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Advanced Quantum Technologies

Parallel Gate Fidelity of Flip‐Flop Qubits in Small 1D‐ and 2D‐Arrays in a Noisy Environment

Marco De Michielis, Davide Rei, Elena Ferraro

Published Apr 28, 2024• 2 citations
Publisher

Abstract

Abstract The long coherence time of donor atom nuclear spin states and of its bounded electron in can be exploited to define a qubit. This work is focused on a type of donor‐ and quantum dot‐based qubit, the flip‐flop (FF) qubit, that leverages antiparallel electron‐nuclear spin states of a donor atom controlled by an electric field. It can provide long‐range inter‐qubit interactions in the order of some hundreds of nanometers, thus relaxing the common constraints and tolerances on inter‐qubit distances in donor‐based qubits. Simulation results of linear array (LA) and square array (SA) of four FF qubits are presented to study the effect of noise, idle qubits, and simultaneous gating (parallel gating) on gate fidelity. The impact of noise and qubit mutual coupling for both considered types of array are presented and the obtained fidelity results are compared.

DOI
10.1002/qute.202300455

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Advanced Quantum Technologies•Dec 3, 2025•0 citations
Abstract The long coherence time of donor atom nuclear spin states and of its bounded electron in can be exploited to define a qubit. This work is focused on a type of donor‐ and quantum dot‐based qubit, the flip‐flop (FF) qubit, that leverages antiparallel electron‐nuclear spin states of a donor atom controlled by an electric field. It can provide long‐range inter‐qubit interactions in the order of some hundreds of nanometers, thus relaxing the common constraints and tolerances on inter‐qubit distances in donor‐based qubits. Simulation results of linear array (LA) and square array (SA) of four FF qubits are presented to study the effect of noise, idle qubits, and simultaneous gating (parallel gating) on gate fidelity. The impact of noise and qubit mutual coupling for both considered types of array are presented and the obtained fidelity results are compared.
Abstract Quantum computers based on silicon are promising candidates for long term universal quantum computation due to the long coherence times of electron and nuclear spin states. Furthermore, the continuous progress of micro‐ and nano‐electronics, also related to the scaling of metal–oxide–semiconductor systems, makes it possible to control the displacement of single dopants thus suggesting their exploitation as qubit holders. Flip‐flop qubit is a donor based qubit where interactions between qubits are achievable for distance up to several hundred nanometers. In this work, a linear array of flip‐flop qubits is considered and the unwanted mutual qubit interactions due to the simultaneous application of two one‐qubit and two two‐qubit gates are included in the quantum gate simulations. In particular, by studying the parallel execution of couples of one‐qubit gates, namely and , and of couples of two‐qubit gate, that is, , a safe inter‐qubit distance is found where unwanted qubit interactions are negligible thus leading to parallel gates fidelity up to 99.9%.
Abstract Successfully implementing a quantum algorithm involves maintaining a low logical error rate by ensuring the validity of the quantum fault‐tolerance theorem. The required number of physical qubits arranged in an array depends on the chosen Quantum Error Correction code and the achievable physical qubit error rate. As the qubit count in the array increases, parallel gating —simultaneously manipulating many qubits— becomes a crucial ingredient for successful computation. In this study, small arrays of a type of donor‐ and quantum dot‐based qubits, known as flip‐flop (FF) qubits, are investigated. Simulation results of gate fidelities in linear, square and star arrays of four FF qubits affected by realistic 1/f noise are presented to study the effect of parallel gating. The impact of two, three and four parallel one‐qubit gates, as well as two parallel two‐qubit gates, on fidelity is calculated by comparing different array geometries. The findings can contribute to the optimized manipulation of small FF qubit arrays and the design of larger ones.
Abstract Impurities hosted in semiconducting solid matrices represent an extensively studied platform for quantum computing applications. In this scenario, the so-called flip-flop qubit emerges as a convenient choice for scalable implementations in silicon. Flip-flop qubits are realized implanting phosphorous donor in isotopically purified silicon, and encoding the logical states in the donor nuclear spin and in its bound electron. Electrically modulating the hyperfine interaction by applying a vertical electric field causes an Electron Dipole Spin Resonance (EDSR) transition between the states with antiparallel spins {∣↓⇑⟩,∣↑⇓⟩}\{|\downarrow \Uparrow \rangle ,|\uparrow \Downarrow \rangle \}{∣↓⇑⟩,∣↑⇓⟩} {|↓⇑〉,|↑⇓〉} , that are chosen as the logical states. When two qubits are considered, the dipole-dipole interaction is exploited to establish long-range coupling between them. A universal set of quantum gates for flip-flop qubits is here proposed and the effect of a realistic 1/f noise on the gate fidelity is investigated for the single qubit Rz(−π2)R_{z}(-\frac{\pi }{2})Rz​(−2π​) Rz(−π2) and Hadamard gate and for the two-qubit iSWAP\sqrt{\mathit{iSWAP}}iSWAP​ iSWAP gate.
Silicon-based donor flip-flop qubits offer a promising path toward scalable, fault-tolerant quantum computing by combining the long coherence times of nuclear spins with fast, fully electrical control and long-range dipole-dipole coupling between qubits. However, realizing high-fidelity entangling operations in this platform remains challenging. The entangling interaction is intrinsically coupled to electron orbital dynamics, which can lead to leakage into non-computational states and unwanted phase accumulation. Furthermore, in multi-qubit architectures, residual dipolar couplings from spectator qubits distort the effective interaction landscape. In this work, we employ a numerical simulation framework, FlipFlopQSim, that models the spin-orbital dynamics of interacting flip-flop qubits to extract effective logical operations from realistic electrical control pulses. Using Makhlin invariants, we map the entangling landscape generated by electrically controlled dipole-dipole interactions and identify operating regions locally equivalent to canonical two-qubit gates, such as iSWAP\sqrt{iSWAP}iSWAP​ and iSWAPiSWAPiSWAP. We then optimize the control parameters of physically realizable, electrically driven RzR_zRz​ rotations to implement the necessary local corrections and maximize composite gate fidelity. Finally, we scale our analysis to multi-qubit registers with various geometries and connectivity patterns to evaluate spectator-induced distortions. Our results demonstrate that high-fidelity entangling operations cannot be optimized in isolation; rather, they require a co-design approach that simultaneously optimizes pulse control, local phase compensation, and physical device geometry. This work provides a robust numerical framework for assessing the scalability of electrically controlled silicon quantum processors and outlines key design principles for robust multi-qubit gate implementation.
Flip-flop qubits, encoded in the antiparallel spin states of electron and nuclear spins in phosphorus donors in silicon, are promising for quantum processors due to their long coherence times, long-range two-qubit coupling, and CMOS compatibility. However, the large Hilbert space complicates understanding and controlling the dynamics. In this work, the authors use sophisticated techniques to derive effective flip-flop qubit Hamiltonians and design optimal control pulses that implement high-fidelity single-qubit gates that are much faster and more robust than previous proposals.
ABSTRACT A large‐scale quantum computer promises quantum algorithms with an exponential speed increase over classical counterparts. Ion implanted donor atom qubits in isotopically enriched have demonstrated leading coherence times and gate fidelities. Large‐scale donor architectures must be tolerant to positional uncertainties owing to ion straggling consistent with the implant energy required to place near surface donor atoms allowing manipulation by surface control electrodes. These issues are addressed with a 40 million silicon atom quantum model based on the atomistic tight‐binding technique in the context of the flip‐flop qubit architecture. The donor electron wavefunction operates in a state of equal superposition between the buried host donor atom and below the surface gate oxide. Key issues include: donor positional uncertainty from ion straggling coupled with non‐uniform control gate potentials, the coupling of donor wave functions to gate‐defined quantum wells, and the effect of bystander donors including the mitigation of non‐functional adventitious channeled ions by re‐implantation employing deterministic ion implantation. An upper constraint of 9 keV ions minimizes straggling allowing quantum superposition and is compatible with existing fabrication techniques. With heavy donors, such as , the constraints are relaxed because, for a given implant depth, the heavy donors straggle less than light donors.