arXiv subjects

M. Karthick Selvan

Publications and source records attributed to M. Karthick Selvan.

7 recordsLinked to original sources

arXiv2026

On the Experimental Determination of Nonlocal Characteristics of Two-Qubit Gates

In this paper, we discuss the experimental determination of the nonlocal characteristics of two-qubit gates. Based on the recently derived expressions for the entangling power and gate typicality of two-qubit gates, we construct two-qubit quantum circuits to measure the entangling power and gate typicality of the two-qubit gates, which are generated by the elements of the su(4) Cartan subalgebra. These elements describe the native interactions in many quantum processors. Hence, these circuits can be used to determine the nonlocal characteristics of native gates of many quantum processors. In each circuit, the native gate is applied twice. In addition, each circuit consists of at least one CNOT gate. A set of six two-qubit circuits is constructed to measure the entangling power. The number of circuits is further reduced to three by increasing the nonlocal resources (the number of CNOT gates). To measure the gate typicality, a set of three two-qubit circuits is constructed. Measurement of gate typicality requires more nonlocal resources than the measurement of entangling power.

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arXiv2026

Optimal Construction of Two-Qubit Gates using the Symmetries of B Gate Equivalence Class

Two applications of gates from the B gate equivalence class can generate all two-qubit gates. This local equivalence class is invariant under the mirror (multiplication with the SWAP gate) operation, inverse (Hermitian conjugate) operation, and the combined inverse and mirror operations. The last two symmetries are associated with the ability of a two-qubit gate to generate the two-qubit local gates and the SWAP gate in two applications. No single local equivalence class of two-qubit gates, except the B gate equivalence class, has these two symmetries. Only the planar regions of the Weyl chamber, describing the mirror operation, contain the local equivalence classes with either one of the two symmetries. We show that there exist one-parameter families of local equivalence classes on these planes, with and without the B gate equivalence class, such that each of them can be used to construct a parameterized universal two-qubit quantum circuit that involves only two nonlocal two-qubit gates. We also discuss the implementation of the gates from a few families of local equivalence classes on superconducting quantum computers for optimal generation of all two-qubit gates. We provide upper bounds on the number of two-qubit gates required to generate an arbitrary $n$-qubit gate for two families, each of which is conjectured to generate all two-qubit gates in two applications. We show that there exists a positive correlation between the area of the convex hull of the squared eigenvalues of the nonlocal part of a parameterized two-qubit gate and the fractional volume of the Weyl chamber covered in two applications of the parameterized two-qubit gate for two families of local equivalence classes.

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arXiv2025

Nonlocal characteristics and argand diagram of two-qubit gates

Nonlocal characteristics of a two-qubit gate are determined by its nonlocal part. The squared eigenvalues of the nonlocal part of a two-qubit gate exist on the unit circle in the complex plane. We show that two sets of chords, the chords connecting the squared eigenvalues with each other and those connecting a squared eigenvalue with the complex conjugate of others in the unit circle, can be used to describe the nonlocal characteristics of two-qubit gates. Lengths of both sets of chords are proportional to the amount of entanglement contained in certain pure states. The entangling power of a two-qubit gate can be expressed in terms of the squared lengths of the first set of chords. Similarly, we show that the gate typicality of a two-qubit gate can be expressed in terms of the squared lengths of the second set of chords and the linear entropy of a two-qubit gate can be expressed using the squared lengths of both sets of chords. Perfect entanglers are known to transform some product states into maximally entangled states. The convex hull of the squared eigenvalues of the nonlocal part of perfect entanglers contain the zero. We analyse the simplices containing the zero in the convex hull of the squared eigenvalues of the nonlocal part of perfect entanglers to construct a pair of orthonormal product states that can be transformed into maximally entangled states by the nonlocal part of perfect entanglers and divide the region of perfect entanglers in the Weyl chamber into three tetrahedral regions and eight bounding planes based on the uniqueness of the simplices containing the zero.

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arXiv2024

Characteristics and Implementation of B$^α$ Gates

In this brief report, we discuss the characteristics of B$^α$ gates. We provide the conditions for the two-qubit gates generated by two applications of a B$^α$ gate. We propose an experimental scheme to implement B$^α$ gates in ion-trap system. In this scheme, we assume that only a single vibrational mode contributes to spin-spin coupling. This scheme is an extension of a recently proposed scheme to realize XY-type interaction in ion-trap system. With the successful implementation of this scheme, B$^α$ gates can be used for doing quantum computation in ion-trap quantum computers.

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arXiv2024

Characteristics, Implementation and Applications of Special Perfect Entangler Circuits

We discuss the characteristics of special perfect entanglers and construct single parameter two-qubit circuits which are locally equivalent to special perfect entanglers. We present the results obtained from the implementation of one of the circuits using cross-resonance interaction and discuss their applications. First, we show that the ability of two-qubit gates to create entangled states can be described using the chords present in the argand diagram of squared eigenvalues of nonlocal part of two-qubit gates. We show that the entangling power of a two-qubit gate is proportional to the mean squared length of the chords. We deduce the entangling characteristics of special perfect entanglers from the argand diagram associated with them. We implement a special perfect entangler circuit using echoed cross-resonance gate and pulse-level programming for nine different circuit parameters. For a particular input state, we perform quantum state tomography and calculate state fidelity and concurrence of the obtained output density matrices. We also measure the average gate fidelity for B gate circuit. We construct two universal two-qubit quantum circuits using the special perfect entangler circuits. These universal circuits can be used to generate all two-qubit gates. We show that (n-1) B gate circuits can be used to generate n-qubit GHZ and perfect W states. We generate three-qubit perfect W state. Perfect W state generated using pulse-level programming shows better fidelity than the state generated using echoed cross-resonance gate.

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arXiv2022

Generation and entanglement study of generalized N-mode single photon perfect W-states

We consider single photon realization of generalized N-qubit perfect W-states which are suitable for perfect teleportation and superdense coding. We propose schemes to generate generalized N-mode single photon perfect W-states and derive entanglement conditions which for single photon states require finding fidelity with generalized N-mode single photon perfect W-states and hence more suitable to detect the genuine entanglement of generalized perfect W-states. Based on the evolution of single photon wavefunction in scalable integrated photonic lattices, we present schemes for the preparation of generalized N-mode single photon perfect W-states at desired propagation distance. The integrated waveguide structures can precisely be fabricated, offer low photon propagation losses and can be integrated on a chip. We consider both planar and ring type waveguide structures for state generation. We derive set of generalized entanglement conditions using the sum uncertainty relations of generalized su(2) algebra operators. We show that any given genuinely entangled N-mode single photon state is a squeezed state of a specific su(2) algebra operator and can be expressed as superposition of a pair of orthonormal generalized N-mode single photon perfect W-states which are eigenstates of that specific su(2) algebra operator. Within the single photon subspace, the eigendecomposition of su(2) algebra operators reduces the generalized entanglement condition to a simplified single photon separability condition. In order to verify the entanglement of given genuinely entangled N-mode single photon state using this condition one has to find the difference between the state fidelities with suitably chosen pair of orthonormal generalized N-mode single photon perfect W-states. Finally, we propose an experimental scheme to verify the entanglement using the proposed conditions...

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arXiv2020

Single photon generation and non-locality of perfect W-state

We study the generation of single photon perfect W-state. An important aspect of this perfect W-state is that, it can be used for perfect teleportation and superdense coding, which are not achievable with maximally entangled W-state. Our scheme for generation involves entanglement between various path degrees of freedom of a single photon in a compact and weakly coupled integrated waveguide system, which can be fabricated precisely with femtosecond laser direct writing technique. These platforms are interferometrically stable, scalable, less sensitive to decoherence and ensures a very low loss factor of 0.1dB/cm during photon propagation and hence are ideal for generation of perfect W-state. In addition to generation of single photon perfect W-state we study its non local properties using theory of local elements of reality.

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