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Chinese Physics B

Distributed quantum computation with superconducting qubit via LC circuit using dressed states

Chao Wu, Mao-Fa Fang, Xing Mao Xiao, Yan‐Ling Li, Shuai Cao

Published Feb 1, 2011• 5 citations
Publisher

Abstract

A scheme is proposed where two superconducting qubits driven by a classical field interacting separately with two distant LC circuits connected by another LC circuit through mutual inductance, are used for implementing quantum gates. By using dressed states, quantum state transfer and quantum entangling gate can be implemented. With the help of the time-dependent electromagnetic field, any two dressed qubits can be selectively coupled to the data bus (the last LC circuit), then quantum state can be transferred from one dressed qubit to another and multi-mode entangled state can also be formed. As a result, the promising perspectives for quantum information processing of mesoscopic superconducting qubits are obtained and the distributed and scalable quantum computation can be implemented in this scheme.

DOI
10.1088/1674-1056/20/2/020305

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A scheme is proposed where two superconducting qubits driven by a classical field interacting separately with two distant LC circuits connected by another LC circuit through mutual inductance, are used for implementing quantum gates. By using dressed states, quantum state transfer and quantum entangling gate can be implemented. With the help of the time-dependent electromagnetic field, any two dressed qubits can be selectively coupled to the data bus (the last LC circuit), then quantum state can be transferred from one dressed qubit to another and multi-mode entangled state can also be formed. As a result, the promising perspectives for quantum information processing of mesoscopic superconducting qubits are obtained and the distributed and scalable quantum computation can be implemented in this scheme.
We study a coupling (decoupling) method between a superconducting qubit and a data bus that uses a controllable time-dependent electromagnetic field (TDEF). As in recent experiments, the data bus can be either an LCLCLC circuit or a cavity field. When the qubit and the data bus are initially fabricated, their detuning should be made far larger than their coupling constant, so these can be treated as two independent subsystems. However, if a TDEF is applied to the qubit, then a ``dressed qubit'' (i.e., qubit plus the electromagnetic field) can be formed. By choosing appropriate parameters for the TDEF, the dressed qubit can be coupled to the data bus and, thus, the qubit and the data bus can exchange information with the assistance of the TDEF. This mechanism allows the scalability of the circuit to many qubits. With the help of the TDEF, any two qubits can be selectively coupled to (and decoupled from) a common data bus. Therefore, quantum information can be transferred from one qubit to another.
A mesoscopic circuit, where field quantization (e.g., coherent states and squeezed states) can be exhibited, is one of the ideal quantum systems for manifesting diverse quantum field theoretical phenomena and thermally statistical characteristics. Because of inevitable electromagnetic coupling (e.g., mutual capacitor coupling and mutual inductor coupling) in two neighboring mesoscopic electric circuits, quantum effects relevant to mesoscopic circuit coupling may play a key role in some devices of quantum information processing. Such a circuit coupling can lead to circuit entangled states, where the Fock number states of energy quanta in different circuits are entangled with each other. Since the time dependence in parameters of coupled-circuit Hamiltonian would result from environmental perturbations (e.g., temperature fluctuations in devices) or from some controllable manipulation (e.g., an incident ultrasonic wave), the circuit entangled states would evolve due to these external conditions. Time evolution of entangled states in coupled mesoscopic circuits is considered within a framework of time-dependent quantum theoretical formalism. Note that an applied photon field can also be coupled to such quantum entangled circuits. Then it is possible that an effect of entanglement transfer (i.e., transportation of superposition coefficients in the entangled state) from the quantum mesoscopic coupled LC circuits to the applied external photon field would also occur under some proper parameter conditions. The present characteristics of both quantized coupled mesoscopic circuits and entanglement transfer can also be found in some alternative microscopic- and mesoscopic-scale devices such as the systems in cavity quantum electrodynamics (QED).
Quantum system based on superconducting circuit is considered as one of the most promising schemes to realize quantum computers due to its controllability, low dissipation and scalability. To implement large scale quantum computation, coherent coupling between qubits is crucial for controlling and transferring quantum states. In this review paper, we summarize the progress of coupled superconducting qubits, including local coupling via capacitance or inductance, multiple qubits coherent interaction through one-dimensional resonator as circuit quantum electrodynamics, and superconducting qubits in a three-dimensional waveguide cavity. Hamiltonians of various coupling schemes are analyzed and classification of these coupling structures is summarized based on the coupling range and tunability.
After a brief review on superconducting qubits, we overview our recent studies on controllable couplings in superconducting flux qubits via a variable frequency (ac) magnetic flux. In particular: (i) we describe how to use a variable frequency magnetic flux to control the coupling between two inductively coupled flux qubits, (ii) Based on this approach, using a variable frequency controlled coupling, we present a proposal on how to achieve scalable quantum computing circuits with flux qubits. We also explain why superconducting qubits can be coupled and addressed as trapped ions, as well as describe how to utilize dressed states to couple and decouple qubits and the data bus.
We propose an effective scheme for manipulating quantum information stored in a superconducting nanocircuit. The Josephson qubits are coupled via their separate interactions with an information bus, a large current-biased Josephson junction treated as an oscillator with adjustable frequency. The bus is sequentially coupled to only one qubit at a time. Distant Josephson qubits without any direct interaction can be indirectly coupled with each other by independently interacting with the bus sequentially, via exciting/deexciting vibrational quanta in the bus. This is a superconducting analog of the successful ion trap experiments on quantum computing. Our approach differs from previous schemes that simultaneously coupled two qubits to the bus, as opposed to their sequential coupling considered here. The significant quantum logic gates can be realized by using these tunable and selective couplings. The decoherence properties of the proposed quantum system are analyzed within the Bloch-Redfield formalism. Numerical estimations of certain important experimental parameters are provided.