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arXiv:2604.15419

Singlet-only always-on gapless exchange (SAGE) spin qubits: Charge noise effects and two-qubit gates

Nathan L. Foulk, Katharina Laubscher, Silas Hoffman, Sankar Das Sarma

cond-mat.mes-hallquant-phSubmitted Apr 16, 2026• Announced Apr 17, 2026• 0 citations
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Abstract

Singlet-only always-on gapless exchange (SAGE) spin qubits are an alternative type of exchange-only (EO) qubits that encode a single qubit in the spins of four electrons located in four tunnel-coupled quantum dots. While conventional EO qubits are susceptible to local magnetic field gradients caused by local nuclear environments and $g$-factor variations, the SAGE qubit subspace is inherently protected from magnetic-gradient-induced Pauli errors by virtue of the singlet-only encoding, which is invariant under magnetic field gradients, and the always-on exchange couplings, which provide energetic leakage protection. However, the always-on operation simultaneously increases the qubit's sensitivity to charge noise. Here, starting from a Hubbard model describing the underlying electronic structure of the coupled quantum dots, we characterize the performance of SAGE qubits in the presence of $1/f$ charge noise that induces fluctuations in both the dot chemical potentials and the interdot tunnel couplings. We calculate SAGE idle coherence times and show that realistic CPMG-like pulse sequences can be used to significantly extend SAGE single-qubit coherence times for experimentally relevant charge noise strengths. We likewise study the fidelity of SAGE two-qubit gates in the presence of charge and magnetic noise and again propose a simple refocusing strategy to mitigate the noise, while increased ramp times of the entangling pulse suppress leakage into noncomputational states.

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We propose a singlet-only always-on gapless exchange (SAGE) spin qubit that encodes a single qubit in the spins of four electrons while allowing universal baseband control. While conventional exchange-only qubits suffer from magnetic-field-gradient-induced leakage and coherent errors due to local nuclear environments and variations in the g-factor, the SAGE qubit subspace is protected from coherent errors due to local magnetic field gradients, and leakage out of the computational subspace is energetically suppressed due to the exchange interactions between electrons being always on. Consequently, we find that when magnetic gradient noise dominates over charge noise, coherence times and single-qubit gate infidelities of the SAGE qubit improve by an order of magnitude compared to conventional exchange-only qubits. Moreover, using realistic parameters, two-qubit gates can be performed with a single interqubit exchange pulse with times comparable in duration to conventional exchange-only qubits but with a significantly simplified pulse sequence.

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A two-level quantum system is the building block of a quantum computer. This pair of quantum states defines the computational unit of a quantum computer, and it is called a quantum bit or qubit in analogy to the bit that is the binary unit of a classical computer. The spin of a single electron naturally defines such a two-level quantum system. A quantum dot can be tuned to the single-electron regime, and an array of singly occupied quantum dots provides a multi-qubit register. This thesis describes the multielectron encoding of a spin qubit using a pair or a trio of quantum dots, and it analyzes the coherence properties and manipulation protocols of this system. The singlet-triplet qubit, coded using the singlet state and the spinless triplet state of a pair of singly occupied quantum dots, can be controlled all electrically when applying voltages to gates close to the quantum dot structure. Rapid, subnanosecond modifications of the double quantum dot's charge configuration have been realized successfully. A small magnetic field gradient across the double quantum dot enables universal qubit control. Two modifications of the normal singlet-triplet encoding are introduced. (1) The six-electron configuration of a double quantum dot encodes a singlet-triplet qubit in the same way as for the two-electron double quantum dot. Two electrons at each quantum dot are irrelevant for the qubit manipulations because they are paired in a singlet state; the remaining two electrons encode the qubit. The qubit's wave function is immune to charge noise at moderate out-of-plane magnetic fields. (2) A singlet-triplet qubit encoded using two quantum dots of different sizes has an orbital state degeneracy of the singlet state and the spinless triplet state at finite out-of-plane magnetic fields. Spin-orbit interactions lift this state degeneracy, while the magnitude of the state coupling is determined by the size difference of the QDs. This setup enables the manipulations of singlet-triplet qubits without the need for magnetic field gradients. Finally, two-qubit gates between singlet-triplet qubits are proposed that use mediated exchange interactions via one quantum state. These operations are well controlled and highly noise insensitive. Orbital interactions alone can control spin qubits coded in a three electron Hilbert space. For example, the exchange-only qubit is encoded using three singly occupied quantum dots. The exchange interactions of two quantum dot pairs need to be modified to manipulate this qubit. The noise sensitivity of the exchange-only qubit is discussed. Alternatively, a three-electron qubit at a double quantum dot can be operated when single electrons are transferred between the quantum dots. Fast, subnanosecond manipulations of the double quantum dot's charge configuration are required to realize single-qubit gates. A novel two-qubit pulse gate for the three-electron double quantum dot qubit is proposed.

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Singlet-only always-on gapless exchange (SAGE) spin qubits are an alternative type of exchange-only (EO) qubits that encode a single qubit in the spins of four electrons located in four tunnel-coupled quantum dots. While conventional EO qubits are susceptible to local magnetic field gradients caused by local nuclear environments and ggg-factor variations, the SAGE qubit subspace is inherently protected from magnetic-gradient-induced Pauli errors by virtue of the singlet-only encoding, which is invariant under magnetic field gradients, and the always-on exchange couplings, which provide energetic leakage protection. However, the always-on operation simultaneously increases the qubit's sensitivity to charge noise. Here, starting from a Hubbard model describing the underlying electronic structure of the coupled quantum dots, we characterize the performance of SAGE qubits in the presence of 1/f1/f1/f charge noise that induces fluctuations in both the dot chemical potentials and the interdot tunnel couplings. We calculate SAGE idle coherence times and show that realistic CPMG-like pulse sequences can be used to significantly extend SAGE single-qubit coherence times for experimentally relevant charge noise strengths. We likewise study the fidelity of SAGE two-qubit gates in the presence of charge and magnetic noise and again propose a simple refocusing strategy to mitigate the noise, while increased ramp times of the entangling pulse suppress leakage into noncomputational states.
We propose a singlet-only always-on gapless exchange (SAGE) spin qubit that encodes a single qubit in the spins of four electrons while allowing universal baseband control. While conventional exchange-only qubits suffer from magnetic-field-gradient-induced leakage and coherent errors due to local nuclear environments and variations in the g-factor, the SAGE qubit subspace is protected from coherent errors due to local magnetic field gradients, and leakage out of the computational subspace is energetically suppressed due to the exchange interactions between electrons being always on. Consequently, we find that when magnetic gradient noise dominates over charge noise, coherence times and single-qubit gate infidelities of the SAGE qubit improve by an order of magnitude compared to conventional exchange-only qubits. Moreover, using realistic parameters, two-qubit gates can be performed with a single interqubit exchange pulse with times comparable in duration to conventional exchange-only qubits but with a significantly simplified pulse sequence.
We analyze a simple exchange-based two-qubit gate for singlet-triplet qubits in gate-defined semiconductor quantum dots that can be implemented in a single exchange pulse. Excitations from the logical subspace are suppressed by a magnetic field gradient that causes spin-flip transitions to be non-energy-conserving. We show that the use of adiabatic pulses greatly reduces leakage processes comapred to square pulses. We also characterize the effect of charge noise on the entanglement fidelity of the gate both analytically and in simulations; demonstrating high entanglement fidelities for physically realistic experimental parameters. Specifically we find that it is possible to achieve fidelities and gate times that are comparable to single-qubit states using realistic magnetic field gradients.
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.
A key ingredient for fault-tolerant quantum computers are sufficiently accurate logic gates on single and multiple qubits in the presence of decohering noise. In this thesis, we theoretically develop and experimentally demonstrate such high-fidelity quantum gates for semiconductor-based quantum computing. Specifically, we consider a qubit encoded in the singlet and one triplet state of two electron spins in GaAs. While its potential for optical coupling makes GaAs an attractive material, highly auto-correlated magnetic field noise from fluctuating nuclear spins leads to considerably lower coherence times than for Si-based devices, where nuclear spins can be removed by isotopic purification. In addition to noise, the control methods used in earlier experiments are based on unrealistic approximations. For these reasons, fidelities well above 99 %, as required by current quantum error correction (QEC) schemes, have not been obtained before this thesis. To tackle these issues, we extend the filter function formalism to describe quantum gates and processes in the presence of experimentally relevant non-Markovian noise. Since this formalism can consider all relevant noise sources in a computationally efficient manner, it can be used to find optimal control pulses by numerical optimization, leading to predicted single-qubit gate fidelities of 99.9 %. Furthermore, we deal with the considerable control challenges associated with this qubit type by experimental calibration of the optimized control pulses. To this end, we extend our previous experimental gate set calibration (GSC) routine to remove systematic gate errors on an arbitrary number of qubits. We apply the numerically optimized single-qubit control pulses to our GaAs sample and experimentally calibrate them with GSC. This procedure yields an average gate fidelity of 99.50 ± 0.04 % and a low leakage rate of 0.13 ± 0.03 % out of the computational subspace, characterized by randomized benchmarking. We also optimize realistic two-qubit control pulses, considering current control hardware as well as interqubit Coulomb and exchange coupling that cannot be fully turned off. Using measured noise spectra, we show that two-qubit gate fidelities of 99.90 % can be reached in GaAs, while 99.99 % can be achieved in Si. These results demonstrate that high-fidelity gates can be realized even in the presence of nuclear spins as in GaAs.
Quantum information processing in semiconductor quantum dots using single and multi-spin qubitsThe idea of a quantum computer, a device capable of processing information using quantum bits (qubit) instead of classical bits that outperforms classical computer in terms of computation speed, is still science ction. However, recent advances in quantum information processing showed that this ction may come true faster than anticipated. A promising platform for the physical realization of a qubit are spin qubits where the information is encoded in the quantum mechanical spin of an electron con ned in a semiconductor quantum dot. There are a variety of di erent implementations how the logical qubit is physically encoded, the use of a single electron spin or the use of the spins of multi electrons. This thesis focuses on the implementation of the spin- 1/2 qubit using the spin of a single electron in a single quantum dot, the exchangeonly (EO) qubit using three electron spins distributed in three quantum dots, and the novel quadrupolar exchange-only (QUEX) qubit using four electron spins distributed in three quantum dots. In this thesis we investigate several theoretical aspects of the physical implementation of the aforementioned qubit encodings. Since all three qubit encodings are allelectric controlled these implementations su er decoherence, the loss of information, from electric uctuations of the environment commonly called charge noise. Typically, the use of more quantum dots increases the decoherence due to charge noise while it decreases the decoherence due to magnetic noise. The rst main aspect investigated in this thesis is the protection of the quantum information encoded in the di erent qubit implementations against charge noise. Special attention is paid to the multi-electron spin implementations where high-symmetry points of operation are discovered which are less sensitive to the charge noise. Protection against charge noise is even better by increasing the number of electrons while keeping the number of quantum dots making the QUEX qubit superior to the EO qubit. So far the main direction in this thesis is the reduction of the qubit sensitivity to electric uctuations. However, coherent electromagnetic elds in form of microwaves v can be used to interconnect qubits. In this thesis also a high-performance coupling between two spin-1/2 is investigated. The use of a resonator, subsequently, allows for a coupling of qubits over macroscopic distances as well as to extract valuable information about the physical system. Because of the larger susceptibility of multi-spin qubits to the electric eld of the resonator, this thesis focuses on the coupling between an EO or a QUEX qubit and a microwave resonator. Points of operations are discovered for both qubit implementations which o er a strong coupling towards a microwave resonator while maintaining their protection against charge noise. Subsequently, a series of measurements are proposed to extract information about the microscopic structure of the quantum dots. Finally, a promising high-performance protocol for coupling two qubits remotely via the resonator is investigated in detail.
A two-level quantum system is the building block of a quantum computer. This pair of quantum states defines the computational unit of a quantum computer, and it is called a quantum bit or qubit in analogy to the bit that is the binary unit of a classical computer. The spin of a single electron naturally defines such a two-level quantum system. A quantum dot can be tuned to the single-electron regime, and an array of singly occupied quantum dots provides a multi-qubit register. This thesis describes the multielectron encoding of a spin qubit using a pair or a trio of quantum dots, and it analyzes the coherence properties and manipulation protocols of this system. The singlet-triplet qubit, coded using the singlet state and the spinless triplet state of a pair of singly occupied quantum dots, can be controlled all electrically when applying voltages to gates close to the quantum dot structure. Rapid, subnanosecond modifications of the double quantum dot's charge configuration have been realized successfully. A small magnetic field gradient across the double quantum dot enables universal qubit control. Two modifications of the normal singlet-triplet encoding are introduced. (1) The six-electron configuration of a double quantum dot encodes a singlet-triplet qubit in the same way as for the two-electron double quantum dot. Two electrons at each quantum dot are irrelevant for the qubit manipulations because they are paired in a singlet state; the remaining two electrons encode the qubit. The qubit's wave function is immune to charge noise at moderate out-of-plane magnetic fields. (2) A singlet-triplet qubit encoded using two quantum dots of different sizes has an orbital state degeneracy of the singlet state and the spinless triplet state at finite out-of-plane magnetic fields. Spin-orbit interactions lift this state degeneracy, while the magnitude of the state coupling is determined by the size difference of the QDs. This setup enables the manipulations of singlet-triplet qubits without the need for magnetic field gradients. Finally, two-qubit gates between singlet-triplet qubits are proposed that use mediated exchange interactions via one quantum state. These operations are well controlled and highly noise insensitive. Orbital interactions alone can control spin qubits coded in a three electron Hilbert space. For example, the exchange-only qubit is encoded using three singly occupied quantum dots. The exchange interactions of two quantum dot pairs need to be modified to manipulate this qubit. The noise sensitivity of the exchange-only qubit is discussed. Alternatively, a three-electron qubit at a double quantum dot can be operated when single electrons are transferred between the quantum dots. Fast, subnanosecond manipulations of the double quantum dot's charge configuration are required to realize single-qubit gates. A novel two-qubit pulse gate for the three-electron double quantum dot qubit is proposed.