arXiv:2310.12656 · Physical review. B./Physical review. B
Impact of measurement backaction on nuclear spin qubits in silicon
Serajum Monir, Edyta N. Osika, Samuel Keith Gorman, Ian Thorvaldson, Yu‐Ling Hsueh, P. Macha, Ludwik Kranz, Jan-Michael Reiner, Michelle Yvonne Simmons, Rajib Rahman
Phosphorus donor nuclear spins in silicon couple weakly to the environment, making them promising candidates for high-fidelity qubits. The state of a donor nuclear spin qubit can be manipulated and read out using its hyperfine interaction with the electron confined by the donor potential. Here we use a master-equation-based approach to investigate how the backaction from this electron-mediated measurement affects the lifetimes of single and multidonor qubits. We analyze this process as a function of electric and magnetic fields and hyperfine interaction strength. Apart from single nuclear spin flips, we identify an additional measurement-related mechanism, the nuclear spin flip-flop, which is specific to multidonor qubits. Although this flip-flop mechanism reduces qubit lifetimes, we show that it can be effectively suppressed by the hyperfine Stark shift. We show that using atomic precision donor placement and engineered Stark shift, we can minimize the measurement backaction in multidonor qubits, achieving larger nuclear spin lifetimes than single donor qubits.
Phosphorus donor nuclear spins in silicon couple weakly to the environment, making them promising candidates for high-fidelity qubits. The state of a donor nuclear spin qubit can be manipulated and read out using its hyperfine interaction with the electron confined by the donor potential. Here we use a master-equation-based approach to investigate how the backaction from this electron-mediated measurement affects the lifetimes of single and multidonor qubits. We analyze this process as a function of electric and magnetic fields and hyperfine interaction strength. Apart from single nuclear spin flips, we identify an additional measurement-related mechanism, the nuclear spin flip-flop, which is specific to multidonor qubits. Although this flip-flop mechanism reduces qubit lifetimes, we show that it can be effectively suppressed by the hyperfine Stark shift. We show that using atomic precision donor placement and engineered Stark shift, we can minimize the measurement backaction in multidonor qubits, achieving larger nuclear spin lifetimes than single donor qubits.
Singlet-triplet qubits typically require large magnetic field gradients on the order of militeslas to achieve high-fidelity electrically-controlled qubit operations. However, such large magnetic field gradients in quantum dot systems also increase charge noise and provide a relaxation pathway from the triplet to singlet qubit state, making high-fidelity readout challenging. Recently, shelving and latched readout have been employed in gate-defined quantum dots and donor-dot systems to achieve readout fidelities of 80% and 99.86%, respectively. In this paper, we theoretically examine shelving and latched singlet-triplet readout techniques for multidonor-based qubits in silicon where the large phosphorus hyperfine interaction of the order of 100 MHz gives rise to large effective magnetic field gradients (equivalent to tens of mT) but where it can change in time due to the presence of nuclear spin flips. Using numerical simulations, we show that shelving readout does not work giving a zero average visibility for mutidonor quantum dots, due to the time-varying nuclear spin polarization. To remedy this we propose adding a calibration step, in which we derive the nuclear spin polarization from a single shelving readout of a singlet state, before every qubit operation. The derived information can then be used via a feed-forward protocol to apply correct readout mapping, greatly improving the overall readout fidelity to >99. We also simulate the latched readout mechanism, which is resistant to nuclear polarization changes and is thus promising for achieving high visibility readout. Here we observe a nonzero readout visibility irrespective of the nuclear spin flipping. Finally, we discuss how to optimize the readout visibility in the presence of strong hyperfine interactions and show that for both readout methods we can obtain readout fidelity >99. These results demonstrate that singlet-triplet qubits based on multidonor quantum dots are a promising route for future electrically controlled qubits in silicon.
Donors in silicon, which combine an electron and nuclear spin, are some of the most promising candidates for quantum information. The electron spin has been proposed as a register with fast manipulation and the nuclear spin as a memory with long coherence times. However, this division reduces the complexity of the donor system, in particular behaviors emerging from their interaction. In natural silicon, there is also the presence of 29Si nuclear spins in the donor environment; though they are generally seen as a source of decoherence, they are quantum systems that can be investigated too. The main subject of this thesis is the study of the interactions between these various spins, using different methods to probe and control them. I first concentrate on the coupling between the donor and the 29Si spins. This coupling can be perturbed by the application of dynamical decoupling on the donor electron spin, whose evolution can be made sensitive to the number of 29Si spins interacting together. I then propose an error correction scheme using the donor and 29Si spins, showing key requirements such as coherence times and methods for manipulation and initialization. Secondly, I focus on the donor itself, in a regime where the hyperfine and Zeeman couplings compete with each other. Here, the spin transitions can have different sensitivities to the magnetic environment, and can even be suppressed to first order, resulting in coherence times up to seconds with electron spin-like manipulation times. Controlling this sensitivity was also used to probe the effect of the donor on the 29Si spin bath evolution. Finally, I use electric fields to modulate the hyperfine coupling within the donor. I first characterize the spins’ sensitivity to the electric field, and then demonstrate electrical switching of the nuclear spin response to an external magnetic excitation.
The spins of atoms and atom-like systems are among the most coherent objects in which to store quantum information. However, the need to address them using oscillating magnetic fields hinders their integration with quantum electronic devices. Here, we circumvent this hurdle by operating a single-atom "flip-flop" qubit in silicon, where quantum information is encoded in the electron-nuclear states of a phosphorus donor. The qubit is controlled using local electric fields at microwave frequencies, produced within a metal-oxide-semiconductor device. The electrical drive is mediated by the modulation of the electron-nuclear hyperfine coupling, a method that can be extended to many other atomic and molecular systems and to the hyperpolarization of nuclear spin ensembles. These results pave the way to the construction of solid-state quantum processors where dense arrays of atoms can be controlled using only local electric fields.
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 Single electron spins bound to multi-phosphorus nuclear spin registers in silicon have demonstrated fast (0.8 ns) two-qubit SWAP SWAP gates and long spin relaxation times (~30 s). In these spin registers, when the donors are ionized, the nuclear spins remain weakly coupled to their environment, allowing exceptionally long coherence times. When the electron is present, the hyperfine interaction allows coupling of the spin and charge degrees of freedom for fast qubit operation and control. Here we demonstrate the use of the hyperfine interaction to enact electric dipole spin resonance to realize high-fidelity ( F=100−6+0 F = 10 0 − 6 + 0 %) initialization of all the nuclear spins within a four-qubit nuclear spin register. By controllably initializing the nuclear spins to ∣⇓⇓⇓⟩ ⇓ ⇓ ⇓ , we achieve single-electron qubit gate fidelities of F = 99.78 ± 0.07% (Clifford gate fidelities of 99.58 ± 0.14%), above the fault-tolerant threshold for the surface code with a coherence time of $${T}_{2}^{\,* }=12\,\upmu {{{\rm{s}}}}$$ T 2 * = 12 μ s .
In the Kane silicon-based electron-mediated nuclear spin quantum computer architecture, phosphorous is doped at precise positions in a silicon lattice, and the P donor nuclear spins act as qubits. Logical operations on the nuclear spins are performed using externally applied magnetic and electric fields. There are two important interactions: the hyperfine and exchange interactions, crucial for logical qubit operations. Single qubit operations are performed by applying radio frequency magnetic fields resonant with targeted nuclear spin transition frequencies, tuned by the gate-controlled hyperfine interaction. Two qubit operations are mediated through the exchange interaction between adjacent donor electrons. It is important to examine how these two interactions vary as functions of experimental parameters. Here we provide such an investigation. First, we examine the effects of varying several experimental parameters: gate voltage, inter donor separation, donor depth below the silicon oxide interface and back gate depth, to explore how these variables affect the donor electro density. Second, we calculate the hyperfine interaction and the exchange coupling as a function of these parameters. These calculations were performed using an anisotropic effective mass Hamiltonian. The electric field potential was obtained using Technology Computer Aided Design software, and the interfaces were modelled as a barrier using a step function. We aim to provide relevant information for the experimental design of these devices and highlight the significance of environmental factors other than gate potential that affect the donor electron.