Unimodular relativity is a theory of gravity and space-time with a fixed absolute space-time volume element, the modulus, which we suppose is proportional to the number of microscopic modules in that volume element. In general relativity an arbitrary fixed measure can be imposed as a gauge condition, while in unimodular relativity it is determined by the events in the volume. Since this seems to break general covariance, some have suggested that it permits a non-zero covariant divergence of the material stress-energy tensor and a variable cosmological "constant." In Lagrangian unimodular relativity, however, even with higher-derivatives of the gravitational field in the dynamics, the usual covariant continuity holds and the cosmological constant is still a constant of integration of the gravitational field equations.

A possible building block for a scalable quantum computer has recently been demonstrated [M. Mariantoni et al., Science 334, 61 (2011)]. 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 controlled-σ z (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 17 ns (23 ns) 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 multiqubit 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. I. QVN ARCHITECTUREReaching the fidelity threshold for fault-tolerant quantum computation with superconducting electrical circuits [1-3] will probably require improvement in three areas: qubit coherence, readout, and qubit-qubit coupling tunability. Fortunately, the coherence times of superconducting transmon qubits [4,5] have increased dramatically, exceeding 10µs in the three-dimensional version [6,7]. Fast, threshold-fidelity nondestructive measurement has not yet been demonstrated, but is being actively pursued [8][9][10][11][12]. Some method for turning off the interaction between device elements-beyond simple frequency detuning-is also desirable for high-fidelity operations.

We analyze the performance of the Resonator/zero-Qubit (RezQu) architecture in which the qubits are complemented with memory resonators and coupled via a resonator bus. Separating the stored information from the rest of the processing circuit by at least two coupling steps and the zero qubit state results in a significant increase of the ON/OFF ratio and the reduction of the idling error. Assuming no decoherence, we calculate such idling error, as well as the errors for the MOVE operation and tunneling measurement, and show that the RezQu architecture can provide high fidelity performance required for medium-scale quantum information processing.

Current quantum computing architectures lack the size and fidelity required for universal faulttolerant operation, limiting the practical implementation of key quantum algorithms to all 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 Schrödinger equation with a real but otherwise arbitrary n×n 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.