John J. L. Morton

Simulation of the time-dynamics of fermionic many-body systems has long been predicted to be one of the key applications of quantum computers. Such simulations -- for which classical methods are often inaccurate -- are critical to advancing our knowledge and understanding of quantum chemistry and materials, underpinning a wide range of fields, from biochemistry to clean-energy technologies and chemical synthesis. However, the performance of all previous digital quantum simulations of fermions has been matched by classical methods, and it has thus far remained unclear whether near-term, intermediate-scale quantum hardware could offer any computational advantage in this area. Here, we implement an efficient quantum simulation algorithm on Quantinuum's System Model H2 trapped-ion quantum computer for the time dynamics of a 56-qubit system that is too complex for exact classical simulation. We focus on the periodic spinful 2D Fermi-Hubbard model and present evidence of spin-charge separation, where the elementary electron's charge and spin decouple. In the limited cases where ground truth is available through exact classical simulation, we find that it agrees with the results we obtain from the quantum device. Employing long-range Wilson operators to study deconfinement of the effective gauge field between spinons and the effective potential between charge carriers, we find behaviour that differs from predictions made by classical tensor network methods. Our results herald the use of quantum computing for simulating strongly correlated electronic systems beyond the capacity of classical computing.

A major challenge in using spins in the solid state for quantum technologies is protecting them from sources of decoherence. This can be addressed, to varying degrees, by improving material purity or isotopic composition for example, or active error correction methods such as dynamic decoupling, or even combinations of the two. However, a powerful method applied to trapped ions in the context of frequency standards and atomic clocks, is the use of particular spin transitions which are inherently robust to external perturbations. Here we show that such `clock transitions' (CTs) can be observed for electron spins in the solid state, in particular using bismuth donors in silicon. This leads to dramatic enhancements in the electron spin coherence time, exceeding seconds. We find that electron spin qubits based on CTs become less sensitive to the local magnetic environment, including the presence of 29Si nuclear spins as found in natural silicon. We expect the use of such CTs will be of additional importance for donor spins in future devices, mitigating the effects of magnetic or electric field noise arising from nearby interfaces.

Silicon is undoubtedly one of the most promising semiconductor materials for spin-based information processing devices. Its highly advanced fabrication technology facilitates the transition from individual devices to large-scale processors, and the availability of an isotopically-purified $^{28}$Si form with no magnetic nuclei overcomes what is a main source of spin decoherence in many other materials. Nevertheless, the coherence lifetimes of electron spins in the solid state have typically remained several orders of magnitude lower than what can be achieved in isolated high-vacuum systems such as trapped ions. Here we examine electron spin coherence of donors in very pure $^{28}$Si material, with a residual $^{29}$Si concentration of less than 50 ppm and donor densities of $10^{14-15}$ per cm$^3$. We elucidate three separate mechanisms for spin decoherence, active at different temperatures, and extract a coherence lifetime $T_2$ up to 2 seconds. In this regime, we find the electron spin is sensitive to interactions with other donor electron spins separated by ~200 nm. We apply a magnetic field gradient in order to suppress such interactions and obtain an extrapolated electron spin $T_2$ of 10 seconds at 1.8 K. These coherence lifetimes are without peer in the solid state by several orders of magnitude and comparable with high-vacuum qubits, making electron spins of donors in silicon ideal components of a quantum computer, or quantum memories for systems such as superconducting qubits.