We propose a mechanism of a long-range coherent interaction between two singlet-triplet qubits dipolarly coupled to a dogbone-shaped ferromagnet. An effective qubit-qubit interaction Hamiltonian is derived and the coupling strength is estimated. Furthermore we derive the effective coupling between two spin-1/2 qubits that are coupled via dipolar interaction to the ferromagnet and that lie at arbitrary positions and deduce the optimal positioning. We consider hybrid systems consisting of spin-1/2 and ST qubits and derive the effective Hamiltonian for this case. We then show that operation times vary between 1MHz and 100MHz and give explicit estimates for GaAs, Silicon, and NV-center based spin qubits. Finally, we explicitly construct the required sequences to implement a CNOT gate. The resulting quantum computing architecture retains all the single qubit gates and measurement aspects of earlier approaches, but allows qubit spacing at distances of order 1$\,μ$m for two-qubit gates, achievable with current semiconductor technology.
We propose a mechanism of a long-range coherent interaction between two singlet-triplet qubits dipolarly coupled to a dogbone-shaped ferromagnet. An effective qubit-qubit interaction Hamiltonian is derived and the coupling strength is estimated. Furthermore we derive the effective coupling between two spin-1/2 qubits that are coupled via dipolar interaction to the ferromagnet and that lie at arbitrary positions and deduce the optimal positioning. We consider hybrid systems consisting of spin-1/2 and ST qubits and derive the effective Hamiltonian for this case. We then show that operation times vary between 1MHz and 100MHz and give explicit estimates for GaAs, Silicon, and NV-center based spin qubits. Finally, we explicitly construct the required sequences to implement a CNOT gate. The resulting quantum computing architecture retains all the single qubit gates and measurement aspects of earlier approaches, but allows qubit spacing at distances of order 1μm for two-qubit gates, achievable with current semiconductor technology.
We analyze and give estimates for the long-distance coupling via floating metallic gates between different types of spin qubits in quantum dots made of different commonly used materials. In particular, we consider the hybrid, the singlet-triplet, and the spin-21 qubits, and the pairwise coupling between each type of these qubits with another hybrid qubit in GaAs, InAs, Si, and Si0.9Ge0.1. We show that hybrid qubits can be capacitively coupled strongly enough to implement two-qubit gates, as long as the distance of the dots from the metallic gates is small enough. Thus, hybrid qubits are good candidates for scalable implementations of quantum computing in semiconducting nanostructures.
Hybrid systems comprising superconducting and semiconducting materials are promising architectures for quantum computing. Superconductors induce long-range interactions between the spin degrees of freedom of semiconducting quantum dots. These interactions are widely anisotropic when the semiconductor material has strong spin-orbit interactions. We show that this anisotropy is tunable and enables fast and high-fidelity two-qubit gates between singlet-triplet (ST) spin qubits. Our design is immune to leakage of the quantum information into noncomputational states and removes always-on interactions between the qubits, thus resolving key open challenges for these architectures. Our ST qubits do not require additional technologically demanding components nor fine-tuning of parameters. They operate at low magnetic fields of a few millitesla and are fully compatible with superconductors. By suppressing systematic errors in realistic devices, we estimate infidelities below ${10}^{\ensuremath{-}3}$, which could pave the way toward large-scale hybrid superconducting-semiconducting quantum processors.
We propose a mechanism of long-range coherent coupling between nuclear spin qubits in semiconductor-heterojunction quantum information processing devices. The coupling is via localized donor electrons which interact with the two-dimensional electron gas. An effective interaction Hamiltonian is derived and the coupling strength is evaluated. We also discuss mechanisms of decoherence and consider gate control of the interaction between qubits. The resulting quantum computing scheme retains all the control and measurement aspects of earlier approaches, but allows qubit spacing at distances of the order of 100 nm, attainable with the present-day semiconductor device technologies.
Fast, high-fidelity single and two-qubit gates are essential to building a viable quantum information processor, but achieving both in the same system has proved challenging for spin qubits. We propose and analyze an approach to perform a long-distance two-qubit controlled phase (CPHASE) gate between two singlet-triplet qubits using an electromagnetic resonator to mediate their interaction. The qubits couple longitudinally to the resonator, and by driving the qubits near the resonator's frequency, they can be made to acquire a state-dependent geometric phase that leads to a CPHASE gate independent of the initial state of the resonator. Using high impedance resonators enables gate times of order 10 ns while maintaining long coherence times. Simulations show average gate fidelities of over 96% using currently achievable experimental parameters and over 99% using state-of-the-art resonator technology. After optimizing the gate fidelity in terms of parameters tuneable in situ, we find it takes a simple power-law form in terms of the resonator's impedance and quality and the qubits' noise bath.
Since the seminal work by Shor who proposed a quantum algorithm factorizing integers into prime factors, it has become manifest that the laws of quantum mechanics provide resources for computation that overpower classical physics. The computational advantages that quantum physics offers have stimulated a tremendous amount of theoretical and experimental research. In this context, spin systems have played a major role, given that the spin degree of freedom -- with the paradigmatic case of the spin-1/2 of electrons -- represents an obvious candidate for the encoding of an elementary bit of quantum information (qubit). \n \nOn the other hand, however, quantum objects are very fragile entities, being very susceptible to the environment they reside in. This fragility of qubits is one of the main obstacles in the realization of a quantum computer. \n \nIn this thesis, we mainly address the two following questions relevant to quantum computation. \n \ni) How is it possible to realize quantum gates both in a reliable and scalable way? \n \nii) How can we store quantum information in a way that is resilient to the errors caused by the thermal environment? \n \nWe focus on spin systems and demonstrate that long-range spin-spin interactions in the models considered can have beneficial effects. \n \nIn their pioneering work, Loss and DiVincenzo proposed a way to perform quantum computation in a semiconductor-based architecture where the spin state of an electron trapped in a quantum dot is chosen to encode the elementary qubit. In this proposal, the spins are required to lie spatially close to each other, and this might complicate the realization of a scalable architecture. \n \nIn the first part of the thesis we thus propose a scheme that allows the constraint on the positioning of the qubits to be relaxed. This is achieved by introducing a ferromagnetic coupler between the distant qubits, to which it is coupled via a dipolar interaction. Most importantly, our proposal is applicable to any type of spin qubits and in particular to the technologically very relevant silicon-based qubits and NV-centers in diamond to which previous coupling schemes do not apply. \n \nAs additional key element, a quantum computer needs a memory capable of reliably storing quantum information in the presence of thermal fluctuations. \n \nThis brings us to the second part of this thesis, where we consider self-correcting memories, for which the protection against thermal noise is built-in at the hardware level. We propose physical models that exhibit these self-correcting properties, using as a starting point the well known topologically ordered toric code. In particular, we investigate how to induce long-range interactions between the spins of the toric code, since such interactions help increase the memory lifetime. \n \nAs a first step, we study a honeycomb quantum spin model coupled to delocalized cavity modes. We investigate the properties of the low-energy toric code Hamiltonian and show that the coupling to cavity modes prolongs the lifetime of the memory and offers a method to detect the presence of excitations. \nWhile the introduction of extended bosonic modes makes the model non-local, we also propose a purely local model consisting of a toric code embedded in a three-dimensional cubic lattice of hopping bosons; the low-energy sector of a toric code coupled to a three-dimensional Heisenberg ferromagnet in a broken-symmetry state realizes this model. Our analysis leads to an energy penalty for the creation of defects that grows linearly with the size L of the memory and thus to a lifetime increasing exponentially with L. \n \nIn the third part of this thesis, we study spin systems that support anyons, i.e., particles with fractional statistics. Similar to the toric code, such systems are topologically ordered: they are immune to local perturbations and quantum gates are implemented by non-local operations, namely the exchange of anyons, whose outcomes depend only on the topology of the exchange. Here again the fault-tolerance is achieved at the level of the hardware and physical systems supporting non-abelian anyons are thus promising platforms for quantum computation. \n \nWe focus on spin systems that exhibit some of these properties and specifically on variations of the honeycomb quantum spin model. We first investigate the exact solution of the honeycomb model in detail and derive an explicit formula for the projector onto the physical subspace. We use this result to study inhomogeneous open spin ladders, related to the honeycomb model, which can be tuned between topological and non-topological phases. We test the robustness of Majorana end states (MES) which emerge at the boundary between sections in different topological phases. Furthermore, we present a trijunction setup where MES can be braided. This is of interest since MES in these spin ladders potentially follow non-abelian braiding statistics. Finally, we study the ground states of the aforementioned ladders and show that they are free of vortices when the signs of the spin couplings are all positive or negative. To prove this, we use exact reflection-positivity-based methods as well as approximate methods. \n \nIn the last part of the thesis, we provide an extension of the Mermin-Wagner theorem to a system of lattice spins that are spin-coupled to itinerant and interacting charge carriers. We prove that neither (anti-) ferromagnetic nor helical long-range order is possible in one and two dimensions at any finite temperature (in the absence of spin-orbit). The fundamental question whether spontaneous ordering of the lattice spins occurs in these systems is of interest in the context of quantum computation; the polarization of nuclear spins coupled to a two-dimensional electron gas is a possible route towards the reduction of decoherence induced by the fluctuating Overhauser field in gate-defined quantum dots. \n \n
Single-spin qubits in semiconductor quantum dots proposed by Loss and DiVincenzo (LD qubits) hold promise for universal quantum computation with demonstrations of a high single-qubit gate fidelity above 99.9 % and two-qubit gates in conjunction with a long coherence time. However, initialization and readout of a qubit is orders of magnitude slower than control, which is detrimental for implementing measurement-based protocols such as error-correcting codes. In contrast, a singlet-triplet (ST) qubit, encoded in a two-spin subspace, has the virtue of fast readout with high fidelity and tunable coupling to the electric field. Here, we present a hybrid system which benefits from the different advantages of these two distinct spin-qubit implementations. A quantum interface between the two codes is realized by electrically tunable inter-qubit exchange coupling. We demonstrate a controlled-phase (CPHASE) gate that acts within 5.5 ns, much faster than the measured dephasing time of 211 ns. The presented hybrid architecture will be useful to settle remaining key problems with building scalable spin-based quantum computers.