Molecular Spin Qubits: Molecular Optimization of Synthetic Spin Qubits, Molecular Spin AQC and Ensemble Spin Manipulation Technology

Abstract

Molecular spin qubits are intrinsically synthetic material spins, because molecular optimization to make matter spin qubits requires use of actual, open shell chemical entities. In this contribution, we describe g-tensor or pseudo g-tensor (hyperfine A) engineering approaches affording a generalized synthetic optimization strategy. Small-scale molecular spin qubits have been synthesized, allowing us to establish Controlled-NOT gate operations in the smallest ensemble molecular electron spin quantum system. In quest of scalable qubit systems, synthetic approaches to the Lloyd model of electron spin versions are described. In most of such molecular spin systems, termed molecular spins, unpaired electrons play the role of bus qubits and nuclear spins in the topological network of molecular frames are client qubits. Thus, extended pulse-based microwave technology for rf and conventional microwave frequency regions has been implemented to control both electron and nuclear spin qubits in an equivalent manner. In this context, molecular-spin based adiabatic quantum computers and multi-spin quantum cybernetic control via a single spin qubit are described as relevant spin technology.

Appendices

Appendices

1.1 Appendix 28.1

The details of the rotation angle are shown in (a) where a _n and b are (n/5)² and 0.028, respectively. The operation times are shown in (b).

• (a) Rotation angles

  	Direction	Angle
  1	x-	30(1 − a n )b/2
  2	y-	84a n b
  3	y-	88a n b
  4	y-	44a n b
  5	x-	30(1 − a n )b/2 + π/2

• (b) Operation times

  	3e system	1e + 2n system
  t 1	−π/j 31	−π/A 31
  t 2	−64s n τ/j 12	−64s n τ/A 12
  t 3	−80s n τ/j 12	−80s n τ/A 12
  t 4	−40s n τ/j 31	−40s n τ/A 31
  t 5	−80s n τ/j 23	–
  t 6	–	−π/A 12

1.2 Appendix 28.2

The Trotter’s formula of the Eq. (28.3) where b is 0.028.

$$ \begin{aligned}\hfill U&={\displaystyle \prod_{m=1}^5 \exp \left\{-i\left(1-{\left(m/5\right)}^2\right){\widehat{H}}_i\left(b/2\right)\right\}}\hfill \\ &\quad \hfill \times \exp \left\{-i{\left(m/5\right)}^2{\widehat{H}}_fb\right\}\times \exp \left\{-i\left(1-{\left(m/5\right)}^2\right){\widehat{H}}_i\left(b/2\right)\right\}\hfill \end{aligned} $$

(28.19)