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Here, we focus on the quantum-classical interface requirements and possible solutions for qubits encoded in electron spins in semiconductor quantum dots and donors.9, 10 We thereby consider specifically quantum dots that are probed and controlled using electrical signals, referring to ref. 1 for a discussion of optically addressed quantum dots. Electrically controlled quantum dots and donors are two promising qubit realizations that have much in common both conceptually and in terms of qubit specifications and hardware requirements. There is significant scope to make these realizations compatible with industrial CMOS technology, which is optimized for high-yield, reproducibility and cleanliness. Indeed, there is a lot of effort in this direction and qubits that are partly fabricated with industrial technology have already been realized.41
We first briefly introduce electron spin qubits in electrically detected quantum dots and donors as a starting point for discussing the control and interfacing requirements (for more extensive reviews, see refs 9, 10).
Schematic diagram of typical electrically measured spin qubit devices. Red (blue) spins and energy levels refer to electron (nuclear) spins. a A double quantum dot device defined in a Si/SiGe quantum well. Quantum dots can be defined either in accumulation mode with a global top gate as depicted in panel c, or in depletion mode using a doping layer. b Donor qubit system in depletion mode and fabricated by silicon metal-oxide-semiconductor technology (material stack in e). The spin states of a single electron are split in a magnetic field and qubit operation is obtained via an ac magnetic field that matches the associated resonance frequency ν e as represented in d for dots and f for donors. An ac magnetic field can be realized directly by sending an ac current through a strip-line b. Alternatively, the motion of a quantum dot due to an ac electric field created by driving a nearby gate results in an effective magnetic field due to the field gradient of a nearby nanomagnet a. The donor system forms an effective two-qubit device due to the presence of a nuclear spin, that is coupled to the electron through the hyperfine interaction with strength A. The gyromagnetic ratio γ of both the quantum dot and donor system are affected by the electric field from the nearby electrostatic gates and nearby charged defects, which causes a non-uniformity between the qubits, but can also be exploited for addressability. For high-fidelity operation it is important that the qubit states are well isolated from excited states. Particularly in silicon quantum dots, a low-energy excited state can appear due to valley degeneracy, which can be lifted in energy via a large vertical electric field.98 The quantum-point-contact (QPC) or single-electron-transistor (SET) is used to probe the number of charges on the dots. They could potentially be avoided via gate-based dispersive read-out57
The canonical encoding of a qubit in these systems is in the spin split levels, \(\left \uparrow \right\rangle \kern 1pt\) and \(\left \downarrow \right\rangle \kern 1pt\), of the electron on each site, in the presence of a static magnetic field.13, 14 However, alternative encodings have been proposed theoretically and explored experimentally, whereby specific collective spin states of two or three electrons in two or three quantum dots are used to represent \(\left 0 \right\rangle \kern 1pt\) and \(\left 1 \right\rangle \kern 1pt\), see Fig. 2.44,45,46,47,48 For each of these encodings, direct current (DC) voltages may be used to fine tune qubit transition frequencies. This is immediate for the encodings based on two or three electron spins, where qubit splittings are directly set by gate voltages. Also for single-spin qubits, the spin splitting is typically sensitive to electric fields.49,50,51
Energy level diagram of spin states in quantum dots. a Low-energy spectrum of two uncoupled spins (black dotted line) and coupled spins (orange solid line) in two quantum dots as a function of the detuning energy ε, the relative energy difference between the left and right dot levels, which is controlled by the corresponding dot gate voltages. The exchange interaction provided by the charge states with double occupancies (S(2, 0) and S(0, 2)) can be used for two-qubit operations between single spin qubits as the exchange interaction J modifies the qubit resonance frequencies. While in the uncoupled situation the transition \(\left \downarrow \downarrow \right\rangle\) to \(\left \uparrow \downarrow \right\rangle \kern 1pt\) has the same energy as the \(\left \downarrow \uparrow \right\rangle\) to \(\left \uparrow \uparrow \right\rangle\) transition, these become different when exchange is on, allowing to drive rotations of one spin conditional on the state of the other.75 Alternatively, when briefly turning on the exchange, the two spin states will exchange over time, which also constitutes a two-qubit gate. While many experimental works exploit the detuning to control the exchange amplitude, directly controlling the tunnel coupling allows to operate the system at the so-called symmetry point, where the exchange energy is less sensitive to charge noise, dramatically improving the gate fidelity.104, 105 The joint state of two coupled spins, for instance the spin singlet and one of the triplet states, can also be used as a single qubit.65 The advantage of such a qubit is that one qubit axis is electrically controlled and two qubits can be coupled capacitively.23 For universal control, a magnetic field gradient is required, for instance induced by a nearby nanomagnet. All electrical control is possible using more advanced combinations of spins, for example, b the so-called exchange-only qubit and c hybrid qubit. b The encoding in the exchange-only qubit is based on three spins in three adjacent quantum dots and control is provided via the exchange between the outer quantum dots and the central dot, J L and J R .46, 77, 78 c The hybrid qubit is based on three spins as well, but requires only two quantum dots.48 Universal qubit control makes use of the anti-crossings between the lowest three energy states to induce rotations about different axes. While these qubit representations are clearly more involved compared to the single-spin qubit, their operation may offer advantages for scaling toward large arrays where not the number of dots per qubit but the number and type of control lines per dot will likely form the largest challenge
Qubit reset or initialization could be achieved by thermalization to the ground state, but that would be very slow given that spin relaxation times are often in the millisecond to second range.9, 10 Faster approaches include initialization by measurement52 and spin-selective tunneling from an electron reservoir or dot to a dot or donor.54, 61, 62
The discussion of electron spin qubits in quantum dots or donors leads us to the following commonly recurring requirements for the control signals. As can be seen from Fig. 2, not all requirements apply to each of the encodings, and this can be a criterion for comparing the merits of different encodings with each other.
This slow-down has two sides. First, it requires that probability of error of a qubit during \(\sqrt N\) read-out cycles stays far below the accuracy threshold. Here, the extremely long memory times of spin qubits under dynamical decoupling, of order one second,49, 69 are crucial. Second, it slows down the net clock cycle of the surface code operation by a factor \(\sqrt N\). Here, we note that it is not clear what the optimal effective clock cycle is. Too slow is not good since it slows down the computation. Too fast is not good either, since then the classical processors cannot keep up processing the massive data streams produced by the surface code syndrome measurements, and this will pose a hard boundary. This flexibility in choosing the clock cycle of the classical computer may turn out to be an important advantage of electron spin qubits over, e.g., superconducting qubits.
When combining coupling mechanisms at a distance with local registers of tunnel coupled qubits, a modular structure arises as illustrated in Fig. 4. Modular architectures are currently considered across a wide variety of platforms, from trapped ions to superconducting qubits to impurity spins of NV centers in diamond.84 Quantum error correction schemes such as the surface code can be naturally implemented on modular or distributed quantum computers. For instance by moving two logical qubits onto the same local register, two-qubit logical gates can be performed with known methods.85
These proposed solutions and approaches are not mutually exclusive. For instance, charge-storage electrodes can be beneficial also in sparse arrays, and a classical layer with (very) limited functionality could be incorporated with dense arrays. Furthermore, it is clear that there is still a big step to take from formulating general ideas as done here, to a complete proposal for an actual device, including device lay-outs, dimensions, power budgets, and so forth. Nevertheless, it is clear that spin qubits offer several particularly attractive possibilities in this direction. Finally, the continuous development of semiconductor technology provides further perspective that the wiring challenges can in fact be overcome, paving the way for the construction of a large-scale universal quantum computer. 041b061a72