Physical systems representing qubits typically have one or more accessible quantum states in addition to the two states that encode the qubit. We demonstrate that active involvement of such auxiliary states can be beneficial in constructing entangling two-qubit operations. We investigate the general case of two multistate quantum systems coupled via a quantum resonator. The approach is illustrated with the examples of three systems: self-assembled InAs/GaAs quantum dots, NV centers in diamond, and superconducting transmon qubits. Fidelities of the gate operations are calculated based on numerical simulations of each system.
Physical systems representing qubits typically have one or more accessible quantum states in addition to the two states that encode the qubit. We demonstrate that active involvement of such auxiliary states can be beneficial in constructing entangling two-qubit operations. We investigate the general case of two multistate quantum systems coupled via a quantum resonator. The approach is illustrated with the examples of three systems: self-assembled InAs/GaAs quantum dots, NV centers in diamond, and superconducting transmon qubits. Fidelities of the gate operations are calculated based on numerical simulations of each system.
Non-local higher-energy auxiliary states have been successfully used to entangle pairs of qubits in different quantum computing systems. Typically a longer-span non-local state or sequential application of few-qubit entangling gates are needed to produce a non-trivial multiqubit gate. In many cases a single non-local state that span over the entire system is difficult to use due to spectral crowding or impossible to have. At the same time, many multiqubit systems can naturally develop a network of multiple nonlocal higher-energy states that span over few qubits each. We show that continuous time quantum walks can be used to address this problem by involving multiple such states to perform local and entangling operations concurrently on many qubits. This introduces an alternative approach to multiqubit gate compression based on available physical resources. We formulate general requirements for such walks and discuss configurations of non-local auxiliary states that can emerge in quantum computing architectures based on self-assembled quantum dots, defects in diamond, and superconducting qubits, as examples. Specifically, we discuss a scalable multiqubit quantum register constructed as a single chain with nearest-neighbor interactions. We illustrate how quantum walks can be configured to perform single-, two- and three-qubit gates, including Hadamard, Control-NOT, and Toffoli gates. Continuous time quantum walks on graphs involved in these gates are investigated.
A central challenge in building a scalable quantum computer with superconducting qubits is the execution of high-fidelity two-qubit gates in the presence of many resonant elements. As more elements are added to the architecture, and as the multiplicity of their couplings grows, the design's frequency space becomes crowded, and performance suffers. The authors present a way to address this difficulty: selective activation of interactions between transmon qubits of fixed frequency and those of tunable frequency. This activation depends on both the amplitude and frequency of modulation, and using the amplitude as an additional condition for resonance alleviates frequency crowding.
We investigate a hybrid quantum system consisting of spatially separated resonant exchange qubits, defined in three-electron semiconductor triple quantum dots, that are coupled via a superconducting transmission line resonator. Drawing on methods from circuit quantum electrodynamics and Hartmann-Hahn double resonance techniques, we analyze three specific approaches for implementing resonator-mediated two-qubit entangling gates in both dispersive and resonant regimes of interaction. We calculate entangling gate fidelities as well as the rate of relaxation via phonons for resonant exchange qubits in silicon triple dots and show that such an implementation is particularly well suited to achieving the strong coupling regime. Our approach combines the favorable coherence properties of encoded spin qubits in silicon with the rapid and robust long-range entanglement provided by circuit QED systems.
Spins in a solid-state environment and photons are both promising physical systems regarding the implementation of qubits. Whereas electron and nuclear spins act very well as localized qubits that are able to store and process quantum information, photons are the primary candidates to transmit quantum information between distant locations. Entanglement, on the other hand, is a fundamental resource of quantum information processing enabling, e.g., secure communication over long distances. The generation and manipulation of entanglement are thus fundamental steps in order to leverage the benefits of quantum information processing. The aim of this dissertation is therefore to theoretically investigate entangling mechanisms for various physical systems. A functioning source of entangled photons is a basic hardware component required for quantum communication. To this end, we study a system composed of semiconductor quantum wells inside a microcavity, known as intersubband cavity system, in which the interaction of the electronic system with the cavity field can reach the ultrastrong coupling regime. The ground state contains a finite number of photons, and we find that these photons are entangled. The amount of entanglement is quantified analytically, and maximal entanglement is found to be possible. The technique of entanglement purification allows to restore maximal entanglement that has decreased, e.g. due to decoherence. Purification requires quantum memory, a role for which electron spins in electrically-defined quantum dots are well suited. However, existing purification protocols are rather unpractical in this case. Here, the concept of asymmetric bilateral two-qubit operations is introduced to purify spin entanglement by harnessing the typical interaction between electrons in neighboring quantum dots. As it turns out, this concept can be applied to a variety of qubit systems, e.g. superconducting qubits or spins in nitrogen-vacancy centers in diamond. The latter example offers several possibilities to implement a qubit, of which the intrinsic nitro- gen nuclear spin has proven its viability in many ways. We develop a scheme to deterministically couple two nuclear spin qubits, in which the interaction is mediated by an optical cavity. It is found that an entangling two-qubit gate, also required for universal quantum computation, can be implemented with operation times below 100 nanoseconds, i.e. several orders of magnitude faster compared to the decoherence time of the nuclear spin. The verification of entanglement, which is required e.g. in entanglement-based quantum com- munication to detect an eavesdropping attack, typically involves a measurement of qubit states. Using the input-output formalism, we derive a fully quantum-mechanical model of an optical readout scheme to measure the spin state of an electron in a self-assembled quantum dot.
We propose the implementation of fast resonant gates in circuit quantum electrodynamics for quantum information processing. We show how a suitable utilization of three-level superconducting qubits inside a resonator constitutes a key tool to perform diverse two-qubit resonant gates, improving the operation speed when compared to slower dispersive techniques. To illustrate the benefit of resonant two-qubit gates in circuit quantum electrodynamics, we consider the implementation of a two-dimensional cluster state in an array of $N\ifmmode\times\else\texttimes\fi{}N$ superconducting qubits by using resonant controlled-phase and one-qubit gates, where the generation time grows linearly with N. For N=3, and taking into account decoherence mechanisms, a fidelity over 60% for the generation of this cluster state is obtained.
Motivated by the recent experimental progress in exploring the use of a nitrogen-vacancy (NV) center in diamond as a quantum computing platform, we propose schemes for fast and high-fidelity entangling gates on this platform. Using both analytical and numerical calculations, we demonstrate that synchronization effects between resonant and off-resonant transitions may be exploited such that spin-flip errors due to strong driving may be eliminated by adjusting the gate time or the driving field. This allows for fast, high-fidelity entangling operations between the electron spin and one or several nuclear spins. We investigate a two-qubit system where the NV center comprises a N 15 atom and a qubit-qutrit system for the case of a N 14 atom. In both cases, we predict a complete suppression of off-resonant driving errors for two-qubit gates when addressing the NV electron spin conditioned on states of nuclear spins of the nitrogen atom of the defect. Additionally, we predict fidelities > 0.99 for multiqubit gates when including the surrounding C 13 atoms in the diamond lattice in the conditioned logic.