Complexity and efficiency of minimum entropy production probability paths from quantum dynamical evolutions

Cafaro, Carlo; Ray, Shannon; Alsing, Paul M.

doi:10.1103/physreve.105.034143

Cited by 10 publications

(3 citation statements)

References 48 publications

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“…In view of our quantitative findings revisited here, along with our more speculative considerations, we have reason to believe that the use of geometric Clifford algebras in QIS together with its employment in the characterization of quantum gate complexity appears to be deserving of further theoretical explorations [63][64][65][66][67]. Moreover, motivated by our revisitation of GA methods in quantum information science together with our findings appeared in Refs.…”

Section: Discussionmentioning

confidence: 66%

“…In Equation (67), GL(2, C) denotes the set of non-singular linear transformations in C 2 specified by 2 × 2 non-singular matrices with complex entries, while the symbol " †" signifies the Hermitian conjugation operation. Interestingly, while the Lie algebras so(3) and su(2) are isomorphic (i.e., so(3) ∼ = su(2)), the Lie groups SO(3) and SU(2) are only locally isomorphic.…”

Section: Preliminaries On So(3) and Su(2)mentioning

confidence: 99%

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From Entanglement to Universality: A Multiparticle Spacetime Algebra Approach to Quantum Computational Gates Revisited

Cafaro,

Bahreyni,

Rossetti

2024

Symmetry

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Alternative mathematical explorations in quantum computing can be of great scientific interest, especially if they come with penetrating physical insights. In this paper, we present a critical revisitation of our application of geometric (Clifford) algebras (GAs) in quantum computing as originally presented in [C. Cafaro and S. Mancini, Adv. Appl. Clifford Algebras 21, 493 (2011)]. Our focus is on testing the usefulness of geometric algebras (GAs) techniques in two quantum computing applications. First, making use of the geometric algebra of a relativistic configuration space (namely multiparticle spacetime algebra or MSTA), we offer an explicit algebraic characterization of one- and two-qubit quantum states together with a MSTA description of one- and two-qubit quantum computational gates. In this first application, we devote special attention to the concept of entanglement, focusing on entangled quantum states and two-qubit entangling quantum gates. Second, exploiting the previously mentioned MSTA characterization together with the GA depiction of the Lie algebras SO3;R and SU2;C depending on the rotor group Spin+3,0 formalism, we focus our attention to the concept of universality in quantum computing by reevaluating Boykin’s proof on the identification of a suitable set of universal quantum gates. At the end of our mathematical exploration, we arrive at two main conclusions. Firstly, the MSTA perspective leads to a powerful conceptual unification between quantum states and quantum operators. More specifically, the complex qubit space and the complex space of unitary operators acting on them merge in a single multivectorial real space. Secondly, the GA viewpoint on rotations based on the rotor group Spin+3,0 carries both conceptual and computational advantages compared to conventional vectorial and matricial methods.

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Section: Discussionmentioning

confidence: 66%

Section: Preliminaries On So(3) and Su(2)mentioning

confidence: 99%

From Entanglement to Universality: A Multiparticle Spacetime Algebra Approach to Quantum Computational Gates Revisited

Cafaro,

Bahreyni,

Rossetti

2024

Symmetry

View full text Add to dashboard Cite

show abstract

“…From a physical point of view, such a circumstance implies that, for such scenarios, we can have a full control of the evolution of the twoqubit system. Moreover, we could analogously take advantage from specific applications developed for single two-level systems [71][72][73][74][75][76] and applying them in two-qubit scenarios.…”

Section: Discussionmentioning

confidence: 99%

SU(2)-Symmetric Exactly Solvable Models of Two Interacting Qubits

Grimaudo

2024

Preprint

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A two-qubit Hamiltonian model exhibiting an SU(2) symmetry is considered. The related dynamical problem results to be then exactly solvable both in the time-independent and in the time-dependent case. Basing on the formal, general form of the related time evolution operator, the time-dependence of the level of entanglement of some initial conditions is studied within both the Rabi and the Landau-Majorana-Stückelber-Zener scenarios.

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Constructions of optimal-speed quantum evolutions: a comparative study

Rossetti,

Cafaro,

Bahreyni

2024

Phys. Scr.

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We present a comparative analysis of two different constructions of optimal-speed quantum Hamiltonian evolutions on the Bloch sphere. In the first approach (Mostafazadeh's approach), the evolution is specified by a traceless stationary Hermitian Hamiltonian and occurs between two arbitrary qubit states by maximizing the energy uncertainty. In the second approach (Bender's approach), instead, the evolution is characterized by a stationary Hermitian Hamiltonian which is not traceless and occurs between an initial qubit state on the north pole and an arbitrary final qubit state. In this second approach, the evolution occurs by minimizing the evolution time subject to the constraint that the difference between the largest and the smallest eigenvalues of the Hamiltonian is kept fixed. For both approaches we calculate explicitly the optimal Hamiltonian, the optimal unitary evolution operator and, finally, the optimal magnetic field configuration. Furthermore, we show in a clear way that Mostafazadeh's and Bender's approaches are equivalent when we extend Mostafazadeh's approach to Hamiltonians with nonzero trace and, at the same time, focus on an initial quantum state placed on the north pole of the Bloch sphere. Finally, we demonstrate in both scenarios that the optimal unitary evolution operator is a rotation about an axis that is orthogonal to the unit Bloch vectors that correspond to the initial and final qubit states.

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Complexity and efficiency of minimum entropy production probability paths from quantum dynamical evolutions

Cited by 10 publications

References 48 publications

From Entanglement to Universality: A Multiparticle Spacetime Algebra Approach to Quantum Computational Gates Revisited

From Entanglement to Universality: A Multiparticle Spacetime Algebra Approach to Quantum Computational Gates Revisited

SU(2)-Symmetric Exactly Solvable Models of Two Interacting Qubits

Constructions of optimal-speed quantum evolutions: a comparative study

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