Holonomic quantum computation using rf superconducting quantum interference devices coupled through a microwave cavity

Superconducting QUantum Interference Device (SQUID) metamaterials are superconducting artificial media whose function relies both on their geometry and the extraordinary properties of superconductivity and the Josephson effect. Recent experiments on one- and two-dimensional radio-frequency (rf) SQUID metamaterials have revealed their wide-band tuneability, significantly reduced losses, dynamic multistability, and tunable broadband transparency. The simplest version of an rf SQUID involves a superconducting ring interrupted by a Josephson junction; this device is a highly nonlinear resonator with a strong response to applied magnetic fields. SQUID metamaterials exhibit peculiar magnetic properties such as negative diamagnetic permeability, predicted both for the quantum and the classical regime. The applied alternating fields induce (super)currents in the SQUID rings, which are therefore coupled through dipole-dipole magnetic forces. This interaction is weak due to its magnetic nature. However, it couples the SQUIDs non-locally since it falls-off as the inverse cube of their center-to-center distance.

The superconducting quantum interference device (SQUID) is a highly sensitive detector for magnetic flux or any quantity that can be efficiently converted into flux. This chapter provides a short introduction into the basic function of a SQUID, its operation, and its design for magnetic field and current sensing. It shows by several examples that the device is very versatile and important for a variety of applications such as biomagnetism, astronomy, low-temperature physics, and metrology. The chapter measures with the commercial variant of the electronics and include the noise contribution from the preamplifier and shows the noise spectra as examples. The dc SQUID is dominant in the field of Nbbased sensors, and the rf SQUID is practically obsolete. The dc SQUID is based on two effects: flux quantization and superconducting tunneling. The chapter presents equations for calculating the inductance and the effective field-sensitive area of two representative superconducting structures.

An rf superconducting quantum interference device (SQUID) has been made from bulk Y-Ba-Cu-O. The device displays quantum interference effects and operates with useful signal levels up to 81 K. The SQUID is formed from a ring of Y-Ba-Cu-O which is broken in the cryogenic environment and then recontacted. Estimates of the SQUID noise performance are given.

We have developed a matching scheme for the operation of a rf superconducting quantum interference device (SQUID) with a lumped-element tank circuit at pumping frequencies up to 1 GHz. This conventional LC resonant circuit is inductively coupled to a matching coil, which is connected to the 50 Ω transmission line. We characterized the flux noise of high-temperature rf SQUIDs at resonant frequencies between 221 and 950 MHz. At about 900 MHz, we obtained the white flux noise of about 14.6 μφ0/Hz with a SQUID inductance LS=150 pH and 20 μφ0/Hz with LS=260 pH. Several of such tank circuits can be driven in parallel or in series with only one cable.

A high-T/sub c/ superconducting galvanometer with a sensitivity of 2*10/sup -12/ A/ square root Hz for input resistance of 250 Omega is reported. Its sensor is a YBaCuO RF SQUID (superconducting quantum interference device) that operates at 77 K. In the absence of high-T/sub c/ superconducting wires, this RF SQUID solves the problem of coupling between the signal and SQUID ring very well. >

A scheme for implementing a conditional z gate in the decoherence-free subspace of superconducting quantum-interference devices (SQUIDs) is presented based on the dispersive interaction. Each logic qubit is encoded in the ground states of two rf SQUIDs, which own lower energy and can be relatively stable in operation. By switching on/off the classical pulses and selecting the gating time appropriately, a high fidelity is obtained. Moreover, this scheme can be generalized to the multi-qubit case without changing the gating time.

Fabrication of low noise high-T c bicrystal junction rf SQUID

A dc-current control using a commercial-type of RF superconducting quantum interference device (SQUID) system has been developed for high-resolution nuclear magnetic resonance (NMR) experiments. The control unit is a superposed regulator designed to increase the stability of ordinary current sources with resistive feedback loops. Thus currents in the range 0.1 A to 1 A have been stabilized to better than 0.01 ppm/h.

The response of a superconducting quantum interference device (SQUID) to an oscillating external flux is studied numerically. Parameter ranges for the appearance of complicated periodic and chaotic behavior are given. It is shown that the strange attractor characterizing the chaotic regimes can be described by a one-dimensional return map.

Since the advent of rf and dc SQUIDs (Superconducting Quantum Interference Devices) in the mid-sixties, new ways to apply their remarkable properties have been sought and developed. The development of applications has paralleled the growing sophistication in fabrication, from simple point-contacts to complex micron-scale thin-film tunnel-junction structures, and has taken full advantage of increases in sensitivity which have come with improved understanding of noise processes. Low-Tc SQUIDs have now been applied in a number of areas including biomagnetism, geophysics, gravity measurement and non-destructive evaluation and there are indications that the story will be repeated as high-Tc SQUIDs develop: existing applications are being explored again with 77 K devices, and new applications are in sight.

Among the many proposals for the realization of a quantum computer, holonomic\nquantum computation (HQC) is distinguished from the rest in that it is\ngeometrical in nature and thus expected to be robust against decoherence. Here\nwe analyze the realization of various quantum gates by solving the inverse\nproblem: Given a unitary matrix, we develop a formalism by which we find loops\nin the parameter space generating this matrix as a holonomy. We demonstrate for\nthe first time that such a one-qubit gate as the Hadamard gate and such\ntwo-qubit gates as the CNOT gate, the SWAP gate and the discrete Fourier\ntransformation can be obtained with a single loop.\n

The controlled-not gate and the single qubit gates are considered elementary gates in quantum computing. It is natural to ask how many such elementary gates are needed to implement more elaborate gates or circuits. Recall that a controlled-U gate can be realized with two controlled-not gates and four single qubit gates. We prove that this implementation is optimal if and only if the matrix U satisfies the conditions trU\neq 0, tr(UX)\neq 0, and detU\neq 1. We also derive optimal implementations in the remaining non-generic cases. realizations of controlled unitary gates (pp139-155) G. Song and A. Klappenecker The controlled-not gate and the single qubit gates are considered elementary gates in quantum computing. It is natural to ask how many such elementary gates are needed to implement more elaborate gates or circuits. Recall that a controlled-U gate can be realized with two controlled-not gates and four single qubit gates. We prove that this implementation is optimal if and only if the matrix U satisfies the conditions trU\neq 0, tr(UX)\neq 0, and detU\neq 1. We also derive optimal implementations in the remaining non-generic cases.

The response of a generic stochastic bistable system to a periodic driving force in the adiabatic limit is investigated, nonperturbatively, with a model based on the steady state probability distribution of the system's dynamic variable. The model reveals important scaling properties of the system. For instance, the effects of noise intensity, modulation strength, and potential asymmetry are found to be universally determined by two dimensionless parameters: the amplitude of energy modulation and the potential energy asymmetry scaled to the noise intensity. We show that, in general, a system's response at the modulation frequency and its harmonics are uniquely characterized by these two parameters. The excellent quantitative agreement between our model calculations and experimental data obtained from a rf superconducting quantum interference device, without any adjustable parameters, demonstrates the power of our simple theoretical treatment of the problem.

There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and two-qubit CNOT gates. A CNOT gate is however not always the natural multi-qubit interaction that can be implemented on a given physical quantum computer, necessitating a compilation step that transforms these CNOT gates to the native gate set. An especially interesting case where compilation is necessary is for ion trap quantum computers, where the natural entangling operation can act on more than two qubits and can even act globally on all qubits at once. This calls for an entirely different approach to constructing efficient circuits. In this paper we study the problem of converting a given circuit that uses two-qubit gates to one that uses global gates. Our three main contributions are as follows. First, we find an efficient algorithm for transforming an arbitrary circuit consisting of Clifford gates and arbitrary phase gates into a circuit consisting of single-qubit gates and a number of global interactions proportional to the number of non-Clifford phases present in the original circuit. Second, we find a general strategy to transform a global gate that targets all qubits into one that targets only a subset of the qubits. This approach scales linearly with the number of qubits that are not targeted, in contrast to the exponential scaling reported in (Maslov and Nam 2018 New J. Phys. 20 033018). Third, we improve on the number of global gates required to synthesise an arbitrary n-qubit Clifford circuit from the 12n − 18 reported in (Maslov and Nam 2018 New J. Phys. 20 033018) to 6n − 8.

Two-qubit gates are important components of quantum computing. However, unwanted interactions between qubits (so-called parasitic gates) can be particularly problematic and degrade the performance of quantum applications. In this work, we present two software methods to mitigate parasitic two-qubit gate errors. The first approach is built upon the Cartan’s KAK decomposition and keeps the original unitary decomposition for the error-free native two-qubit gate. It counteracts a parasitic two-qubit gate by only applying single-qubit rotations and therefore has no two-qubit gate overhead. We show the optimal choice of single-qubit mitigation gates. The second approach applies a numerical optimisation algorithm to re-compile a target unitary into the error-parasitic two-qubit gate plus single-qubit gates. We demonstrate these approaches on the CPhase-parasitic iSWAP-like gates. The KAK-based approach helps decrease unitary infidelity by a factor of 3 compared to the noisy implementation without error mitigation. When arbitrary single-qubit rotations are allowed, recompilation could completely mitigate the effect of parasitic errors but may require more native gates than the KAK-based approach. We also compare their average gate fidelity under realistic noise models, including relaxation and depolarising errors. Numerical results suggest that different approaches are advantageous in different error regimes, providing error mitigation guidance for near-term quantum computers.