To observe or control a quantum system, one must interact with it via an interface. This article exhibits simple universal quantum interfaces---quantum input/output ports consisting of a single two-state system or quantum bit that interacts with the system to be observed or controlled. It is shown that under very general conditions the ability to observe and control the quantum bit on its own implies the ability to observe and control the system itself. The interface can also be used as a quantum communication channel, and multiple quantum systems can be connected by interfaces to become an efficient universal quantum computer. Experimental realizations are proposed, and implications for controllability, observability, and quantum information processing are explored.
To observe or control a quantum system, one must interact with it via an interface. This article exhibits simple universal quantum interfaces---quantum input/output ports consisting of a single two-state system or quantum bit that interacts with the system to be observed or controlled. It is shown that under very general conditions the ability to observe and control the quantum bit on its own implies the ability to observe and control the system itself. The interface can also be used as a quantum communication channel, and multiple quantum systems can be connected by interfaces to become an efficient universal quantum computer. Experimental realizations are proposed, and implications for controllability, observability, and quantum information processing are explored.
A feedback loop consists of three dynamical systems: an observer, a controller, and the system to be manipulated. Because of back-action in quantum systems, quantum controllers can act. as quantum observers and vice-versa. We demonstrate that under very general conditions, a single quantum bit can serve as both a full controller and full observer of a quantum system for a feedback loop. By similar techniques, we show that a qubit can be harnessed to serve as a quantum communication channel between two systems, and that multiple systems call be connected together to create all efficient universal quantum computer. We propose experimental realizations of our approach, and explore the implications for controllability, observability, and quantum information processing.
A quantum computer is similar to an ordinary computer, except that instead of bits it uses two-level quantum systems (qubits), and the usual logical operations on bits are replaced with noiseless quantum dynamics in the form of unitary gates or Hamiltonian interactions. Many sets of resources that are universal for quantum computation (that is, capable of implementing any quantum computation) have been found, but general conditions for universality are still only partially understood. Improving our understanding of these conditions contributes to two broad goals. On the one hand, understanding what class of physical systems is suitable for quantum computation allows us choose the systems that are most easily controlled or built in the laboratory. On the other hand, identifying the unifying characteristics of such a class provides insight into the fundamental physics responsible for the much greater computational power of quantum computers. The original results presented in this thesis are a contribution to our understanding of the physical requirements for universal quantum computation. These results lead to the identification of a new, large class of universal dynamics. More specifically, the main problem that is addressed is the following: consider a physical system that is made up of a finite number of qubits that are subject to a natural, fixed interaction described by a two-body Hamiltonian. Suppose we have the ability to control the system only by applying fast one-qubit operations. Under what conditions is this system capable of universal quantum computation? The first original result of the thesis is to prove that universal quantum computation is possible under these conditions given the single extra constraint that the Hamiltonian must entangle, or connect, all of the qubits. In other words, since a two-body Hamiltonian is expressible as a sum of coupling terms each of which acts nontrivially on a pair of qubits, consider the graph whose vertices correspond to qubits and whose edges connect qubits that are coupled by a term in the Hamiltonian. Then this Hamiltonian, together with fast one-qubit unitaries, is universal for quantum computation precisely when the corresponding graph is connected. This result suggests many potential generalizations, three of which are explored in this thesis. The first generalization is to show that the same result holds for a two-body Hamiltonian that acts on D-dimensional quantum systems (qudits), given fast one-qudit unitaries. A second extension is to the case of a many-body Hamiltonian, that is, a Hamiltonian that has coupling terms that act on more than two qubits. Again, we find that under mild restrictions, such Hamiltonians are universal provided they are connected and that arbitrary one-qubit unitaries are available. We also discover and explore some surprising structure in many-body Hamiltonians that is associated with the parity of the couplings. A third related problem that is addressed is the question of what two-qubit unitaries are universal for quantum computation. This problem was originally solved by J.-L. and R. Brylinski [BB02], who gave a technical proof of the universality of any two-qudit gate that is not the swap gate or a product of one-qudit unitaries, given one-qudit unitaries as a free resource. We develop an elementary and constructive proof for the case of qubits, and prove that our construction is very close to optimal in the number of uses of the two-qubit gate. Given a qualitative understanding of what dynamical resources are universal for quantum computation, it is natural to consider developing a quantitative measure of the usefulness of quantum dynamics for quantum information processing. This is done in the final chapter of the thesis, in which the beginnings of a quantitative theory of quantum dynamics are developed.
We have seen how information can be encoded onto a quantum system by selecting the state in which it is prepared. Retrieving the information is achieved by performing a measurement, and the optimal measurement in any given situation is usually a generalized measurement. In between preparation and measurement, the information resides in the quantum state of the system, which evolves in a manner determined by the Hamiltonian. The associated unitary transformation may usefully be viewed as quantum information processing; if we can engineer an appropriate Hamiltonian then we can use the quantum evolution to assist in performing computational tasks. Our objective in quantum information processing is to implement a desired unitary transformation. Typically this will mean coupling together a number, perhaps a large number, of qubits and thereby generating highly entangled states. It is fortunate, although by no means obvious, that we can realize any desired multiqubit unitary transformation as a product of a small selection of simple transformations and, moreover, that each of these need only act on a single qubit or on a pair of qubits. The situation is reminiscent of digital electronics, in which logic operations are decomposed into actions on a small number of bits. If we can realize and control a very large number of such operations in a single device then we have a computer. Similar control of a large number of qubits will constitute a quantum computer. It is the revolutionary potential of quantum computers, more than any other single factor, that has fuelled the recent explosion of interest in our subject. We shall examine the remarkable properties of quantum computers in the next chapter. In digital electronics, we represent bit values by voltages: the logical value 1 is a high voltage (typically +5 V) and 0 is the ground voltage (0 V). The voltage bits are coupled and manipulated by transistor-based devices, or gates. The simplest gates act on only one bit or combine two bits to generate a single new bit, the value of which is determined by the two input bits. For a single bit, with value 0 or 1, the only possible operations are the identity (which does not require a gate) and the bit flip.
The routing capability is a requisite in quantum network. Although the quantum routing of signals has been investigated in various systems both in theory and experiment, the general form of quantum routing with many output terminals still needs to be explored. Here we propose a scheme to achieve the multi-channel quantum routing of the single photons in a waveguide-emitter system. The channels are composed by the waveguides and are connected by intermediate two-level emitters. By adjusting the intermediate emitters, the output channels of the input single photons can be controlled. This is demonstrated in the cases of one output channel, two output channels and the generic N output channels. The results show that the multi-channel quantum routing of single photons can be well achieved in the proposed system. This offers a scheme for the experimental realization of general quantum routing of single photons.
We describe a digital microwave platform called Presto, designed for measurement and control of multiple quantum bits (qubits) and based on the third-generation radio-frequency system on a chip. Presto uses direct digital synthesis to create signals up to 9 GHz on 16 synchronous output ports, while synchronously analyzing responses on 16 input ports. Presto has 16 DC-bias outputs, four inputs and four outputs for digital triggers or markers, and two continuous-wave outputs for synthesizing frequencies up to 15 GHz. Scaling to a large number of qubits is enabled through deterministic synchronization of multiple Presto units. A Python application programming interface configures a firmware for synthesis and analysis of pulses, coordinated by an event sequencer. The analysis integrates template matching (matched filtering) and low-latency (184-254 ns) feedback to enable a wide range of multi-qubit experiments. We demonstrate Presto's capabilities with experiments on a sample consisting of two superconducting qubits connected via a flux-tunable coupler. We show single-shot readout and active reset of a single qubit; randomized benchmarking of single-qubit gates showing 99.972% fidelity, limited by the coherence time of the qubit; and calibration of a two-qubit iSWAP gate.