Transferring arbitrary d-dimensional quantum states of a superconducting transmon qudit in circuit QED

Liu, Tong; Su, Qi-Ping; Yang, Jingsong; Xiong, Shao-Jie; Yang, Chui‐Ping

doi:10.1038/s41598-017-07225-5

Cited by 21 publications

(16 citation statements)

References 69 publications

(96 reference statements)

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“…The method involves successively swapping over the population of different levels from one qudit to another via a cavity mode. By the end of step IV of their process (Figure 2 of [35]) they have transferred the population of each individual state to the second qubit, but the states are in the wrong order. Therefore, in the final step of their process, Liu et al apply a succession of pulses on different transitions within the qudit to rearrange the state populations so that they are in the exact reverse order compared to where they started.…”

Section: Appendix D: Applications To Other D-level Systemsmentioning

confidence: 99%

“…Here we show that, using our technique, a multi-level control method can instead be found to put the state populations back in their original order (not reversed) in a single step. Specifically, one must apply this four-level method to the top four levels of the second qudit ( Figure 2 of [35]) so as to reverse the order of their amplitudes. The required unitary matrix to carry out this operation is as follows:…”

Section: Appendix D: Applications To Other D-level Systemsmentioning

confidence: 99%

“…First we refer to the work of Liu et al [35], who proposed a method to transfer the state of one d-level superconducting qudit to another in circuit QED. They illustrate their method in detail for the five-level case and show that it can be generalised to any number of levels.…”

Section: Appendix D: Applications To Other D-level Systemsmentioning

confidence: 99%

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Generation of high-fidelity quantum control methods for multilevel systems

et al. 2018

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In recent decades there has been a rapid development of methods to experimentally control individual quantum systems. A broad range of quantum control methods has been developed for two-level systems, however the complexity of multi-level quantum systems make the development of analogous control methods extremely challenging. Here, we exploit the equivalence between multilevel systems with SU(2) symmetry and spin-1/2 systems to develop a technique for generating new robust, high-fidelity, multi-level control methods. As a demonstration of this technique, we develop new adiabatic and composite multi-level quantum control methods and experimentally realise these methods using an 171 Yb + ion system. We measure the average infidelity of the process in both cases to be around 10 −4 , demonstrating that this technique can be used to develop high-fidelity multi-level quantum control methods and can, for example, be applied to a wide range of quantum computing protocols including implementations below the fault-tolerant threshold in trapped ions.

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Section: Appendix D: Applications To Other D-level Systemsmentioning

confidence: 99%

Section: Appendix D: Applications To Other D-level Systemsmentioning

confidence: 99%

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Generation of high-fidelity quantum control methods for multilevel systems

et al. 2018

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“…Using this basis set of QNSV, it is possible to define distinct units of quantum information that can be realized by a quantum system in terms of a superposition of mutually orthogonal quantum states 4,40 . These arbitrary vectors will be also called qunits, with n = 0, 1, 2, ..., instead of using the nomenclature qudits for a d-dimensional space (commonly employed in quantum information 41 ).…”

Section: The Integer Number Representationmentioning

confidence: 99%

A quantum number theory

Daiha¹,

Rivelino²

2021

Preprint

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We employ an algebraic procedure based on quantum mechanics to propose a 'quantum number theory' (QNT) as a possible extension of the 'classical number theory'. We built our QNT by defining pure quantum number operators (q-numbers) of a Hilbert space that generate classical numbers (c-numbers) belonging to discrete Euclidean spaces. To start with this formalism, we define a 2-component natural q-number N, such that N 2 ≡ N 2 1 +N 2 2 , satisfying a Heisenberg-Dirac algebra, which allows to generate a set of natural c-numbers n ∈ N. A probabilistic interpretation of QNT is then inferred from this representation.Furthermore, we define a 3-component integer q-number Z, such thatand obeys a Lie algebra structure. The eigenvalues of each Z component generate a set, albeit all components do not generate Z 3 simultaneously. We interpret the eigenvectors of the q-numbers as 'q-number state vectors' (QNSV), which form multidimensional orthonormal basis sets useful to describe state-vector superpositions defined here as qunits. To interconnect QNSV of different dimensions, associated to the same c-number, we propose a quantum mapping operation to relate distinct Hilbert subspaces, and its structure can generate a subset W ⊆ Q * , the field of non-zero rationals. In the present description, QNT is related to quantum computing theory and allows dealing with nontrivial computations in high dimensions.

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“…Special graphs can be studied under this model of perfect state transfer for qudits. PST for qudits has been demonstrated experimentally on superconducting transmon qudits in [48]. Qudit PST for pseudo-regular networks is explored in [49].…”

Section: 24)mentioning

confidence: 99%

A switching approach for perfect state transfer over a scalable and routing enabled network architecture with superconducting qubits

Singh

2020

Preprint

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We propose a hypercube switching architecture for the perfect state transfer (PST) where we prove that it is always possible to find an induced hypercube in any given hypercube of any dimension such that PST can be performed between any two given vertices of the original hypercube. We then generalise this switching scheme over arbitrary number of qubits where also this routing feature of PST between any two vertices is possible. It is shown that this is optimal and scalable architecture for quantum computing with the feature of routing. This allows for a scalable and growing network of qubits. We demonstrate this switching scheme to be experimentally realizable using superconducting transmon qubits with tunable couplings. We also propose a PST assisted quantum computing model where we show the computational advantage of using PST against the conventional resource expensive quantum swap gates. In addition, we present the numerical study of signed graphs under Corona product of graphs and show few examples where PST is established, in contrast to pre-existing results in the literature for disproof of PST under Corona product. We also report an error in pre-existing research for qudit state transfer over Bosonic Hamiltonian where unitarity is violated.

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Transferring arbitrary d-dimensional quantum states of a superconducting transmon qudit in circuit QED

Cited by 21 publications

References 69 publications

Generation of high-fidelity quantum control methods for multilevel systems

Generation of high-fidelity quantum control methods for multilevel systems

A quantum number theory

A switching approach for perfect state transfer over a scalable and routing enabled network architecture with superconducting qubits

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