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arXiv:quant-ph/0506261 · Physical Review B

Unified approach for universal quantum gates in a coupled superconducting two-qubit system with fixed always-on coupling

Zhongyuan Zhou, Shih‐I Chu, Siyuan Han

Published Mar 30, 2006• 6 citations
arXivHTMLPDF

Abstract

We demonstrate that in a coupled two-qubit system any single-qubit gate can be decomposed into \ensuremath{\mid}0⟩-controlled and \ensuremath{\mid}1⟩-controlled two-qubit gates which can be implemented by manipulations analogous to that used for a controlled NOT (CNOT) gate. Based on this we present a unified approach to implement universal single-qubit and two-qubit gates in a coupled two-qubit system with fixed always-on coupling. This approach requires neither supplementary circuit or additional physical qubits to control the coupling nor extra hardware to adjust the energy level structure. The feasibility of this approach is demonstrated by numerical simulation of single-qubit gates and creation of two-qubit Bell states in rf-driven inductively coupled two superconducting quantum interference device flux qubits with realistic device parameters and constant always-on coupling.

DOI
10.1103/physrevb.73.104521

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We demonstrate that in a coupled two-qubit system any single-qubit gate can be decomposed into \ensuremath{\mid}0⟩-controlled and \ensuremath{\mid}1⟩-controlled two-qubit gates which can be implemented by manipulations analogous to that used for a controlled NOT (CNOT) gate. Based on this we present a unified approach to implement universal single-qubit and two-qubit gates in a coupled two-qubit system with fixed always-on coupling. This approach requires neither supplementary circuit or additional physical qubits to control the coupling nor extra hardware to adjust the energy level structure. The feasibility of this approach is demonstrated by numerical simulation of single-qubit gates and creation of two-qubit Bell states in rf-driven inductively coupled two superconducting quantum interference device flux qubits with realistic device parameters and constant always-on coupling.
We present an approach to realize universal two-bit quantum gates using two SQUID flux qubits. In this approach the basic unit consists of two inductively coupled SQUIDs with realistic device parameters. Quantum logical gates are implemented by applying resonant microwave pulse to the qubits. This procedure is demonstrated by realizing a controlled-NOT (CNOT) gate and the maximally entangled states of the coupled qubits through highly accurate numerical solution of the time-dependent Schrodinger equation of the system. This coupling scheme is simple and can be readily extended to many-qubit circuits required for scalable quantum information processing.
We apply the quantum optimal control theory based on the Krotov method to implement single-qubit XXX and ZZZ gates and two-qubit cnot gates for inductively coupled superconducting flux qubits with fixed qubit transition frequencies and fixed off-diagonal qubit-qubit coupling. Our scheme shares an advantage with other direct-coupling schemes in that it requires no additional coupler subcircuit and control lines. The control lines needed are only for the manipulation of individual qubits (e.g., a time-dependent magnetic flux or field applied on each qubit). The qubits are operated at the optimal coherence points and the gate operation times (less than 1 ns for single-qubit gates and $\ensuremath{\sim}2$ ns for cnotgates) are much shorter than the corresponding qubit decoherence time. A cnot gate or other general quantum gates can be implemented in a single run of the pulse sequence rather than being decomposed into several single-qubit and several entangled two-qubit operations in series by composite pulse sequences. Quantum gates constructed via our scheme are all with very high fidelity (very low error) as our optimal control scheme takes into account the fixed qubit detuning and fixed two-qubit interaction as well as all other time-dependent magnetic-field-induced single-qubit interactions and two-qubit couplings. The effect of leakage to higher-energy-level states and the effect of qubit decoherence on the quantum-gate operations are also discussed.
A register of quantum bits with fixed transition frequencies and weakly coupled to one another through simple linear circuit elements is an experimentally minimal architecture for a small-scale superconducting quantum information processor. Presently, the known schemes for implementing two-qubit gates in this system require microwave signals having amplitudes and frequencies precisely tuned to meet a resonance condition, leaving only the signal phases as free experimentally adjustable parameters. Here, we report a minimal and robust microwave scheme to generate fast, tunable universal two-qubit gates: simply irradiate one qubit (the ``control'') at the transition frequency of another (the ``target''). The effective coupling between them is then switched on by tuning only the frequency of this single drive tone; the drive amplitude adjusts the effective coupling strength; and the drive phase selects the particular two-qubit gate implemented. This cross-resonance effect turns on linearly with the ratio of the drive amplitude $\ensuremath{\Omega}$ to the qubit-qubit detuning $\ensuremath{\Delta}$, as compared with earlier proposals that turn on as ${(\ensuremath{\Omega}/\ensuremath{\Delta})}^{4}$.
Among all the quantum computer candidates, the superconducting system is one of the most convincing platforms due to its strong couplings and scalability. To be more specific, this thesis focuses on the superconducting system, in which the artificial atoms are controlled longitudinally and coupled without any intermediate devices. We propose a superconducting decoupling method in this thesis. Firstly, we state that our algorithm can effectively ‘turn off’ arbitrary couplings. Then, we analyze the errors of our decoupling method and prove that the errors are ignorable when a sequence of decoupling gates are applied on non-nearest-neighboring qubits. We verify the efficiency of our decoupling method using the numerical simulations, which are well-matched with the theoretical predictions. Using 99.6% fidelity isolated CNOT and 99.89% single-qubit gates, we obtain a fidelity of 97.8% with the CNOT implementation in a five-qubit system over 14.84 ns.
A superconducting fluxonium circuit is an RF-superconducting quantum interference device-type flux qubit that uses a large inductance built from an array of Josephson junctions or a high kinetic inductance material. This inductance suppresses charge sensitivity exponentially and flux sensitivity quadratically. In contrast to the transmon qubit, the anharmonicity of fluxonium can be large and positive, allowing for better separation between the low energy qubit manifold of the circuit and higher-lying excited states. Here, we propose a tunable coupling scheme for implementing two-qubit gates on fixed-frequency fluxonium qubits, biased at half flux quantum. In this system, both qubits and couplers are coupled capacitively and implemented as fluxonium circuits with an additional harmonic mode. We investigate the performance of the scheme by simulating a universal two-qubit fSim gate. In the proposed approach, we rely on a planar on-chip architecture for the whole device. Our design is compatible with existing hardware for transmon-based devices with the additional advantage of lower qubit frequency facilitating high-precision gating.
We propose an approach to realize an nnn-qubit controlled-UUU gate with superconducting quantum interference devices (SQUIDs) in cavity QED. In this approach, the two lowest levels of a SQUID represent the two logical states of a qubit while a higher-energy intermediate level serves the gate manipulation. Our method operates essentially by creating a single photon through one of the control SQUIDs and then performing an arbitrary unitary transformation on the target SQUID with the assistance of the cavity photon. In addition, we show that the method can be applied to implement an nnn-qubit controlled-UUU gate with atomic qubits in cavity QED.