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arXiv:1202.3057 · Physical Review A

Magnon qubit and quantum computing on magnon Bose-Einstein condensates

S. N. Andrianov, Sergey A. Moiseev

Published Oct 2, 2014• 41 citations
arXivHTMLPDF

Abstract

Recently, great progress has been made in the creation of a solid-state quantum computer using superconducting qubits on Cooper pairs of charged electrons. However, this approach has met limitations due to decoherence effects caused by the strong Coulomb interaction of the superconducting qubit with the environment. Here, we propose the solution of this problem by switching to another Bose-Einstein condensate (BEC), uncharged long-lived magnons, wherein the magnon BEC qubit can be realized due to the magnon blockade isolating a pair of the magnon condensate energy levels in the mesoscopic and nanoscopic ferromagnetic dielectric sample. We demonstrate the single-qubit gates by operating quantum transition between these states in the external microwave field. We also consider implementation of the two-qubit gates by using the interaction between such magnon BEC qubits due to exchange by virtual photons in a microwave cavity. Finally, we discuss the condition for long-lived magnon BEC qubits, a scalable architecture, and promising advantages of the multiqubit quantum computer based on the magnon qubit.

DOI
10.1103/physreva.90.042303

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Recently, great progress has been made in the creation of a solid-state quantum computer using superconducting qubits on Cooper pairs of charged electrons. However, this approach has met limitations due to decoherence effects caused by the strong Coulomb interaction of the superconducting qubit with the environment. Here, we propose the solution of this problem by switching to another Bose-Einstein condensate (BEC), uncharged long-lived magnons, wherein the magnon BEC qubit can be realized due to the magnon blockade isolating a pair of the magnon condensate energy levels in the mesoscopic and nanoscopic ferromagnetic dielectric sample. We demonstrate the single-qubit gates by operating quantum transition between these states in the external microwave field. We also consider implementation of the two-qubit gates by using the interaction between such magnon BEC qubits due to exchange by virtual photons in a microwave cavity. Finally, we discuss the condition for long-lived magnon BEC qubits, a scalable architecture, and promising advantages of the multiqubit quantum computer based on the magnon qubit.
Rigidity of an ordered phase in condensed matter results in collective excitation modes spatially extending in macroscopic dimensions. Magnon is a quantum of an elementary excitation in the ordered spin system, such as ferromagnet. Being low dissipative, dynamics of magnons in ferromagnetic insulators has been extensively studied and widely applied for decades in the contexts of ferromagnetic resonance, and more recently of Bose-Einstein condensation as well as spintronics. Moreover, towards hybrid systems for quantum memories and transducers, coupling of magnons and microwave photons in a resonator have been investigated. However, quantum-state manipulation at the single-magnon level has remained elusive because of the lack of anharmonic element in the system. Here we demonstrate coherent coupling between a magnon excitation in a millimetre-sized ferromagnetic sphere and a superconducting qubit, where the interaction is mediated by the virtual photon excitation in a microwave cavity. We obtain the coupling strength far exceeding the damping rates, thus bringing the hybrid system into the strong coupling regime. Furthermore, we find a tunable magnon-qubit coupling scheme utilising a parametric drive with a microwave. Our approach provides a versatile tool for quantum control and measurement of the magnon excitations and thus opens a new discipline of quantum magnonics.
Quantum computation using qubits made of two component Bose-Einstein condensates (BECs) is analyzed. We construct a general framework for quantum algorithms to be executed using the collective states of the BECs. The use of BECs allows for an increase of energy scales via bosonic enhancement, resulting in two qubit gate operations that can be performed at a time reduced by a factor of N, where N is the number of bosons per qubit. We illustrate the scheme by an application to Deutsch-s and Grover-s algorithms, and discuss possible experimental implementations. Decoherence effects are analyzed under both general conditions and for the experimental implementation proposed.
Units of superconducting circuitry that exploit the concept of the single- Cooper-pair box (SCB) have been built and are undergoing testing as prototypes of logic gates that could, in principle, constitute building blocks of clocked quantum computers. These units utilize quantized charge states as the quantum information-bearing degrees of freedom. An SCB is an artificial two-level quantum system that comprises a nanoscale superconducting electrode connected to a reservoir of Cooper-pair charges via a Josephson junction. The logical quantum states of the device, .0. and .1., are implemented physically as a pair of charge-number states that differ by 2e (where e is the charge of an electron). Typically, some 109 Cooper pairs are involved. Transitions between the logical states are accomplished by tunneling of Cooper pairs through the Josephson junction. Although the two-level system contains a macroscopic number of charges, in the superconducting regime, they behave collectively, as a Bose-Einstein condensate, making possible a coherent superposition of the two logical states. This possibility makes the SCB a candidate for the physical implementation of a qubit. A set of quantum logic operations and the gates that implement them is characterized as universal if, in principle, one can form combinations of the operations in the set to implement any desired quantum computation. To be able to design a practical quantum computer, one must first specify how to decompose any valid quantum computation into a sequence of elementary 1- and 2-qubit quantum gates that are universal and that can be realized in hardware that is feasible to fabricate. Traditionally, the set of universal gates has been taken to be the set of all 1-qubit quantum gates in conjunction with the controlled-NOT (CNOT) gate, which is a 2-qubit gate. Also, it has been known for some time that the SWAP gate, which implements square root of the simple 2-qubit exchange interaction, is as computationally universal as is the CNOT operation.
A hybrid system established by the direct interaction between a magnon mode and a superconducting transmon qubit is used to realize a high-degree blockade for magnon. It is a fundamental way toward quantum manipulation at the level of a single magnon and preparation of single magnon sources. Through weakly driving the magnon and probing the qubit, our magnon-blockade proposal can be optimized when the transversal coupling strength between the magnon and qubit is equivalent to the detuning of the qubit and the probing field or that of the magnon and the driving field. Under this condition, the equal-time second-order correlation function g(2)(0){g}^{(2)}(0)g(2)(0) can be analytically minimized when the probing intensity is about three times the driving intensity. Moreover, the magnon blockade could be further enhanced by proper driving intensity and system decay rate, whose magnitudes outrange the current systems of cavity QED and cavity optomechanics. In particular, the correlation function achieves ${g}^{(2)}(0)\ensuremath{\sim}{10}^{\ensuremath{-}7}$, about two orders lower than that for the photon blockade in cavity optomechanics. Also, we discuss the effects on g(2)(0){g}^{(2)}(0)g(2)(0) from thermal noise and the extra longitudinal interaction between the magnon and qubit. Our optimized conditions for blockade are found to persist in these nonideal situations.
The techniques of microwave quantum optics are applied to collective spin excitations in a macroscopic sphere of a ferromagnetic insulator. We demonstrate, in the single-magnon limit, strong coupling between a magnetostatic mode in the sphere and a microwave cavity mode. Moreover, we introduce a superconducting qubit in the cavity and couple the qubit with the magnon excitation via the virtual photon excitation. We observe the magnon–vacuum-induced Rabi splitting. The hybrid quantum system enables generation and characterization of non-classical quantum states of magnons.
The concept of a quantum computer was invented in the beginning of the 1980s as a quantum generalization of the reversible classical computer. After discoveries in the middle of the 1990s of quantum algorithms, which wouldsolve some problems considered intractable for classical computers, the field of quantum computing has developed rapidly. A wide range of quantum systems are investigated for their possible ability to implement quantum algorithms in practice. The most promising solid state implementations are superconducting electrical circuits based on the Josephson effect, and the Coulomb blockade effect. Superconducting circuits are macroscopic quantum systems which can be fabricated using standard lithography technologies. Superconducting qubits - basic building blocks of a quantum computer - have been developed at several research laboratories, among others the MC2 here at Chalmers. This thesis presents a theoretical investigation of controllable coupling of superconducting qubits based on the single Cooper-pair box. Two coupling schemes are investigated in detail: current-controlled coupling via large Josephson junctions, and coupling via a superconducting stripline cavity. Both coupling designs are scalable and suitable for the charge regime of the single Cooper-pair box, as well as for the charge-phase regime where the qubit is better protected from environmental noise. Quantum gate protocols which are relevant for these physical couplings are discussed. The investigations show that, for both considered designs, the simplest two-qubit gate is the conditional phase-shift gate. This gate is universal for quantum computing, and it can create maximallyentangled qubit pairs in only one run. The investigation combines methods from electrical engineering, quantum mechanics and quantum computer science.