The rfSQUID Quantum Bit the superconducting flux qubit
The rf-SQUID Quantum Bit (the superconducting flux qubit) C. E. Wu(吳承恩), C. C. Chi(齊正中) Materials Science Center and Department of Physics, National Tsing Hua University, Hsinchu , Taiwan, R. O. C.
A rf-SQUID qubit is a superconducting loop interrupted by a small Josephson junction x -- external flux applied to loop 0 -- flux quanta (=2. 07*10 -15 wb) -- total flux in the loop L -- loop inductance C -- junction capacitance i -- supercurrent in the loop Ic -- junction critical current EJ -- junction coupling energy(=Ic 0/2π ) L EJ C ( x, ) i ( /2 ) 0 + = n 0 = x + i. L (n = integer) BCS: i = Ic sin( ) -- phase difference across junction
The Hamiltonian of the rf-SQUID qubit L EJ C ( x, ) i
A double well potential
Dimensionless Hamiltonian
Energy levels quantization and lowest two states wave function in a symmetric double well potential βJ=1. 10, βc=7. 55*10 -4 , x=0. 5 ε 3 ε 2 -1/2 ε 1 ε 0 |E>1 st |G>
parameters βJ > ~ 1 → 2 -local well, small barrier height ε 2 > βJ >ε 1 →only 2 states bellow the barrier ε 2 -ε 1 >>ε 1 -ε 0>k. T/U 0 →No thermal excitation to high levels →definite Rabi frequency βJ >>βc →flux quantum number is a good quantum number →SQUID loop size
“ 0” and “ 1” of an rf-SQUID qubit :Wave function is localized at left well. flux quanta n=0, clockwise current. ⊙ x=0. 5 0 i :Wave function is localized at right well. Flux quanta n=1, counter-clockwise current.
Approximated two-state system x~ 0. 5 0 Where Δ= E 1( x = ½) - E 0( x = ½) ε~difference of two local minimum ( x - ½)
spin analog Bz Bx Bz Rabi frequency = g(q Bx/2 m) -pulse: a pulse of Bx apply with a duration = / /2 -pulse: = /2 |1> → 1/√ 2(|0> + |1>) |1> → |0>
Time evolution and one qubit rotation Consider an arbitrary state at time t: If, initially, the wave function of the rf-SQUID is localized in left well, i. e. | >t=0 = |0>t=0 = 1/√ 2(|G>+|E>1 st), so C 0(0)=C 1(0)=1/√ 2, then the probability of finding it in right well at time t is: Rabi frequency: = The system will oscillate between |0> and |1> (Macroscopic Quantum Coherence Oscillation)
Try to measure the coherence time
Physical systems actively considered for quantum computer implementation • Liquid-state NMR • NMR spin lattices • Linear ion-trap spectroscopy • Neutral-atom optical lattices • Cavity QED + atoms • Linear optics with single photons • Nitrogen vacancies in diamond • Electrons on liquid He • Small Josephson junctions – “charge” qubits – “flux” qubits • Spin spectroscopies, impurities in semiconductors • Coupled quantum dots – Qubits: spin, charge, excitons – Exchange coupled, cavity coupled From IBM
Superconducting Josephson qubits Advantage: scalable, easy manipulation Disadvantage: short coherence time dissipative quantum system
Flux measurement I V ? Qubit DC SQUID
- Slides: 15