Abstract

The performance of superconducting qubits has improved by several orders of magnitude in the past decade. These circuits benefit from the robustness of superconductivity and the Josephson effect, and at present they have not encountered any fundamental physical limits. However, building an error-corrected information processor with many such qubits will require solving specific architecture problems that constitute a new field of research. For the first time, physicists will have to master quantum error correction to design and operate complex active systems that are dissipative in nature, yet remain coherent indefinitely. We offer a view on some directions for the field and speculate on its future. The concept of solving problems with the use of quantum algorithms, introduced in the early 1990s 1,2 , was welcomed as a revolutionary change in the theory of computational complexity, but the feat of actually building a quantum computer was then thought to be impossible. The invention of quantum error correction (QEC) Below, we discuss the specific physical implementation of general-purpose QIP with superconducting qubits Toward a Quantum Computer Developing a quantum computer involves several overlapping and interconnecting stages coherence time that is longer than any of the individual components. This goal is as yet unfulfilled in any system. The final two stages in reaching the ultimate goal of faulttolerant quantum information processing 26 require the ability to do all single qubit operations on one logical qubit (which is an effective qubit protected by active error correction mechanisms), and the ability to perform gate operations between several logical qubits; in both stages the enhanced coherence lifetime of the qubits should be preserved. Superconducting Circuits: Hamiltonians by Design Unlike microscopic entities-electrons, atoms, ions, and photons-on which other qubits are based, superconducting quantum circuits are based on the electrical (LC) oscillator ( When several of these qubits, which are nonlinear oscillators behaving as artificial atoms, are coupled to true oscillators (photons in a microwave cavity), one obtains, for low-lying excitations, an effective multiqubit, multicavity system Hamiltonian of the form can perform arbitrary quantum operations at speeds determined by the nonlinear interaction strengths  and , typically 43,44 resulting in single-qubit gate times within 5 to 50 ns (/2 ≈ 200 MHz) and two qubit entangling gate times within 50 to 500 ns (/2 ≈ 20 MHz). We have neglected here the weak induced anharmonicity of the cavity modes. Proper design of the qubit circuit to minimize dissipation coming from the dielectrics surrounding the metal of the qubit, and to minimize radiation of energy into other electromagnetic modes or the circuit environment, led to qubit transition quality factors Q exceeding 1 million or coherence times on the order of 100 ms, which in turn make possible hundreds or even thousands of operations in one coherence lifetime (see There are three figures of merit that characterize this type of readout. The first is QNDness, the probability that the qubit remains in the same state after the measurement, given that the qubit is initially in a definite state |g> or |e>. The second is the intrinsic fidelity, the difference between the probabilities-given that the qubit is initially in a definite state |g> or |e>-that the readout gives the correct and wrong answers (with this definition, the fidelity is zero when the readout value is uncorrelated with the qubit state). The last and most subtle readout figure of merit is efficiency, which characterizes the ratio of the number of controlled and uncontrolled information channels in the readout. Maximizing this ratio is of utmost importance for performing remote entanglement by measurement 50 . Like qubit coherence, and benefiting from it, progress in QND performance has been spectacular Is It Just About Scaling Up? Up to now, most of the experiments have been done on a relatively small scale, involving only a handful of interacting qubits or degrees of freedom; see We argue that the answers to both questions will probably be "No." The work by the community during the past decade and a half, leading up to the capabilities summarized in the first part of Superconducting circuits 7 What Will We Learn About Active Architectures During the Next Stage? How long might it take to realize robust and practical error correction with superconducting circuits? This will depend on how rapidly the experimental techniques and capabilities Superconducting circuits 8 Here, information is redundantly encoded in a register of entangled physical qubits (typically, at least seven) to create a single logical qubit. Assuming that errors occur singly, one detects them by measuring a set of certain collective properties (known as stabilizer operators) of the qubits, and then applies appropriate additional gates to undo the errors before the desired information is irreversibly corrupted. Thus, an experiment to perform gates between a pair of logically encoded qubits might take a few dozen qubits, with hundreds to thousands of individual operations. To reach a kind of "break-even" point and perform correctly, it is required that there should be less than one error on average during a single pass of the QEC. For a large calculation, the codes must then be concatenated, with each qubit again being replaced by a redundant register, in a tree like hierarchy. The so-called error correction threshold, where the resources required for this process of expansion begin to converge, is usually estimated 26 to lie in the range of error rates of 10 −3 to 10 −4 , requiring values of 10 3 to 10 4 for the elements of Superconducting circuits 9 Finally, the best strategy might include ideas that are radically different from those considered standard fare in quantum information science. Much may be gained by looking for shortcuts that are hardware-specific and optimized for the particular strengths and weaknesses of a particular technology. For instance, all of the schemes described above are based on a "qubit register model," where one builds the larger Hilbert space and the required redundancy from a collection of many individual two-level systems. But for superconducting circuits, the "natural units" are oscillators with varying degrees of nonlinearity, rather than true two-level systems. The use of noncomputational states beyond the first two levels is of course known in atomic physics, and has already been used as a shortcut to two-and three qubit gates in superconducting circuits 23, The Path Forward The field of QIP with superconducting circuits has made dramatic progress, and has already demonstrated most of the basic functionality with reasonable (or even surprising) levels of performance. Remarkably, we have not yet encountered any fundamental physical principles that would prohibit the building of quite large quantum processors. The demonstrated capabilities of superconducting circuits, as in trapped ions and cold atoms, mean that QIP is beginning what may be one of its most interesting phases of development. Here, one enters a true terra incognita for complex quantum systems, as QEC becomes more than a theoretical discipline. As in the past, this era will include new scientific innovations and basic questions to be answered. Even if this stage is successful, there will remain many further stages of development and technical challenges to be mastered before useful quantum information processing could become a reality. However, we think it is unlikely to become a purely technological enterprise, like sending a man to the Moon, in the foreseeable future. After all, even the Moore's law progression of CMOS integrated circuits over the past four decades has not brought the end of such fields as semiconductor physics or nanoscience, but rather enabled, accelerated, and steered them in unanticipated directions. We feel that future progress in quantum computation will always require the robust, continual development of both scientific understanding and engineering skill within this new and fascinating arena.