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arXiv:2607.15993

Qubit encodings in the p-orbital-valley spectrum for enhanced coherence and tunable two-qubit interaction

John H. Caporaletti, J. P. Kestner

Published Jul 17, 2026• 0 citations
arXivHTMLPDF

Abstract

We propose encoding a qubit in a two-level subspace spanned by the lowest $p$-orbital state in the excited valley of an anisotropic quantum dot and the excited $p$-orbital in the ground valley, which we dub the $pOv$ qubit. There is an avoided crossing between these states due to valley-orbit coupling (VOC) induced by alloy disorder, enabling complete single-qubit control using baseband electrical control of the dot anisotropy. We find that `sweet spots' exist at specific dot orientations where the instantaneous eigenstates are first-order insensitive to charge noise. Using a phenomenological two-level fluctuator (TLF) dipole noise model, we estimate an average dephasing time of $T_2^*\approx 10\,μ\text{s}$ and a quality factor of $Q\sim 10^4$. Alternatively, encoding in the $p$-orbital states in the ground valley near the isotropic dot point, we show that one can induce a similar sweet spot via an out-of-plane magnetic field. Finally, we find that two-qubit gates for the $pOv$ qubit are mediated by the quadrupole-quadrupole Coulomb interaction and can be electrically tuned from zero to $\sim 1~\text{GHz}$ by adjusting the relative orientation of the anisotropic dots, providing a novel pathway towards scalable quantum computation.

DOI
10.13016/m2etbs-fx1k

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Simulation code for "Qubit encodings in the p-orbital-valley spectrum for enhanced coherence and tunable two-qubit interaction"

John H. Caporaletti

Python notebooks reproducing the numerical results and figures of the manuscript "Qubit encodings in the p-orbital-valley spectrum for enhanced coherence and tunable two-qubit interaction" by John H. Caporaletti and J. P. Kestner (University of Maryland Baltimore County). The manuscript proposes the pOv qubit, an encoding in the two-level subspace spanned by the lowest p-orbital state in the excited valley and the excited p-orbital in the ground valley of an anisotropic silicon quantum dot, coupled by disorder-induced valley-orbit coupling (VOC). This archive contains three self-contained notebooks: VOC_std_calc.ipynb — evaluates the VOC statistics of Appendix VI A using the discretized effective-mass theory of alloy disorder: the vertical envelope function is obtained from a finite-difference solve of the heterostructure confinement potential, and the standard deviations of the disorder-induced generator coefficients, together with the mean valley splitting and mean VOC magnitude, follow from the lattice sum over independent cells. The correlation matrix of the VOC generators is also reported. fig6_Qeff_hist.ipynb — reproduces Fig. 6. For each of $10^4$ alloy-disorder realizations it finds the pair of dot orientations that switches off the two-qubit coupling Omega_zz while maximizing the effective two-qubit quality factor Q_eff, and histograms the result. fig7_inf_scatter_plot.ipynb — reproduces Fig. 7. It synthesizes the R_ZZ($\pi$/2) entangling gate for each disorder realization and evaluates its infidelity against a Monte-Carlo ensemble of quasistatic two-level-fluctuator dipole configurations, comparing a single-segment analytic pulse with a three-segment composite pulse obtained from a two-stage optimization (L-BFGS-B on the deterministic infidelity with analytic gradients, then SLSQP minimizing total gate time subject to a deterministic-infidelity budget). All notebooks use the device parameters of Table I, run top to bottom with no input files, and require only NumPy, SciPy, and Matplotlib (developed under Python 3.12). All random draws are seeded, so the published figures reproduce exactly.

•Jul 16, 2026•1 citation

A Degenerate Singlet-Triplet Qubit with All-Electrical Orthogonal Control

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Proposed Five-Electron Charge Quadrupole Qubit

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The use of noise-robust qubit encodings provides a way of extending the lifetime of quantum information at the hardware level. In this work, we introduce the spin Kerr-cat encoding, which leverages a sweet spot near a clock transition in the spectrum of quadrupolar nuclei (having spin $I\geq 1$) to achieve a suppression of charge and magnetic noise leading to qubit dephasing. The basis states of the spin Kerr-cat qubit are given by the two lowest levels of a $\mathbb{Z}_2$-symmetric nuclear-spin Hamiltonian and are well approximated by spin cat states for sufficiently high asymmetry parameters. For nuclei in highly asymmetric electric-field gradients, the nuclear spin could therefore be initialized in the spin-Kerr-cat subspace using SU(2) rotations and measurement rather than full SU($2I+1$) control. We calculate the dephasing time of the spin Kerr-cat qubit under a model of $1/f$ noise, as well as relaxation of the qubit due to breaking of the $\mathbb{Z}_2$ symmetry by charge-noise-induced fluctuations of the quadrupolar tensor. Using measured parameters for antimony (${}^{123}\mathrm{Sb}$) donors in silicon, we estimate that second-scale $T_2^*$ times could be achieved with this encoding, with bitflips and leakage occurring on significantly longer timescales. We propose a two-qubit gate acting on spin Kerr-cat qubits and electron-spin qubits, enabled by adiabatically moving an electron on and off the donor potential. Based on numerical simulations, we estimate that with an enhancement of measured quadrupolar couplings by a factor of ${\approx} 2$, a gate fidelity exceeding $99\%$ could be achieved for spin Kerr cats encoded in ${}^{123}\mathrm{Sb}$, with a gate time under $100$ ns. By entangling the nuclear spin with an electron spin in this way, the spin Kerr-cat qubit could then be measured using a Pauli spin blockade readout of the electron.

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Two-axis quantum control of a fast valley qubit in silicon

Nicholas E. Penthorn, Joshua S. Schoenfield, John Rooney +2 more

Abstract Quantum dots in silicon are a promising architecture for semiconductor quantum computing due to a high degree of electric control and compatibility with existing silicon fabrication processes. Although electron charge and spin are prominent methods for encoding the qubit state, valley states in silicon can also store quantum information via valley-orbit coupling with protection against charge noise. By observing coherent oscillations between valley states in a Si/SiGe double quantum dot device tuned to the two-electron charge configuration, we measure the valley energy splitting in both quantum dots individually. We further demonstrate two-axis quantum control of the valley qubit using gated pulse sequences with X and Z rotations occurring within a fast operation time of 300 ps. This control is used to completely map out the surface of the Bloch sphere in a single phase-space plot that is subsequently used for state and process tomography.

npj Quantum Information•Nov 6, 2019•36 citations
We propose encoding a qubit in a two-level subspace spanned by the lowest ppp-orbital state in the excited valley of an anisotropic quantum dot and the excited ppp-orbital in the ground valley, which we dub the pOvpOvpOv qubit. There is an avoided crossing between these states due to valley-orbit coupling (VOC) induced by alloy disorder, enabling complete single-qubit control using baseband electrical control of the dot anisotropy. We find that `sweet spots' exist at specific dot orientations where the instantaneous eigenstates are first-order insensitive to charge noise. Using a phenomenological two-level fluctuator (TLF) dipole noise model, we estimate an average dephasing time of T2∗≈10 μsT_2^*\approx 10\,μ\text{s}T2∗​≈10μs and a quality factor of Q∼104Q\sim 10^4Q∼104. Alternatively, encoding in the ppp-orbital states in the ground valley near the isotropic dot point, we show that one can induce a similar sweet spot via an out-of-plane magnetic field. Finally, we find that two-qubit gates for the pOvpOvpOv qubit are mediated by the quadrupole-quadrupole Coulomb interaction and can be electrically tuned from zero to ∼1 GHz\sim 1~\text{GHz}∼1 GHz by adjusting the relative orientation of the anisotropic dots, providing a novel pathway towards scalable quantum computation.
Python notebooks reproducing the numerical results and figures of the manuscript "Qubit encodings in the p-orbital-valley spectrum for enhanced coherence and tunable two-qubit interaction" by John H. Caporaletti and J. P. Kestner (University of Maryland Baltimore County). The manuscript proposes the pOv qubit, an encoding in the two-level subspace spanned by the lowest p-orbital state in the excited valley and the excited p-orbital in the ground valley of an anisotropic silicon quantum dot, coupled by disorder-induced valley-orbit coupling (VOC). This archive contains three self-contained notebooks: VOC_std_calc.ipynb — evaluates the VOC statistics of Appendix VI A using the discretized effective-mass theory of alloy disorder: the vertical envelope function is obtained from a finite-difference solve of the heterostructure confinement potential, and the standard deviations of the disorder-induced generator coefficients, together with the mean valley splitting and mean VOC magnitude, follow from the lattice sum over independent cells. The correlation matrix of the VOC generators is also reported. fig6_Qeff_hist.ipynb — reproduces Fig. 6. For each of 10410^4104 alloy-disorder realizations it finds the pair of dot orientations that switches off the two-qubit coupling Omega_zz while maximizing the effective two-qubit quality factor Q_eff, and histograms the result. fig7_inf_scatter_plot.ipynb — reproduces Fig. 7. It synthesizes the R_ZZ(π\piπ/2) entangling gate for each disorder realization and evaluates its infidelity against a Monte-Carlo ensemble of quasistatic two-level-fluctuator dipole configurations, comparing a single-segment analytic pulse with a three-segment composite pulse obtained from a two-stage optimization (L-BFGS-B on the deterministic infidelity with analytic gradients, then SLSQP minimizing total gate time subject to a deterministic-infidelity budget). All notebooks use the device parameters of Table I, run top to bottom with no input files, and require only NumPy, SciPy, and Matplotlib (developed under Python 3.12). All random draws are seeded, so the published figures reproduce exactly.
Singlet-triplet qubits offer an attractive encoding for semiconductor quantum computing, combining ancilla-free readout, reduced sensitivity to common-mode noise, and baseband voltage control. However, the Zeeman energy difference ΔEZΔE_\mathrm{Z}ΔEZ​ is typically fixed by local magnetic field gradients or ggg-factor inhomogeneities, leaving the exchange interaction JJJ as the only dynamically tunable parameter. This always-on ΔEZΔE_\mathrm{Z}ΔEZ​ precludes orthogonal control of the qubit's rotation axes and introduces unwanted state rotations during idling. Here we demonstrate all-electrical orthogonal control of a degenerate singlet-triplet (DST) qubit formed by two hole spins in a germanium double quantum dot. Exploiting the electrically tunable anisotropic ggg-factors of the two spins, we identify a regime where both ΔEZΔE_\mathrm{Z}ΔEZ​ and JJJ vanish, making the SSS and T0T_0T0​ states degenerate at the idle point. By applying only baseband voltage pulses, we independently control both JJJ and ΔEZΔE_\mathrm{Z}ΔEZ​, enabling fully orthogonal ZZZ- and XXX-axis rotations. Randomized benchmarking yields an average physical single-qubit gate fidelity of 99.53\% for a gate duration of approximately 100 ns. Finally, we electrically tune the degenerate point across a wide range of magnetic field orientations, enabling operation in a regime of enhanced coherence time and offering a route towards multi-qubit scaling under a shared global magnetic field.
A charge qubit couples to environmental electric field fluctuations through its dipole moment, resulting in fast decoherence. We propose the p-orbital (pO) qubit, formed by the single-electron, p-like valence states of a five-electron Si quantum dot, which couples to charge noise through the quadrupole moment. We demonstrate that the pO qubit offers distinct advantages in quality factor, gate speed, readout, and size. We use a phenomenological, dipole two-level-fluctuator charge noise model to estimate a T_{2}^{*}∼80 ns. In conjunction with Rabi frequencies of order 10 GHz, an order of magnitude improvement in qubit quality factor is expected relative to state-of-the-art semiconductor spin qubits. The pO qubit features all-electrical control via modulating the dot's eccentricity. We also show how to perform two-qubit gates via the 1/r^{5} quadrupole-quadrupole interaction. We find a universal gate set using gradient ascent-based control pulse optimization, subject to 10 GHz maximum allowable bandwidth and 1 ns pulse times.
We investigate the behavior of qubits consisting of three electron spins in double and triple quantum dots subject to external electric fields. Our model includes two independent bias parameters, $\ensuremath{\varepsilon}$ and ${\ensuremath{\varepsilon}}_{M}$, which both couple to external electromagnetic fields and can be controlled by gate voltages applied to the quantum dot structures. By varying these parameters, one can switch the qubit type by shifting the energies in the single quantum dots, thus changing the electron occupancy in each dot. Starting from the asymmetric resonant exchange qubit with a (2,0,1) and (1,0,2) charge admixture, one can smoothly cross over to the resonant exchange qubit with a detuned (1,1,1) charge configuration, and to the exchange-only qubit with the same charge configuration but equal energy levels down to the hybrid qubits with (1,2,0) and (0,2,1) charge configurations. Here, (l,m,n)(l,m,n)(l,m,n) describes a configuration with lll electrons in the left dot, mmm electrons in the center dot, and nnn electrons in the right dot. We first focus on random electromagnetic field fluctuations, i.e., ``charge noise,'' at each quantum dot resulting in dephasing of the qubit, and we provide a complete map of the resulting dephasing time as a function of the bias parameters. We pay special attention to the so-called sweet spots and double sweet spots of the system, which are least susceptible to noise. In the second part, we investigate the coupling of the qubit system to the coherent quantized electromagnetic field in a superconducting strip-line cavity, and we also provide a complete map of the coupling strength as a function of the bias parameters. We analyze the asymmetric qubit-cavity coupling via $\ensuremath{\varepsilon}$ and the symmetric coupling via ${\ensuremath{\varepsilon}}_{M}$.
The use of noise-robust qubit encodings provides a way of extending the lifetime of quantum information at the hardware level. In this work, we introduce the spin Kerr-cat encoding, which leverages a sweet spot near a clock transition in the spectrum of quadrupolar nuclei (having spin I≥1I\geq 1I≥1) to achieve a suppression of charge and magnetic noise leading to qubit dephasing. The basis states of the spin Kerr-cat qubit are given by the two lowest levels of a Z2\mathbb{Z}_2Z2​-symmetric nuclear-spin Hamiltonian and are well approximated by spin cat states for sufficiently high asymmetry parameters. For nuclei in highly asymmetric electric-field gradients, the nuclear spin could therefore be initialized in the spin-Kerr-cat subspace using SU(2) rotations and measurement rather than full SU(2I+12I+12I+1) control. We calculate the dephasing time of the spin Kerr-cat qubit under a model of 1/f1/f1/f noise, as well as relaxation of the qubit due to breaking of the Z2\mathbb{Z}_2Z2​ symmetry by charge-noise-induced fluctuations of the quadrupolar tensor. Using measured parameters for antimony (123Sb{}^{123}\mathrm{Sb}123Sb) donors in silicon, we estimate that second-scale T2∗T_2^*T2∗​ times could be achieved with this encoding, with bitflips and leakage occurring on significantly longer timescales. We propose a two-qubit gate acting on spin Kerr-cat qubits and electron-spin qubits, enabled by adiabatically moving an electron on and off the donor potential. Based on numerical simulations, we estimate that with an enhancement of measured quadrupolar couplings by a factor of ≈2{\approx} 2≈2, a gate fidelity exceeding 99%99\%99% could be achieved for spin Kerr cats encoded in 123Sb{}^{123}\mathrm{Sb}123Sb, with a gate time under 100100100 ns. By entangling the nuclear spin with an electron spin in this way, the spin Kerr-cat qubit could then be measured using a Pauli spin blockade readout of the electron.
Abstract Quantum dots in silicon are a promising architecture for semiconductor quantum computing due to a high degree of electric control and compatibility with existing silicon fabrication processes. Although electron charge and spin are prominent methods for encoding the qubit state, valley states in silicon can also store quantum information via valley-orbit coupling with protection against charge noise. By observing coherent oscillations between valley states in a Si/SiGe double quantum dot device tuned to the two-electron charge configuration, we measure the valley energy splitting in both quantum dots individually. We further demonstrate two-axis quantum control of the valley qubit using gated pulse sequences with X and Z rotations occurring within a fast operation time of 300 ps. This control is used to completely map out the surface of the Bloch sphere in a single phase-space plot that is subsequently used for state and process tomography.