Experimental detection of entanglement in superconducting qubits has been mostly limited, for more than two qubits, to witness-based and related approaches that can certify the presenceof some entanglement, but not rigorously quantify how much. Here we measure the entanglement of three- and four-qubit GHZ and linear cluster states prepared on the 16-qubit IBM Rueschlikon (ibmqx5) chip, by estimating their entanglement monotones. GHZ and cluster states not only have wide application in quantum computing, but also have the convenient property of having similar state preparation circuits and fidelities, allowing for a meaningful comparison of their degree of entanglement. We also measure the decay of the monotones with time, and find in the GHZ case that they actually oscillate, which we interpret as a drift in the relative phase between the |0⟩⊗n and |1⟩⊗n components, but not an oscillation in the actual entanglement. After experimentally correcting for this drift with virtual Z rotations we find that the GHZ states appear to be considerably more robust than cluster states, exhibiting higher fidelity and entanglement at later times. Our results contribute to the quantification and understanding of the strength and robustness of multi-qubit entanglement in the noisy environment of a superconducting quantum computer.
We study a circuit, the Josephson sampler, that embeds a real vector into an entangled state of n qubits, and optionally samples from it. We measure its fidelity and entanglement onthe 16-qubit ibmqx5 chip. To assess its expressiveness, we also measure its ability to generate Haar random unitaries and quantum chaos, as measured by Porter-Thomas statistics and out-of-time-order correlation functions. The circuit requires nearest-neighbor CZ gates on a chain and is especially well suited for first-generation superconducting architectures.
Multiple bosons undergoing coherent evolution in a coupled network of sites constitute a so-called quantum walk system. The simplest example of such a two-particle interference is thecelebrated Hong-Ou-Mandel interference. When scaling to larger boson numbers, simulating the exact distribution of bosons has been shown, under reasonable assumptions, to be exponentially hard. We analyze the feasibility and expected performance of a globally connected superconducting resonator based quantum walk system, using the known characteristics of state-of-the-art components. We simulate the sensitivity of such a system to decay processes and to perturbations and compare with coherent input states.
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 study a recently demonstrated design for a high-performance tunable coupler suitable for superconducting Xmon and planar transmon qubits. The coupler circuit uses a single flux-biasedJosephson junction and acts as a tunable current divider. We calculate the effective qubit-qubit interaction Hamiltonian by treating the nonlinearity of the qubit and coupler junctions perturbatively. We find that the qubit nonlinearity has two principal effects: The first is to suppress the magnitude of the transverse XX coupling from that obtained in the harmonic approximation by about 15%. The second is to induce a small diagonal ZZ coupling. The effects of the coupler junction nonlinearity are negligible in the parameter regime considered.
We introduce a superconducting qubit architecture that combines high-coherence qubits and tunable qubit-qubit coupling. With the ability to set the coupling to zero, we demonstratethat this architecture is protected from the frequency crowding problems that arise from fixed coupling. More importantly, the coupling can be tuned dynamically with nanosecond resolution, making this architecture a versatile platform with applications ranging from quantum logic gates to quantum simulation. We illustrate the advantages of dynamic coupling by implementing a novel adiabatic controlled-Z gate, at a speed approaching that of single-qubit gates. Integrating coherence and scalable control, our „gmon“ architecture is a promising path towards large-scale quantum computation and simulation.
A controlled-phase gate was demonstrated in superconducting Xmon transmon qubits with fidelity reaching 99.4%, relying on the adiabatic interaction between the |11> and |02> states.We explain how adiabaticity is achieved even for fast gate times, based on a theory of non-linear mapping of state errors to a power spectral density and use of optimal window functions. With a solution given in the Fourier basis, optimization is shown to be straightforward for practical cases of an arbitrary state change and finite bandwidth of control signals. We find that errors below 10^-4 are readily achievable for realistic control waveforms.
. 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.