Quantum Entanglement and Controlled Logical Gates Using Coupled SQUID Flux Qubits

Zhou, Zhóngyuan; Chu, Shih‐I; Han, Siyuan

doi:10.1109/tasc.2005.850074

Cited by 5 publications

(12 citation statements)

References 20 publications

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“…LC t and H R nn 0 E n nn 0 njVjn 0 =@! LC [25]. The probability of being in the state jn is jc n j 2 , from which the maximum probabilities on the undesired states and the leakage One of the advantages of ITA is that it provides clear physical intuition and insight into the origin of intrinsic gate errors and thus how to reduce the problem by selecting appropriate WPs.…”

Section: -2mentioning

confidence: 99%

“…For weak coupling 1, the eigenstate of the coupled qubits, denoted by jn jiji, can be well approximated by the product of the control qubit's state jii and the target qubit's state jji, jn jiijji. When biased at x e1 , x e2 1=2 the potential of coupled qubits have four wells [7,25]. The lowest eigenstates in each of the four wells, denoted as j1 j00i, j2 j01i, j3 j10i, and j4 j11i, are used as the computational states of the coupled qubits.…”

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confidence: 99%

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Rapid Optimization of Working Parameters of Microwave-Driven Multilevel Qubits for Minimal Gate Leakage

Zhou

Chu²,

Han³

2005

Phys. Rev. Lett.

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We propose an effective method to optimize the working parameters (WPs) of microwave-driven quantum gates implemented with multilevel qubits. We show that by treating transitions between each pair of levels independently, intrinsic gate errors due primarily to population leakage to undesired states can be determined by spectroscopic properties of the qubits and minimized by choosing proper WPs. The validity and efficiency of the approach are demonstrated by applying it to optimize the WPs of two coupled rf SQUID flux qubits for controlled-NOT operation. The result of this independent transition approximation (ITA) is in good agreement with that of dynamic method (DM). The ratio of the speed of ITA to that of DM scales exponentially as 2 n when the number of qubits n increases. DOI: 10.1103/PhysRevLett.95.120501 PACS numbers: 03.67.Lx, 85.25.Dq, 89.70.+c A practical quantum computer would be comprised of a large number of coupled qubits which must be kept in highdegree quantum coherence states for a sufficiently long time. During the past decade, significant progress has been made on quantum computation. High-degree quantum coherence has been demonstrated experimentally in systems such as trapped ions [1,2], nuclear spins [3,4], atoms in optical resonators [5], and photons in microwave cavities [6]. However, it seems quite difficult to realize a large number of coupled qubits using these systems. Meanwhile, solid-state qubits are of particular interest because of their advantages of large-scale integration, flexibility in design, and easy connection to conventional electronic circuits [7]. Of those, qubits based on superconducting devices have recently attracted much attention [8] as manipulation of quantum coherent states has been successfully demonstrated in a variety of single qubits [9-13] and coupled two-qubit systems [14 -18].However, the solid-state qubits demonstrated in experiments so far all have relatively short coherence time and high probability of gate errors [9][10][11][12][13][14][15]17]. One of the causes of these problems is extrinsic gate error arising from interaction between the environment and qubits resulting in decoherence, such as dephasing and relaxation [8]. Another cause is intrinsic gate error resulting from population leakage to undesired states due to the typical multilevel structures of solid-state qubits [19,20]. The intrinsic gate error is crucial since it determines the ultimate performance of the quantum gates and cannot be eliminated by reducing the environmentally caused decoherence.The leakage of a gate can be characterized quantitatively by summing up the maximum transition probabilities to all undesired states of a multilevel qubit [19,20]. It depends strongly on energy level structure and transition matrix elements, i.e., spectroscopic properties of the multilevel qubit determined completely by device parameters (DPs) and external control parameters of the qubit, which we call working parameters (WPs) for simplicity. For instance, inductance (capacitance) of the super...

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Section: -2mentioning

confidence: 99%

mentioning

confidence: 99%

Rapid Optimization of Working Parameters of Microwave-Driven Multilevel Qubits for Minimal Gate Leakage

Zhou

Chu²,

Han³

2005

Phys. Rev. Lett.

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“…26 In this case, the state of Q2 flips if and only if the state of Q1 is ͉1͘. Since the energy level structure for the singlequbit gates and the CNOT gate could be the same the universal single-qubit gates and CNOT gate can be implemented in the same fashion without adjusting interqubit coupling as long as Q1 and Q2 can be addressed individually by microwave pulses which is straightforward to realize, through control/microwave lines of each qubit, with engineered solid-state qubits in general and with rf SQUID flux qubits in particular.…”

mentioning

confidence: 99%

“…In this case, C i = C, L i = L, and I ci = I c for i =1,2. The Hamiltonian of the coupled qubits is 26 the coupling strength. The coupled SQUID qubits are a multilevel system.…”

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

2006

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We demonstrate that in a coupled two-qubit system any single-qubit gate can be decomposed into ͉0͘-controlled and ͉1͘-controlled two-qubit gates which can be implemented by manipulations analogous to that used for a controlled NOT ͑CNOT͒ 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. However, building a practical quantum computer requires the simultaneous operation of a large number of multiqubit gates in a coupled multiqubit system. It has been proved theoretically that any type of multiqubit gate can be decomposed into a set of universal single-qubit gates and a twoqubit gate, such as the controlled-NOT ͑CNOT͒ gate. 16,17 Thus it is imperative to implement the universal single-qubit and two-qubit gates in a multiqubit system with the minimum resource and maximum efficiency. 18 Implementing universal single-qubit gates and two-qubit gates in coupled multiqubit systems can be achieved by turning off and on the coupling between qubits. [18][19][20][21] In these schemes, supplementary circuits were required to control interqubit coupling. However, rapid switching of the coupling results in two serious problems. The first one is gate errors caused by population propagation between qubits. Because the computational states of the single-qubit gates are not a subset of the eigenstates of the two-qubit gates the populations of the computational states propagate from one qubit to another when the coupling is changed, resulting in additional gate errors. The second one is additional decoherence introduced by the supplementary circuits. 22,23 This is one of the biggest obstacles for quantum computing with solid-state qubits, particularly in coupled multiqubit systems. 2 In addition, the use of supplementary circuits also significantly increases the complexity of fabrication and manipulation of the coupled qubits.To circumvent these problems, a couple of alternative schemes, such as those with untunable coupling 22 and always-on interaction, 24 have been proposed. In the first scheme, each logic qubit is encoded by extra physical qubits and coupling between the encoded qubits is constant but can be turned off and on effectively by putting the qubits in and driving them out of the interaction free subspace. In the second scheme, the coupling is always on but the transition energies of the qubits are tuned individually or collectively. These schemes can overcome the problem of undesired population propagation but still suffer from those caused by the supplemen...

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Multistability and self-organization in disordered SQUID metamaterials

Lazarides

Tsironis

2013

Supercond. Sci. Technol.

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Planar arrays of magnetoinductively coupled rf SQUIDs (Superconducting Quantum Interference Devices) belong to the emergent class of superconducting metamaterials that encompass the Josephson effect. These SQUID-based metamaterials acquire their electromagnetic properties from the resonant characteristics of their constitutive elements, i.e., the individual rf SQUIDs. In its simplest version, an rf SQUID consists of a superconducting ring interrupted by a Josephson junction. We investigate the response of a two-dimensional rf SQUID metamaterial to frequency variation of an externally applied alternating magnetic field in the presence of disorder arising from critical current fluctuations of the Josephson elements; in effect, the resonance frequencies of individual SQUIDs are distributed randomly around a mean value. Bistability is observed in the total current-frequency curves both in ordered and disordered SQUID metamaterials; moreover, bistability is favoured by disorder through the improvement of synchronization between SQUID oscillators. Relatively weak disorder widens significantly the bistability region by helping the system to self-organize itself and leads to nearly homogeneous states that change smoothly with varying driving frequency. Also, the total current of the metamaterial is enhanced compared with that of uncoupled SQUIDs, through the synergetic action of coupling and synchronization. The existence of simultaneously stable states that provide either high or low total current, allows the metamaterial to exhibit different magnetic responses that correspond to different values of the magnetic permeability. and provide either high or low total current, allows the metamaterial to exhibit two different magnetic responses that correspond to different values of its magnetic permeability. At low power of the incident field, high-current states exhibit extreme diamagnetic properties corresponding to negative magnetic permeability in a narrow frequency region.

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Quantum Entanglement and Controlled Logical Gates Using Coupled SQUID Flux Qubits

Cited by 5 publications

References 20 publications

Rapid Optimization of Working Parameters of Microwave-Driven Multilevel Qubits for Minimal Gate Leakage

Rapid Optimization of Working Parameters of Microwave-Driven Multilevel Qubits for Minimal Gate Leakage

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

Multistability and self-organization in disordered SQUID metamaterials

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