Philip R. Johnson: Superconducting Qubit Research |
A quantum computer exploits the intrinsic parallelism of quantum physics in which the quantum state of a single object can behave as if it exists simultaneously in many possible classical configurations. The most basic element of a quantum computer is the quantum bit (qubit). An ordinary (i.e. classical) computer stores information as bits: a classical bit is a physical device that has two possible configurations which are assigned either the value 1 or 0 (e.g. a transistor which is on or off). What makes a bit classical is that it must be either 0 or 1, never both at the same time. A qubit can be in a quantum superposition of two distinct configurations (1 and 0), and hence, in a sense, can store the values 0 and 1 simultaneously. Consequently, when many qubits are connected together they can manipulate exponentially more information than an equal number of classical bits! For example, under idealized conditions, a 100 qubit device can (in some sense) manipulate a thousand, billion, billion, billion numbers at one time! Potentially, this could lead to quantum computers that can solve problems that no foreseeable classical computer will ever be able to handle.
One of the most important known problems that a quantum computer can solve is the factoring of large numbers; the present day inability of normal computers to factor large numbers is the basis for one of the most important forms of computer encryption called RSA. Not a lot is known about what else a quantum computer can do; thinking in terms of quantum information rather than familiar classical information does not come naturally to most of us. Perhaps the most important application of a quantum computer will be to study other important and complex quantum systems. Examples include the complex systems that are at the heart of molecular chemistry and biology, nanoscale and mesoscopic systems, large atoms and nuclei, quantum plasmas, condensed matter, etc... It seems likely that a full-scale quantum computer would herald a revolution in our understanding of the quantum physics of complex systems.
To achieve these goals, we must first fully understand the quantum physics of simpler systems that will be the building blocks of an eventual full-scale quantum computer. The first step requires building and controlling single qubits. Excellent possible qubits (provided to us ready-made by nature) include atoms, nuclei, electrons, molecules, or even photons, and considerable research exploring the use of these elementary objects is ongoing. We, along with a number of other groups, are attempting to build qubits not out of elementary objects likes atoms, but from macroscopic solid-state superconducting electrical devices. These devices are attractive because they are relatively easy to control and measure, and, in principle, it is straightforward to connect many together to make a scalable quantum computer. However, observing and preserving coherent quantum behavior in any macroscopic device presents special challenges.
Quantum coherence is the essential ingredient that a quantum computer needs in exploiting quantum parallelism; usable quantum coherence is lost when quantum systems interact with their environment--this process is called decoherence. It is believed that decoherence helps explain why we don't easily see quantum coherent phenomena on large scales (like cells, people, and planets). The exploration of macroscopic quantum mechanics is an important problem at the heart of quantum physics; whether quantum physics truly applies to macroscopic objects has profound implications for the nature of reality.
As a step toward building macroscopic quantum device, we have built two-coupled qubit devices using superconducting (Josephson) tunnel junctions. The circuit diagram for this device is shown below. The two qubits are indicated by the dashed-black lines, the Josephson tunnel junctions are marked by x's. The two-qubit device is controlled by an externally applied bias currents (b1 and b2) and applied microwaves.
Experimental measurements (Entangled macroscopic quantum states in two superconducting qubits, Science, 2003) provide evidence that these coupled junctions are true quantum bits (these measurements were performed at approximately 1/100th of a degree above absolute zero within a carefully isolated chamber to reduce the decohering affect of noise from the environment).
The figure above shows (in red) the measured energy levels versus applied bias-current of the superconducting two-qubit device shown below. The white lines in the top figure are the theoretical energy levels found by numerical solution of the Schrödinger equation. The black-dashed lines are the energy levels of the qubits when dynamically uncoupled.
These experimental measurements agree remarkably well with our earlier theoretical predications (Spectroscopy of capacitively coupled Josephson-junction qubits, PRB-Rapid 2003). Numerically determined wavefunctions for the two-qubit devices are shown in the figure below. These metastable states where calculated using a split-operator imaginary time non-perturbative algorithm that incorporates both the full nonlinearity of the Hamiltonian, and the effects of quantum tunneling out of the qubit potential well. The avoided crossing data shown above corresponds to the two bell states |01> ± |10> shown in the figure below.
A lower-order form of the split-operator (FFT-grid) algorithm is shown in flowchart form below.
A present goal is to demonstrate quantum logic gates, which requires coherent control of coupled quantum qubits. Two qubits connected together can form a quantum gate, which may then be used to perform quantum logic. A quantum computer is made from many connected quantum gates, just as a classical computer is made from many connected classical logic gates. We have recently shown, through theoretical analysis and computer simulation, that two coupled superconducting tunnel junctions can, in principle, be a controllable universal quantum gate (Quantum gates for coupled superconducting phase qubits, PRL). Click here to see a movie of a numerically simulated two-qubit swap gate, using the split-operator algorithm. The figure below shows the numerically simulated two-qubit phase gate at initial, intermediate, and final times. Both types of gates are controlled by ramping externally applied bias currents to move the system to (and from) energy degeneracy's in the Hilbert space, while at the same time minimizing both tunneling out of the qubit potential well and unwanted evolution (leakage) of the quantum state out of the computational subspace of the full Hilbert space. Single qubit gates (e.g. the Hadamard gate) are obtained by applying microwaves.
