A silicon-based surface code quantum computer

Individual impurity atoms in silicon can make superb individual qubits, but it remains an immense challenge to build a multi-qubit processor: there is a basic conflict between nanometre separation desired for qubit–qubit interactions and the much larger scales that would enable control and addressing in a manufacturable and fault-tolerant architecture. Here we resolve this conflict by establishing the feasibility of surface code quantum computing using solid-state spins, or ‘data qubits’, that are widely separated from one another. We use a second set of ‘probe’ spins that are mechanically separate from the data qubits and move in and out of their proximity. The spin dipole–dipole interactions give rise to phase shifts; measuring a probe’s total phase reveals the collective parity of the data qubits along the probe’s path. Using a protocol that balances the systematic errors due to imperfect device fabrication, our detailed simulations show that substantial misalignments can be handled within fault-tolerant operations. We conclude that this simple ‘orbital probe’ architecture overcomes many of the difficulties facing solid-state quantum computing, while minimising the complexity and offering qubit densities that are several orders of magnitude greater than other systems

X- and Q-band EPR with cryogenic amplifiers independent of sample temperature

Inspired by the success of NMR cryoprobes, we recently reported a leap in X-band EPR sensitivity by equipping an ordinary EPR probehead with a cryogenic low-noise microwave amplifier placed closed to the sample in the same cryostat [Šimėnas et al. J. Magn. Reson. 322, 106876 (2021)]. Here, we explore, theoretically and experimentally, a more general approach, where the amplifier temperature is independent of the sample temperature. This approach brings a number of important advantages, enabling sensitivity improvement irrespective of sample temperature, as well as making it more practical to combine with ENDOR and Q-band resonators, where space in the sample cryostat is often limited. Our experimental realisation places the cryogenic preamplifier within an external closed-cycle cryostat, and we show CW and pulsed EPR and ENDOR sensitivity improvements at both X- and Q-bands with negligible dependence on sample temperature. The cryoprobe delivers signal-to-noise ratio enhancements that reduce the equivalent pulsed EPR measurement time by 16× at X-band and close to 5× at Q-band. Using the theoretical framework we discuss further improvements of this approach which could be used to achieve even greater sensitivity

First-principles calculations of hyperfine interaction, binding energy, and quadrupole coupling for shallow donors in silicon

Spin qubits based on shallow donors in silicon are a promising quantum information technology with enormous potential scalability due to the existence of robust silicon-processing infrastructure. However, the most accurate theories of donor electronic structure lack predictive power because of their reliance on empirical fitting parameters, while predictive ab initio methods have so far been lacking in accuracy due to size of the donor wavefunction compared to typical simulation cells. We show that density functional theory with hybrid and traditional functionals working in tandem can bridge this gap. Our first-principles approach allows remarkable accuracy in binding energies (67 meV for bismuth and 54 meV for arsenic) without the use of empirical fitting. We also obtain reasonable hyperfine parameters (1263 MHz for Bi and 133 MHz for As) and superhyperfine parameters. We demonstrate the importance of a predictive model by showing that hydrostatic strain has much larger effect on the hyperfine structure than predicted by effective mass theory, and by elucidating the underlying mechanisms through symmetry analysis of the shallow donor charge density

Pipeline quantum processor architecture for silicon spin qubits

We propose a quantum processor architecture, the qubit ‘pipeline’, in which run-time scales additively as functions of circuit depth and run repetitions. Run-time control is applied globally, reducing the complexity of control and interconnect resources. This simplification is achieved by shuttling N-qubit states through a large layered physical array of structures which realise quantum logic gates in stages. Thus, the circuit depth corresponds to the number of layers of structures. Subsequent N-qubit states are ‘pipelined’ densely through the structures to efficiently wield the physical resources for repeated runs. Pipelining thus lends itself to noisy intermediate-scale quantum (NISQ) applications, such as variational quantum eigensolvers, which require numerous repetitions of the same or similar calculations. We illustrate the architecture by describing a realisation in the naturally high-density and scalable silicon spin qubit platform, which includes a universal gate set of sufficient fidelity under realistic assumptions of qubit variability

Pipeline quantum processor architecture for silicon spin qubits

We propose a quantum processor architecture, the qubit ‘pipeline’, in which run-time scales additively as functions of circuit depth and run repetitions. Run-time control is applied globally, reducing the complexity of control and interconnect resources. This simplification is achieved by shuttling N-qubit states through a large layered physical array of structures which realise quantum logic gates in stages. Thus, the circuit depth corresponds to the number of layers of structures. Subsequent N-qubit states are ‘pipelined’ densely through the structures to efficiently wield the physical resources for repeated runs. Pipelining thus lends itself to noisy intermediate-scale quantum (NISQ) applications, such as variational quantum eigensolvers, which require numerous repetitions of the same or similar calculations. We illustrate the architecture by describing a realisation in the naturally high-density and scalable silicon spin qubit platform, which includes a universal gate set of sufficient fidelity under realistic assumptions of qubit variability

Signatures of discrete time crystalline order in dissipative spin ensembles

Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a discrete time crystal, an exotic new phase of matter. We present observations characteristic of discrete time crystalline order in a driven system of paramagnetic P-donor impurities in isotopically enriched 28Si cooled below 10 K. The observations exhibit a stable subharmonic peak at half the drive frequency which remains pinned even in the presence of pulse error, a signature of discrete time crystalline order. This signal has a finite lifetime of ∼ 100 Floquet periods, but this effect is long-lived relative to coherent spin–spin interaction timescales, lasting ∼ 104 times longer.We present simulations of the system based on the paradigmatic central spin model and show good agreement with experiment. We investigate the role of dissipation and interactions within this model, and show that both are capable of giving rise to discrete time crystal-like behaviour

Remote Capacitive Sensing in Two-Dimensional Quantum-Dot Arrays

We investigate gate-induced quantum dots in silicon nanowire field-effect transistors fabricated using a foundry-compatible fully depleted silicon-on-insulator (FD-SOI) process. A series of split gates wrapped over the silicon nanowire naturally produces a 2 × n bilinear array of quantum dots along a single nanowire. We begin by studying the capacitive coupling of quantum dots within such a 2 × 2 array and then show how such couplings can be extended across two parallel silicon nanowires coupled together by shared, electrically isolated, “floating” electrodes. With one quantum dot operating as a single-electron-box sensor, the floating gate serves to enhance the charge sensitivity range, enabling it to detect charge state transitions in a separate silicon nanowire. By comparing measurements from multiple devices, we illustrate the impact of the floating gate by quantifying both the charge sensitivity decay as a function of dot-sensor separation and configuration within the dual-nanowire structure

Will Spin-Relaxation Times in Molecular Magnets Permit Quantum Information Processing?

Using X-band pulsed electron-spin resonance, we report the intrinsic spin-lattice (T1) and phase-coherence (T2) relaxation times in molecular nanomagnets for the first time. In Cr7M heterometallic wheels, with M=Ni and Mn, phase-coherence relaxation is dominated by the coupling of the electron spin to protons within the molecule. In deuterated samples T2 reaches 3  μs at low temperatures, which is several orders of magnitude longer than the duration of spin manipulations, satisfying a prerequisite for the deployment of molecular nanomagnets in quantum information applications

Line Broadening and Decoherence of Electron Spins in Phosphorus-Doped Silicon Due to Environmental 29^Si Nuclear Spins

Phosphorus-doped silicon single crystals with 0.19 % <= f <= 99.2 %, where f is the concentration of 29^Si isotopes, are measured at 8 K using a pulsed electron spin resonance technique, thereby the effect of environmental 29^Si nuclear spins on the donor electron spin is systematically studied. The linewidth as a function of f shows a good agreement with theoretical analysis. We also report the phase memory time T_M of the donor electron spin dependent on both f and the crystal axis relative to the external magnetic field.Comment: 5 pages, 4 figure

Nuclear spin decoherence of neutral P-31 donors in silicon: Effect of environmental Si-29 nuclei

Spectral diffusion arising from Si29 nuclear spin flip-flops, known to be a primary source of electron spin decoherence in silicon, is also predicted to limit the coherence times of neutral donor nuclear spins in silicon. Here, the impact of this mechanism on P31 nuclear spin coherence is measured as a function of Si29 concentration using X-band pulsed electron nuclear double resonance. The P31 nuclear spin echo decays show that decoherence is controlled by Si29 flip-flops resulting in both fast (exponential) and slow (nonexponential) spectral diffusion processes. The decay times span a range from 100 ms in crystals containing 50% Si29 to 3 s in crystals containing 1% Si29. These nuclear spin echo decay times for neutral donors are orders of magnitude longer than those reported for ionized donors in natural silicon. The electron spin of the neutral donors “protects” the donor nuclear spins by suppressing Si29 flip-flops within a “frozen core,” as a result of the detuning of the Si29 spins caused by their hyperfine coupling to the electron spin