem1']}). In (b), the driven qubits are coupled to other qubits of different species via ZZ interactions; in principle, these auxiliary qubits could also be addressed. The blockade regime enables the equivalence and the realization of the unitary $\hat{W}$ stated in Corollary \ref{['corollary1']}.
• Figure 3: Schematic description of a globally driven 2D ladder quantum computer with two species of qubits, an alternative version with respect to the three-species architecture described in Ref. menta2024globally. Two species, $A$, $B$ of superconducting qubits (red and blue squares, respectively) occupy the horizontal rows of a 2D ladder. Black springs and colored continuous lines represents respectively ZZ interactions among neighbor qubits and control lines. Element with crosses and double crosses correspond to crossed and double crossed-qubits. Filled circles and triangles on a square emphasize that the corresponding site has coordination number 1 or 3, respectively (the other sites have all coordination number 2) -- see Eq. (\ref{['coordination']}). Electrical wires depicted as continuous red and blue lines connect all elements within each group, facilitating global control through independent classical electrical pulses. During the computation, the logical information is encoded in the qubits of one of the columns of the processing area (highlighted in yellow in the figure): qubits on the left (right) hand side of such information carrier column are in a "Néel" ("ferromagnetic") $geg$ ($ggg$) phase. The illustration pertains to a $n=4$ computational qubit quantum computer.
• Figure 4: Schematic description of an alternative two-species variant to the conveyor-belt superconducting quantum computer introduced in Ref. cioni2024conveyorbelt. Two types, $A$ and $B$ of superconducting qubits (red and blue squares, respectively) are separately driven by three classical sources $V_{A,B}(t)$ (red and blue continuous lines). They are coupled via a longitudinal ZZ coupling (black and grey springs). Black springs, crosses and double crosses, filled circles and triangles are defined as in Fig. \ref{['fig:square']}. The $A$-type double-crossed qubit (red square inside the loop) enables one-shot Toffoli gate (three-qubit gate) -- the corresponding interactions are depicted in gray. The $B$-type double crossed qubit performs universal single-qubit gates. The elements highlighted in yellow indicate the information carrying sites $Q_1$, $Q_2$, $\cdots$, $Q_n$, separated by alternating $A$--type regular and crossed qubits. The $Q_j$'s host the computational qubits through well-formed configurations. The figure pertains to a $n=8$ qubit quantum computer.
• Figure 5: Dynamics and quantum computation scheme of (a) 2D ladder architecture and (b) conveyor-belt architecture.

Theorems & Definitions (4)

• Theorem 1: Global control enables local addressing
• proof
• Corollary 2: Case of interacting qubits
• proof