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arXiv:1108.2984 · Physical Review A

Quantum logic gates for superconducting resonator qudits

Frederick W. Strauch

Published Nov 11, 2011• 45 citations
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Abstract

We study quantum information processing using superpositions of Fock states in superconducting resonators as quantum $d$-level systems (qudits). A universal set of single and coupled logic gates is theoretically proposed for resonators coupled by superconducting circuits of Josephson junctions. These gates use experimentally demonstrated interactions and provide an attractive route to quantum information processing using harmonic oscillator modes.

DOI
10.1103/physreva.84.052313

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We study quantum information processing using superpositions of Fock states in superconducting resonators as quantum ddd-level systems (qudits). A universal set of single and coupled logic gates is theoretically proposed for resonators coupled by superconducting circuits of Josephson junctions. These gates use experimentally demonstrated interactions and provide an attractive route to quantum information processing using harmonic oscillator modes.
Two-level system fluctuators in superconducting devices have demonstrated coherent coupling with superconducting qubits. Here, we show that universal quantum logic gates can be realized in these two-level systems solely by tuning a superconducting resonator in which they are imbedded. Because of the large energy separation between the fluctuators, conventional gate schemes in the cavity QED approach that are widely used for solid-state qubits cannot be directly applied to the fluctuators. We study a scheme to perform the gate operations by exploiting the controllability of the superconducting resonator with realistic parameters. Numerical simulation that takes into account the decay of the resonator mode shows that the quantum logic gates can be realized with high fidelity at moderate resonator decay rate. The quantum logic gates can also be realized between fluctuators inside different Josephson junctions that are connected by a superconducting loop. Our scheme can be applied to explore the coupling between two-level system fluctuators and superconducting resonators as well as the coherent properties of the fluctuators.
Recent experiments motivated by applications to quantum information processing are probing a new and fascinating regime of electrical engineering—that of quantum electrical circuits—where macroscopic collective variables such as polarization charge and electric current exhibit quantum coherence. Here I discuss the problem of constructing a quantum mechanical Hamiltonian for the low-frequency modes of such a circuit, focusing on the case of a superconducting qubit coupled to a harmonic oscillator or resonator, an architecture that is being pursued by several experimental groups. 1 Quantum gate design In the quantum circuit model of quantum information processing, an arbitrary unitary transformation on N qubits can be decomposed into a sequence of certain universal two-qubit logical operations acting on pairs of qubits, combined with arbitrary single-qubit rotations [1]. The purpose of quantum gate design is to develop experimental protocols or “machine language code ” to implement these elementary operations. For quantum information processing architectures based on superconducting circuits [2, 3], the first step is to construct an effective Hamiltonian for the system. Whereas the fully
Quantum computing holds the promise of a novel form of information processing in which data resides in quantum states. By exploiting superpositions and entanglement among these states, quantum logic operations are expected to far surpass conventional digital logic in certain classes of problems. To realize this prospect, we employ superconducting circuits at millikelvin temperatures. The nonlinearity of a Josephson tunnel junction enables a two-level quantum system, or qubit, with excitation energy in the microwave regime. Key recent advances in such devices are the demonstration of robust and simple multi-qubit gates, the integration of superconducting qubits into arrays of four or more, and gate fidelities reaching 99%. [1,2,3]
We propose a tunable nonlinear interaction for the implementation of quantum logic operations on pairs of superconducting resonators, where the two-resonator interaction is mediated by a transmon quantum bit (qubit). This interaction is characterized by a high on-to-off coupling ratio and allows for fast qubit-type and ddd-level system (qudit)-type operations for quantum information processing with multiphoton cavity states. We present analytical and numerical calculations showing that these operations can be performed with practically unit fidelity in absence of any dissipative phenomena, whereas physical two-photon two-resonator operations can be realized with a fidelity of 99.9% in presence of qubit and resonator decoherence. The resonator-qubit-resonator system proposed in this Letter can be implemented using available planar or three-dimensional microwave technology.
Gate-based quantum computers typically encode and process information in two-dimensional units called qubits.Using d-dimensional qudits instead may offer intrinsic advantages, including more efficient circuit synthesis, problem-tailored encodings and embedded error correction.In this work, we design a superconducting qudit-based quantum processor wherein the logical space of transmon qubits is extended to higher-excited levels.We propose a universal gate set featuring a two-qudit cross-resonance entangling gate, for which we predict fidelities beyond 99% in the d = 4 case of ququarts with realistic experimental parameters.Furthermore, we present a decomposition routine that compiles general qudit unitaries into these elementary gates, requiring fewer entangling gates than qubit alternatives.As proof-of-concept applications, we numerically demonstrate the synthesis of SU(16) gates for noisy quantum hardware and an embedded error-correction sequence that encodes a qubit memory in a transmon ququart to protect against pure dephasing noise.We conclude that universal qudit control-a valuable extension to the operational toolbox of superconducting quantum information processing-is within reach of current transmon-based architectures and has applications to near-term and long-term hardware.
The two-level systems (TLSs) naturally occurring in Josephson junctions constitute a major obstacle for the operation of superconducting phase qubits. Since these TLSs can possess remarkably long decoherence times, we show that such TLSs can themselves be used as qubits, allowing for a well controlled initialization, universal sets of quantum gates, and readout. Thus, a single current-biased Josephson junction can be considered as a multiqubit register. It can be coupled to other junctions to allow the application of quantum gates to an arbitrary pair of qubits in the system. Our results indicate an alternative way to realize superconducting quantum information processing.