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arXiv:2512.13558

Three-qubit entangling gates with simultaneous exchange controls in spin qubit systems

Miguel G. Rodriguez, Yun-Pil Shim

quant-phcond-mat.mes-hallSubmitted Dec 15, 2025• Announced Dec 16, 2025• 0 citations
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Abstract

Pairwise exchange couplings have long been the standard mechanism for entangling spin qubits in semiconductor systems. However, implementing quantum circuits based on pairwise exchange gates often requires a lengthy sequence of elementary gate operations. In this work, we present an alternative approach: multi-qubit entangling gate operations that simultaneously drive the exchange couplings between multiple pairs of spin qubits. We explore three spin qubit systems in linear or triangular configurations. We derive analytical expressions for these multi-exchange entangling operations and demonstrate how to use the resulting three-qubit gates to construct quantum circuits capable of generating standard entangled states such as GHZ and W states, and the Toffoli gate, by optimizing control parameters. Our results show that this multi-qubit strategy significantly reduces the number of required operations, offering a pathway to more efficient, shallower, and more coherent circuits for spin-qubit processors.

Comments
7 pages, 4 figures

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Pairwise exchange couplings have long been the standard mechanism for entangling spin qubits in semiconductor systems. However, implementing quantum circuits based on pairwise exchange gates often requires a lengthy sequence of elementary gate operations. In this work, we present an alternative approach: multi-qubit entangling gate operations that simultaneously drive the exchange couplings between multiple pairs of spin qubits. We explore three spin qubit systems in linear or triangular configurations. We derive analytical expressions for these multi-exchange entangling operations and demonstrate how to use the resulting three-qubit gates to construct quantum circuits capable of generating standard entangled states such as GHZ and W states, and the Toffoli gate, by optimizing control parameters. Our results show that this multi-qubit strategy significantly reduces the number of required operations, offering a pathway to more efficient, shallower, and more coherent circuits for spin-qubit processors.
Abstract In conventional exchange-only (EO) spin qubit demonstrations, quantum gates have been implemented using sequences of individually pulsed pairwise exchange interactions with only one exchange coupling active at a time. Alternatively, multiple non-commuting exchange interactions can be pulsed simultaneously, reducing circuit depths and providing protection against leakage. We demonstrate high-fidelity quantum control of an always-on exchange-only (AEON) qubit, operated using simultaneous exchange pulses in a triangular quantum dot (QD) array. We use blind randomized benchmarking to characterize the performance of the full AEON single-qubit Clifford gate set, achieving an average Clifford gate fidelity F C1 = 99.86%. Extensions of this work may enable more efficient EO two-qubit entangling gates as well as the implementation of native i -Toffoli gates in Loss-DiVincenzo single-spin qubits.
The benefit of exchange-only qubits compared to other spin-qubit types is the universal control using only voltage-controlled exchange interactions between neighboring spins. As a compromise, qubit operations have to be constructed from nonorthogonal rotation axes of the Bloch sphere and result in rather long pulsing sequences. This paper aims to develop a faster implementation of single-qubit gates using simultaneous exchange pulses and manifests their potential for the construction of two-qubit gates. We introduce pulse sequences in which single-qubit gates could be executed faster and show that subsequences on three spins in two-qubit gates could be implemented in fewer steps. Our findings can particularly speed up gate sequences for realistic idle times between sequential pulses and we show that this advantage increases with more interconnectivity of the quantum dots. We further demonstrate how a phase operation can introduce a relative phase between the computational and some of the leakage states, which can be advantageous for the construction of two-qubit gates. In addition to our theoretical analysis, we experimentally demonstrate and characterize a simultaneous exchange implementation of X rotations in a Si Ge quantum dot device and compare to the state of the art with sequential exchange pulses.
Quantum algorithms on near-term quantum processors are typically executed using shallow quantum circuits composed of one- and two-qubit gates. However, as circuit depth and gate number increase, gate imperfections and qubit decoherence begin to dominate, limiting algorithmic complexity. An alternative approach is to explore gates involving more than two qubits. In previous work (X. Wu et al., Physical Review X 14, 041030 (2024)), we demonstrated a new superconducting qubit architecture with user-selectable two-qubit interactions via a reconfigurable router, used to connect pairs of qubits. Here, we leverage this novel architecture to realize programmable and efficient multi-qubit operations involving more than two qubits, resulting in faster preparation of multi-qubit entangled states with good fidelities. We also successfully apply model-free reinforcement learning to perform multi-qubit gates, including training a two-qubit controlled-Z gate as well as three-qubit controlled-SWAP and controlled-controlled-phase (Fredkin and Toffoli) gates. Higher nnnth-order gates may also be feasible, using our high-connectivity router design. This could provide a more efficient and higher-fidelity implementation of complex quantum algorithms and a more practical approach to quantum computation.
Spin-based quantum architectures offer a promising route toward scalable and practical quantum computing owing to their long coherence times, high-fidelity gate operations, and compatibility with established semiconductor fabrication processes. This work focuses on the design, decomposition, and simulation of fundamental multi-qubit logic gates on spin-based architectures. An optimized CNOT gate decomposition is presented, achieving a 36.36%36.36 \%36.36% reduction in elementary operations, verified through quantum circuit simulation. Furthermore, a resource-efficient Toffoli (CCNOT) gate is developed, yielding a 38%38 \%38% reduction in elementary gates and demonstrating improved T-depth efficiency. Finally, a four-qubit circuit example is presented, illustrating the scalability of the pseudocode and validating the correctness of the proposed approach.
We propose a protocol for implementing Barenco-type multi-qubit controlled gates using short driven spin chains. Starting from an Ising interaction with a transverse drive on the last spin, we construct an effective two-qubit Hamiltonian whose time evolution implements the Barenco gate V2(φ,ω,φ)V_2(\varphi,ω,φ)V2​(φ,ω,φ) and, in particular, a CNOT gate. We then embed this construction into a three-qubit XXZXXZXXZ chain to realize the three-qubit Barenco gate V3(φ,ω,φ)V_3(\varphi,ω,φ)V3​(φ,ω,φ), which includes the Toffoli gate as a special case. The derivation is fully analytical: we perform a sequence of unitary transformations, identify decoupled subspaces, and apply a rotating-wave approximation to obtain simple effective Hamiltonians. We derive explicit conditions on the coupling strengths and driving parameters, provide closed-form expressions for the time-evolution operators in each relevant subspace, and characterize the quality of the implementation using the operator fidelity. Numerical simulations show that the protocol achieves high fidelities over broad parameter ranges, demonstrating its robustness and suitability for quantum information processing in spin-chain platforms.
Silicon-based spin qubits have emerged as a promising platform for scalable quantum computation due to their compatibility with advanced semiconductor fabrication and integration with classical CMOS electronics. As fabrication capabilities advance toward larger, higher-yield devices, the field is transitioning from academic prototypes toward processors ultimately requiring millions of qubits. This shift places increasing emphasis on developing operating techniques that scale with qubit number. In this thesis, a four qubit SiMOS processor is used to investigate three key aspects of multi-qubit operation for spin-based quantum computing. First, tuning and operation techniques for parallel double-quantum-dot unit cells are developed. Electron loading strategies enable four-qubit operation in an isolated charge configuration, and universal single- and two-qubit control is demonstrated. The native gate set is characterised using gate set tomography. The processor is operated as two unit cells that can be initialised and read out in parallel, providing two independent parity measurements per shot, without increasing operation time or degrading state preparation and measurement fidelity. Second, control techniques for generating multi-qubit entangled states and executing general quantum circuits are established. Three-qubit maximally entangled states, including cluster and Greenberger–Horne–Zeilinger states, are generated and measured with a maximum fidelity of 82.5%. A Mermin value of 3.14 is achieved, certifying genuine tripartite entanglement. A fully symmetric dynamically decoupled gate sequence is developed, extending the entanglement lifetime beyond T2* to a limit set by T2-Hahn. A workflow for compiling, executing, and analysing arbitrary circuits from OpenQASM is also demonstrated. Finally, the first mid-circuit measurements in a silicon spin-qubit system are presented. This capability is extended to feedforward control, including a novel “in-layer” method that performs conditional phase operations without routing information to the classical control layer. This approach leverages measurement-induced backaction as a control mechanism. Both in-layer and FPGA-enabled feedforward strategies are benchmarked, and their dominant error channels are identified.