panos aliferis IBM Jan. 09 quantum computing hardware with highly biased noise

biased noise - for a resting qubit, biased noise means,i.e., relaxation and leakage much weaker than dephasing.

biased noise j 0 i j 1 i j 2 i leakage relaxation energy dephasing - for a resting qubit, biased noise means,i.e., relaxation and leakage much weaker than dephasing.

biased noise - for a qubit undergoing a noisy operation, ideal superoperator noise superoperator N ¢ O N ( X ) = P k N k XN y k

biased noise - for a qubit undergoing a noisy operation, ideal superoperator noise superoperator N ¢ O N ( X ) = P k N k XN y k diagonal qubit operator leakage operator non-diagonal qubit operator identity N k = I k + N k ; l + N k ; : d + N k ; d

biased noise - for a qubit undergoing a noisy operation, ideal superoperator noise superoperator N ¢ O N ( X ) = P k N k XN y k diagonal qubit operator leakage operator non-diagonal qubit operator identity N k = I k + N k ; l + N k ; : d + N k ; d = ³ ^ I + F l + F : d + F d ´ ( X )

biased noise - for a qubit undergoing a noisy operation, ideal superoperator noise superoperator N ¢ O N ( X ) = P k N k XN y k diagonal qubit operator leakage operator non-diagonal qubit operator identity N k = I k + N k ; l + N k ; : d + N k ; d noise is biased if. jj F l jj ¦. jj F : d jj ¦ ¿ jj F d jj ¦ = ³ ^ I + F l + F : d + F d ´ ( X )

biased noise - for a qubit undergoing a noisy operation, ideal superoperator noise superoperator N ¢ O N ( X ) = P k N k XN y k diagonal qubit operator leakage operator non-diagonal qubit operator identity N k = I k + N k ; l + N k ; : d + N k ; d noise is biased if. jj F l jj ¦. jj F : d jj ¦ ¿ jj F d jj ¦ - most resting qubits have biased noise; but noisy operations may not. - highly biased noise can be engineered by using (quasi) adiabatic control. = ³ ^ I + F l + F : d + F d ´ ( X )

e.g., integrated-circuit qubits - dissipation in metallic parts must be low at the operating temp. and freq. - energy spectrum must be unharmonic ( ) so qubits are usable use low-temperature superconductors ( Al, Nb, etc. ) build circuits with non-linear components ¢E 01 6 = ¢E 12

¼ 1 nm e.g., integrated-circuit qubits - dissipation in metallic parts must be low at the operating temp. and freq. - energy spectrum must be unharmonic ( ) so qubits are usable use low-temperature superconductors ( Al, Nb, etc. ) build circuits with non-linear components ¢E 01 6 = ¢E 12 the Josephson junction: a nondissipative nonlinear inductor = L J C J L

flux qubits zoo © 0 2 energy j 0 i / j L i + j R ij 1 i / j L i ¡ j R ij L ij R i

flux qubits zoo © 0 2 © 0 2 © 0 2 ¡ © 0 2 energy j 0 i / j L i + j R ij 1 i / j L i ¡ j R ij L ij R i © c © c

IBM flux qubit © 0 2 ¡ © 0 2 © c ² = 0

² = 0 bare (unstabilized) qubit oscillator- stabilized qubit

IBM flux qubit

E 11 6 = E 01 + E 10 and we can implement a conditional phase gate. the pulses are adiabatic, except at the two level crossings where we want to tunnel perfectly through the very small gap. during the 35ns pulsing,

IBM flux qubit - by numerical simulations, we can estimate the effect of noise on this CPHASE ¼ 3 : 5 £ 10 ¡ 6 ¼¼ 3 : 5 £ 10 ¡ 6 2 £ 10 ¡ 3 which also apply for preparing, and measuring. e i µ ¾ z ¾ x µ IO O ¾ z ¶ jj F l jj ¦. jj F : d jj ¦ ¿ jj F d jj ¦ ; j + i / j 0 i + j 1 i

IBM flux qubit - by numerical simulations, we can estimate the effect of noise on this CPHASE ¼ 3 : 5 £ 10 ¡ 6 ¼¼ 3 : 5 £ 10 ¡ 6 2 £ 10 ¡ 3 - since noise is mostly diagonal, we can encode in a classical code, e.g., µ IO O ¾ z ¶ j + i ! j + i ­ j + i ­ ¢¢¢ ­ j + i |{z} n ; j ¡ i ! j ¡ i ­ j ¡ i ­ ¢¢¢ ­ j ¡ i |{z} n then, the error-correction circuit looks like and similar circuits allow implementing a universal set of logical operations. jj F l jj ¦. jj F : d jj ¦ ¿ jj F d jj ¦ ; which also apply for preparing, and measuring. e i µ ¾ z ¾ x j + i / j 0 i + j 1 i

hard realities - resonators: T 1 ¼ 3 ¹s - flux qubits: T 1 ¼ 10 ns IBM experiments:

hard realities - resonators: T 1 ¼ 3 ¹s - flux qubits: T 1 ¼ 10 ns - however, other flux qubits work much better… IBM experiments: Delft: small & symmetric Berkeley: large & symmetric

hard realities - why is symmetry important ? = L J C J LC g C c Z 0 © 0 2 I

hard realities - why is symmetry important ? = L J C J LC g C c Z 0 © 0 2 I vs. L J C J C g C c Z 0 I L 2 L 2 C g I

hard realities Berkeley qubit T 1 ¼ 200 ns

hard realities Berkeley qubit T 1 ¼ 200 ns IBM qubit - also, play with the UCSB phase qubit.

references quantum computing against biased noise PA and Preskill, arXiv: PA, Brito, DiVincenzo, Preskill, Steffen, and Terhal, arXiv: IBM flux qubit Berkeley flux qubit Koch et. al., PRL 96 (2006) Koch et. al., PRB 72 (2005) Plourde et. al., PRB 72 (2005) Hime et. al., Science 314 (2006) 1427

panos aliferis IBM, January 09 quantum computing against highly biased noise