We propose to use the continuous version of the quantum Zeno effect to eliminate leakage to higher energy states in superconducting quantum computing architectures based on Josephsonphase and flux qubits. We are particularly interested in the application of this approach to the single-step Greenberger-Horne-Zeilinger (GHZ) state protocol described in [A. Galiautdinov and J. M. Martinis, Phys. Rev. A 78, 010305(R) (2008)]. While being conceptually appealing, the protocol was found to be plagued with a number of spectral crowding and leakage problems. Here we argue that by coupling the qubits to a measuring device which continuously monitors leakage to higher energy states (say, to a very lossy resonator of frequency omega = E3(qubit)-E1(qubit), with 1 labeling the ground state of the qubit), we could potentially restrict the multi-qubit system’s evolution to its computational subspace, thus circumventing the above mentioned problems.

Current quantum computing architectures lack the size and fidelity required for universal fault-tolerant operation, limiting the practical implementation of key quantum algorithms toall but the smallest problem sizes. In this work we propose an alternative method for general-purpose quantum computation that is ideally suited for such „prethreshold“ superconducting hardware. Computations are performed in the n-dimensional single-excitation subspace (SES) of a system of n tunably coupled superconducting qubits. The approach is not scalable, but allows many operations in the unitary group SU(n) to be implemented by a single application of the Hamiltonian, bypassing the need to decompose a desired unitary into elementary gates. This feature makes large, nontrivial quantum computations possible within the available coherence time. We show how to use a programmable SES chip to perform fast amplitude amplification and phase estimation, two versatile quantum subalgorithms. We also show that an SES processor is well suited for Hamiltonian simulation, specifically simulation of the Schrodinger equation with a real but otherwise arbitrary nxn Hamiltonian matrix. We discuss the utility and practicality of such a universal quantum simulator, and propose its application to the study of realistic atomic and molecular collisions.

We analyze single-shot readout for superconducting qubits via controlled catch, dispersion, and release of a microwave field. A tunable coupler is used to decouple the microwave resonatorfrom the transmission line during the dispersive qubit-resonator interaction, thus circumventing damping from the Purcell effect. We show that if the qubit frequency tuning is sufficiently adiabatic, a fast high-fidelity qubit readout is possible even in the strongly nonlinear dispersive regime. Interestingly, the Jaynes-Cummings nonlinearity leads to the quadrature squeezing of the resonator field below the standard quantum limit, resulting in a significant decrease of the measurement error.

. This architecture
consists of superconducting"]qubits capacitively coupled both to individual
memory resonators as well as a common bus. In this work we study a natural
primitive entangling gate for this and related resonator-based architectures,
which consists of a CZ operation between a qubit and the bus. The CZ gate is
implemented with the aid of the non-computational qubit |2> state [F. W.
Strauch et al., Phys. Rev. Lett. 91, 167005 (2003)]. Assuming phase or transmon
qubits with 300 MHz anharmonicity, we show that by using only low frequency
qubit-bias control it is possible to implement the qubit-bus CZ gate with 99.9%
(99.99%) fidelity in about 17ns (23ns) with a realistic two-parameter pulse
profile, plus two auxiliary z rotations. The fidelity measure we refer to here
is a state-averaged intrinsic process fidelity, which does not include any
effects of noise or decoherence. These results apply to a multi-qubit device
that includes strongly coupled memory resonators. We investigate the
performance of the qubit-bus CZ gate as a function of qubit anharmonicity,
indentify the dominant intrinsic error mechanism and derive an associated
fidelity estimator, quantify the pulse shape sensitivity and precision
requirements, simulate qubit-qubit CZ gates that are mediated by the bus
resonator, and also attempt a global optimization of system parameters
including resonator frequencies and couplings. Our results are relevant for a
wide range of superconducting hardware designs that incorporate resonators and
suggest that it should be possible to demonstrate a 99.9% CZ gate with existing
transmon qubits, which would constitute an important step towards the
development of an error-corrected superconducting quantum computer.