Holonomic Quantum Control with Continuous Variable Systems

Albert, Victor V.; Shu, Chi-Wang; Krastanov, Stefan; Shen, Chao; Liu, Ren‐Bao; Yang, Zhen‐Biao; Schoelkopf, Robert; Mirrahimi, Mazyar; Devoret, Michel; Jiang, Liang

doi:10.1103/physrevlett.116.140502

Cited by 96 publications

(98 citation statements)

References 92 publications

(35 reference statements)

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“…A highlight of this research is the first realization of quantum error correction for a quantum memory at the break-even point [21]. Some initial theoretical proposals [22][23][24][25][26] and a few experiments [27][28][29] indicate that this encoding can be extended to a logical qubit with the possibility of performing protected logical gates. However, the protection remains limited to first-order errors due to photon loss, the major decay channel of a superconducting cavity.…”

Section: Introductionmentioning

confidence: 99%

Repetition Cat Qubits for Fault-Tolerant Quantum Computation

2019

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We present a 1D repetition code based on the so-called cat qubits as a viable approach toward hardware-efficient universal and fault-tolerant quantum computation. The cat qubits that are stabilized by a two-photon driven-dissipative process, exhibit a tunable noise bias where the effective bit-flip errors are exponentially suppressed with the average number of photons. We propose a realization of a set of gates on the cat qubits that preserve such a noise bias. Combining these base qubit operations, we build, at the level of the repetition cat qubit, a universal set of fully protected logical gates. This set includes single-qubit preparations and measurements, NOT, controlled-NOT, and controlled-controlled-NOT (Toffoli) gates. Remarkably, this construction avoids the costly magic state preparation, distillation, and injection. Finally, all required operations on the cat qubits could be performed with slight modifications of existing experimental setups.

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Section: Introductionmentioning

confidence: 99%

Repetition Cat Qubits for Fault-Tolerant Quantum Computation

2019

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“…Therefore, geometric quantum computation [9], where quantum gates are induced by geometric transformations, is a promising candidate to achieve high-fidelity quantum manipulation. Moreover, due to the intrinsic noncommutativity, non-Abelian geometric phases [2] can naturally lead to universal quantum gates, i.e., the so-called holonomic quantum computation [10][11][12][13]. However, geometric phases based on adiabatic evolutions are so slow that decoherence will introduce considerable gate errors [14,15].…”

Section: Introductionmentioning

confidence: 99%

Single-Loop and Composite-Loop Realization of Nonadiabatic Holonomic Quantum Gates in a Decoherence-Free Subspace

et al. 2019

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High-fidelity quantum gates are essential for large scale quantum computation, which can naturally be realized in a noise resilient way. It is well-known that geometric manipulation and decoherence-free subspace encoding are promising ways towards robust quantum computation. Here, by combining the advantages of both strategies, we propose and experimentally realize universal holonomic quantum gates in both a single-loop and composite scheme, based on nonadiabatic and non-Abelian geometric phases, in a decoherence-free subspace with nuclear magnetic resonance. Our experiment only employs two-body resonant spin-spin interactions and thus is experimental friendly. In particularly, we also experimentally verify that the composite scheme is more robust against the pulse errors over the single-loop scheme. Therefore, our experiment provides a promising way towards faithful and robust geometric quantum manipulation.

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“…The states of the second class have a Poissonian distribution of photons and have been recently generated for microwave cavity field coupled to a superconducting qubit by nonlinear Kerr effect [8,9]. The states of both classes have been extensively studied as models of decoherence [2,3,10], sources of quantum instabilities [11,12] and resources for quantum computation [13,14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Quantum teleportation of qudits by means of generalized quasi-Bell states of light

Horoshko

Patera

Kolobov

2019

Optics Communications

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Quantum superpositions of coherent states are produced both in microwave and optical domains, and are considered realizations of the famous "Schrödinger cat" state. The recent progress shows an increase in the number of components and the number of modes involved. Our work creates a theoretical framework for treatment of multicomponent two-mode Schrödinger cat states. We consider a class of single-mode states, which are superpositions of N coherent states lying on a circle in the phase space. In this class we consider an orthonormal basis created by rotationally-invariant circular states (RICS). A two-mode extension of this basis is created by splitting a single-mode RICS on a balanced beam-splitter. We show that these states are generalizations of Bell states of two qubits to the case of N-level systems encoded into superpositions of coherent states on the circle, and we propose for them the name of generalized quasi-Bell states. We show that using a state of this class as a shared resource, one can teleport a superposition of coherent states on the circle (a qudit). Differently from some other existing protocols of quantum teleportation, the proposed protocol provides the unit fidelity for all input states of the qudit. We calculate the probability of success for this type of teleportation and show that it approaches unity for the average number of photons in one component above N 2 . Thus, the teleportation protocol can be made unit-fidelity and deterministic at finite resources.

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Holonomic Quantum Control with Continuous Variable Systems

Cited by 96 publications

References 92 publications

Repetition Cat Qubits for Fault-Tolerant Quantum Computation

Repetition Cat Qubits for Fault-Tolerant Quantum Computation

Single-Loop and Composite-Loop Realization of Nonadiabatic Holonomic Quantum Gates in a Decoherence-Free Subspace

Quantum teleportation of qudits by means of generalized quasi-Bell states of light

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