A surface code quantum computer in silicon

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Science Advances  30 Oct 2015:
Vol. 1, no. 9, e1500707
DOI: 10.1126/sciadv.1500707
  • Fig. 1 Physical layout of the donor-based surface code quantum computer.

    (A) The system comprises three layers. The 2D donor qubit array resides in the middle layer. A mutually perpendicular (crisscross) pattern of control gates (initially chosen to be 5 nm in width and 30 nm in pitch) in the upper and lower planes form a regular grid of (3D) cells. In the upper plane, the control lines alternate as source (S) and gate A (GA), and in the bottom plane, the control gates alternate as drain (D) and gate B (GB). (B) In the middle plane directly below each intersection of S and D lines is a STM fabricated Si:P monolayer quantum dot, which forms the island of a vertically defined SET facilitating electron loading/unloading and readout. (C) A single P donor is located at the center of each cell defined by the boundaries of GA, GB, S, and D lines. In the noninteracting memory state, the qubit states are encoded on the long-lived zero-leakage/zero-loss spin states of the spin-½ P nucleus (31P+). A specific qubit is activated/deactivated by applying voltages to the proximal gates (S, D, GA, GB, GA′, and GB′) to create the local bias condition to load/unload an electron onto the donor or to place the system into the readout configuration (see the Supplementary Materials and fig. S1). By virtue of the shared-control lines, this process can be carried out in parallel at multiple locations. Activation switches on the hyperfine interaction on single donors, and spin-spin interactions for neighboring activated donors, allowing single- and two-qubit gates to be carried out via global ESR and/or NMR control. Nonactivated qubits are detuned from these control fields and remain unaffected. The computer operates at millikelvin temperatures in a background static field of ~2 T.

  • Fig. 2 Schematic of single-qubit states, activation, and initialization/readout.

    (A) Single donor qubit cell and SET island (side view), addressed by the intersection of source/drain gates and proximal gates. In the memory state, the donor is ionized (P+) and the energy splitting between the computational states is ΔEmem = 2gnμnBz (designated RF0). (B) The qubit is activated by loading a spin-down electron, where RF NMR (RF1 and RF2) and MW ESR (MW1 and MW2) transitions allow global nuclear/electron spin control, leaving unactivated qubits unaffected. (C) Top view showing the control lines biased to activate a qubit (deactivation occurs in reverse). Shared control allows qubits to be activated at multiple locations. (D) Readout is performed by swapping the nuclear state to the electron spin and placing the SET-donor system in the spin-dependent tunneling position (5). Readout signals from S/D lines are time-correlated to pinpoint the qubit cell and, by generalization, allow readout across multiple qubit cells. (E) Phase-matched (PM) loading/unloading incorporated into quantum operations. For load/unload configurations, voltages on gates (S, D, GA, GB, GA′, and GB′) are pulsed to only allow SET-donor tunneling during intervals t, which are phase-locked to the hyperfine frequency 1/tA = 2A/h, preventing stochastic phase accumulation on the nuclear spin when the electron loads/unloads (see the Supplementary Materials).

  • Fig. 3 Overview of the two-qubit CNOT gate.

    (A) Circuit-process diagram for a CNOT between target/control nuclear spin qubits (n1/n2), mediated by the spin-spin interaction between loaded electrons (e1/e2). (B) The target qubit is activated using the gates (S, D, GA, GB, GA′, and GB′). (C) A global ESR X gate flips the loaded electron spin to the up state, thereby distinguishing the target qubit resonant frequency from the control qubit when activated. (D) A Hadamard gate, H, is applied to the data on the target qubit nuclear spin. During the subsequent control qubit load process (E), a global decoupling pulse is applied, in phase with the PM loading cycle, to switch off the (nonqubit) electron-electron interaction until required. The electron and nuclear spin states are swapped (F), marking the beginning of the two-qubit interaction mediated by the (qubit-encoded) electron-electron interaction (G). With exactly opposite nuclear spins, the interaction is an Ising ZZ coupling executing a control-Z (CZ) gate. The X gates extend electron spin coherence during this interaction phase. At the completion of the CZ gate, the qubit data are swapped back to the nuclear spins, and the second Hadamard gate on the target qubit converts the CZ gate to a CNOT. (H) The electrons are unloaded to deactivate the control and target qubits. Memory (spectator) donors are unaffected by these operations.

  • Fig. 4 Surface code operations on the 2D array.

    (A) A small section of the surface code, highlighting Z and X stabilizer measurements for QEC. (B) Circuit/process diagram for the measurement of the Z stabilizer on an ancilla qubit with respect to its data qubit neighbors. Electron spins are shown as dotted lines; nuclear spins are shown as solid lines. (C to G) The voltage control lines (S, green; D, blue; GA/GB, gray; GA′/GB′, light gray) required for the loading and unloading of the electrons. (C) shows the loading configuration for syndrome ancilla qubits across one-quarter of the lattice, whereas (D) to (G) show the loading configurations to implement the CNOT sequence to neighboring data qubits [north (D), west (E), east (F), and south (G)] required in the surface code stabilizer measurements. By moving to the other ancilla sublattices and repeating, the syndrome measurement across the entire lattice is achieved in four steps.

  • Fig. 5 Simulations of PM qubit activation and the CNOT gate.

    (A) Total PM loading error with respect to the surface code threshold, including residual qubit dephasing, as a function of PM pulse window, t, and overall pulse train length, TPM, for a range of SET-donor tunneling rates τ = 100, 500, and 1000 ns. (B) CNOT gate error and total operation time (including PM loading and unloading operations) for PM pulse window widths Δt = 0.2, 0.4, 0.6, and 0.8 ns [fixed parameters: τ = 500 ns, 30 nm qubit spacing, and T2(e) = 2 s (42)].

Supplementary Materials

  • Supplementary material for this article is available at

    Experimental considerations: 3D electrostatic simulations

    PM qubit activation/deactivation

    Fig. S1. 3D electrostatic simulations of gate control for qubit addressing.

    Fig. S2. Implementation of the PM activation/deactivation sequence.

    References (62, 63)

  • Supplementary Materials

    This PDF file includes:

    • Experimental considerations: 3D electrostatic simulations PM qubit activation/deactivation
    • Fig. S1. 3D electrostatic simulations of gate control for qubit addressing.
    • Fig. S2. Implementation of the PM activation/deactivation sequence.
    • References (62, 63)

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