UNIVERSITY OF INNSBRUCK Quantum Reservoir Engineering (Discussion in the Quantum Coherent Control Program) IQOQI AUSTRIAN ACADEMY OF SCIENCES €U AQUTE €U COHERENCE Peter Zoller UQUAM AFOSR Tuesday, March 12, 13 Quantum reservoir engineering? Environment E dissipation as System a resource S fundamentally quantum information unevitable coupling diss. preparation of multi-qubit quantum states dissipative quantum computation non-equilibrium dynamics t ⇢mixed eL result in open many-body quantum systems t !1 bosons spins Tuesday, March 12, 13 Entanglement by Dissipation “Optical Pumping” theoretical concepts: Review: M. Müller, S. Diehl, G. Pupillo, P. Zoller, Engineered Open Systems and Quantum Simulations with Atoms and Ions, arXiv:1203.6595; published in Advances of Atomic, Molecular and Optical Physics 2012 F. Verstraete, M.M. Wolf, J.I.Cirac, Nature Physics (2009) first experiments: J. Barreiro, M. Müller, P. Schindler, D. Nigg, T. Monz, M. Chwalla, M. Hennrich, C. F. Roos, P. Zoller & R. Blatt Nature 470, 486 (2011) H. Krauter, E. Polzik, I. Cirac et al. PRL 2011. 3 Tuesday, March 12, 13 Entanglement via Unitary Evolution • quantum logic network model qubits quantum gates read out time √ U √ | ⇥ t | ⇥ coherent Hamiltonian evolution - quantum gates - deterministic 4 Tuesday, March 12, 13 Entanglement via Unitary Evolution • quantum logic network model • atomic physics: trapped ions qubits quantum gates read out time √ Ut √ | ⇥ | ⇥ R. Blatt coherent Hamiltonian evolution - quantum gates - deterministic 4 Tuesday, March 12, 13 Entanglement via Unitary Evolution • quantum logic network model • atomic physics: trapped ions qubits quantum gates read out time √ Ut √ | ⇥ | ⇥ R. Blatt coherent Hamiltonian evolution - quantum gates - deterministic • decoherence ☹ spontaneous dissipation by coupling to environment - spontaneous emission etc. emission ☹ 4 Tuesday, March 12, 13 Entanglement via Unitary Evolution • quantum logic network model • atomic physics: trapped ions qubits quantum gates read out time √ Ut √ | ⇥ | ⇥ R. Blatt coherent Hamiltonian evolution - quantum gates - deterministic • decoherence ☹ spontaneous dissipation by coupling to environment - spontaneous emission etc. emission ☹ Q.: Dissipation as an engineering tool? For entanglement? 4 Tuesday, March 12, 13 Open System Dynamics [& Decoherence ☹] • open system dynamics system environ- not ment observed 5 Tuesday, March 12, 13 Open System Dynamics [& Decoherence ☹] • open system dynamics system environ- not ment observed completely positive maps: † Ω E (Ω) Ek ΩEk → = k X Kraus operator 5 Tuesday, March 12, 13 Entanglement from (Engineered) Dissipation • open system dynamics system √ √ | ⇥ | environ- not ment observed 6 Tuesday, March 12, 13 Entanglement from (Engineered) Dissipation • open system dynamics system √ √ | ⇥ | environ- not ment observed engineering Kraus operators: † Ω E (Ω) Ek ΩEk → = k ! X √ √ =| ⇥ | desired (pure) quantum state “cooling” into a pure state - non-unitary - deterministic 6 Tuesday, March 12, 13 Entanglement from (Engineered) Dissipation • open system dynamics • atomic physics: single particle optical pumping system √ √ | ⇥ | environ- not ment observed engineering Kraus operators: † Ω E (Ω) Ek ΩE t → = k ρ(t) ⇥ D D k −−−⇥ | ⌅ ⇤ | ! X √ √ =| ⇥ | pumping into a pure “dark state” desired (pure) quantum state “cooling” into a pure state - non-unitary - deterministic 6 Tuesday, March 12, 13 Entanglement from (Engineered) Dissipation • open system dynamics • atomic physics: single particle optical pumping system √ √ | ⇥ | environ- not ment observed engineering Kraus operators: † Ω E (Ω) Ek ΩE t → = k ρ(t) ⇥ D D k −−−⇥ | ⌅ ⇤ | ! X √ √ =| ⇥ | pumping into a pure “dark state” desired (pure) quantum state “cooling” into a pure state - non-unitary Q.: generalize to entangled states? - deterministic 6 Tuesday, March 12, 13 Entanglement from (Engineered) Dissipation • open system dynamics • atomic physics: single particle optical pumping system √ √ | ⇥ | environ- not ment observed engineering Kraus operators: † Ω E (Ω) Ek ΩE t → = k ρ(t) ⇥ D D k −−−⇥ | ⌅ ⇤ | ! X √ √ =| ⇥ | pumping into a pure “dark state” desired (pure) quantum state “cooling” into a pure state - non-unitary Q.: generalize to entangled states? - deterministic see also: D Bacon et al. PRA 2001; S. Lloyd & L. Viola, PRA 2001; D. Lidar, et al. PRL 1998; G. Baggio, et al. arxiv:1209.5568 (2012). 6 Tuesday, March 12, 13 Dark States: Many Particle qubits or particles on a lattice cα quasi-local Lindblad operators • master equation quantum jump operator (nonhermitian) Ω˙ i[H,Ω] = − † 1 † 1 † ∞Æ cÆΩc c cÆΩ Ω c cÆ + Æ − 2 Æ − 2 Æ Æ µ ∂ X 7 Tuesday, March 12, 13 Dark States: Many Particle qubits or particles on a lattice cα quasi-local Lindblad operators • master equation quantum jump operator (nonhermitian) Ω˙ i[H,Ω] = − † 1 † 1 † ∞Æ cÆΩc c cÆΩ Ω c cÆ + Æ − 2 Æ − 2 Æ Æ µ ∂ X • desired state as “dark state” t H D E D Ω(t) ⇥ D D | 〉 = | 〉 ⇧ | ⌅⇤ | Æ cÆ D 0 ∀ | ⇥ = construct a parent Liouvillian desired state 7 Tuesday, March 12, 13 Dark States: Many Particle qubits or particles on a lattice cα Questions: ✓ given resources → states (?) ✓ uniqueness quasi-local ✓ implementation Lindblad operators • master equation quantum jump operator (nonhermitian) Ω˙ i[H,Ω] = − † 1 † 1 † ∞Æ cÆΩc c cÆΩ Ω c cÆ + Æ − 2 Æ − 2 Æ Æ µ ∂ X • desired state as “dark state” t H D E D Ω(t) ⇥ D D | 〉 = | 〉 ⇧ | ⌅⇤ | Æ cÆ D 0 ∀ | ⇥ = construct a parent Liouvillian desired state 7 Tuesday, March 12, 13 Bell State Pumping • Bell States two spins / qubits 1 Ψ− = ( 01 + 10 ) | ⇥2 | | 1 Φ+ = ( 00 11 ) | ⇥ ⇤2 | ⇥| ⇥ 1 Φ− = ( 01 10 ) | ⇥ ⇤2 | ⇥| ⇥ 1 Ψ+ = ( 00 + 11 ) | ⇥2 | | 8 Tuesday, March 12, 13 Bell State Pumping • Bell States two spins / qubits Z1Z2 1 1 1 Ψ− = ( 01 + 10 ) + ° | ⇥2 | | + + 1 1 Φ Φ+ = ( 00 11 ) + | ⇥ ⇤2 | ⇥| ⇥ X1X2 1 1 Φ− − Φ− = ( 01 10 ) ° | ⇥ ⇤2 | ⇥| ⇥ 1 Ψ+ = ( 00 + 11 ) Bell states as eigenstates of (commuting) | ⇥2 | | stabilizer operators X1X2 and Z1Z2 8 Tuesday, March 12, 13 Bell State Pumping • Bell States two spins / qubits Z1Z2 1 1 1 Ψ− = ( 01 + 10 ) + ° | ⇥2 | | + + 1 1 Φ Φ+ = ( 00 11 ) + | ⇥ ⇤2 | ⇥| ⇥ X1X2 1 1 Φ− − Φ− = ( 01 10 ) ° | ⇥ ⇤2 | ⇥| ⇥ 1 Ψ+ = ( 00 + 11 ) Bell states as eigenstates of (commuting) | ⇥2 | | stabilizer operators X1X2 and Z1Z2 Goal: Bell state pumping Ω(t) ™⌅ ™⌅ • ⌅ | ⇤⇥ | 9 Tuesday, March 12, 13 Bell State Pumping • Bell States two spins / qubits Z1Z2 1 1 1 Ψ− = ( 01 + 10 ) + ° | ⇥2 | | + + 1 1 Φ Φ+ = ( 00 11 ) + | ⇥ ⇤2 | ⇥| ⇥ X1X2 1 1 Φ− − Φ− = ( 01 10 ) ° | ⇥ ⇤2 | ⇥| ⇥ 1 Ψ+ = ( 00 + 11 ) Bell states as eigenstates of (commuting) | ⇥2 | | stabilizer operators X1X2 and Z1Z2 Goal: Bell state pumping Ω(t) ™⌅ ™⌅ • ⌅ | ⇤⇥ | + + Φ z1z2 Φ− − 9 Tuesday, March 12, 13 Bell State Pumping • Bell States two spins / qubits Z1Z2 1 1 1 Ψ− = ( 01 + 10 ) + ° | ⇥2 | | + + 1 1 Φ Φ+ = ( 00 11 ) + | ⇥ ⇤2 | ⇥| ⇥ X1X2 1 1 Φ− − Φ− = ( 01 10 ) ° | ⇥ ⇤2 | ⇥| ⇥ 1 Ψ+ = ( 00 + 11 ) Bell states as eigenstates of (commuting) | ⇥2 | | stabilizer operators X1X2 and Z1Z2 Goal: Bell state pumping Ω(t) ™⌅ ™⌅ • ⌅ | ⇤⇥ | + + Φ z1z2 Φ− − quantum jump c1 X1(1 Z1Z2) operators = + 9 Tuesday, March 12, 13 Bell State Pumping • Bell States two spins / qubits Z1Z2 1 1 1 Ψ− = ( 01 + 10 ) + ° | ⇥2 | | + + 1 1 Φ Φ+ = ( 00 11 ) + | ⇥ ⇤2 | ⇥| ⇥ X1X2 1 1 Φ− − Φ− = ( 01 10 ) ° | ⇥ ⇤2 | ⇥| ⇥ 1 Ψ+ = ( 00 + 11 ) Bell states as eigenstates of (commuting) | ⇥2 | | stabilizer operators X1X2 and Z1Z2 Goal: Bell state pumping Ω(t) ™⌅ ™⌅ • ⌅ | ⇤⇥ | + + + + Φ 2 Φ x 1 z1z2 x Φ− − Φ− − quantum jump c1 X1(1 Z1Z2) operators = + 9 Tuesday, March 12, 13 Bell State Pumping • Bell States two spins / qubits Z1Z2 1 1 1 Ψ− = ( 01 + 10 ) + ° | ⇥2 | | + + 1 1 Φ Φ+ = ( 00 11 ) + | ⇥ ⇤2 | ⇥| ⇥ X1X2 1 1 Φ− − Φ− = ( 01 10 ) ° | ⇥ ⇤2 | ⇥| ⇥ 1 Ψ+ = ( 00 + 11 ) Bell states as eigenstates of (commuting) | ⇥2 | | stabilizer operators X1X2 and Z1Z2 Goal: Bell state pumping Ω(t) ™⌅ ™⌅ • ⌅ | ⇤⇥ | + + + + Φ 2 Φ x 1 z1z2 x Φ− − Φ− − quantum jump c1 X1(1 Z1Z2) c2 Z1(1 X1X2) operators = + = + 9 Tuesday, March 12, 13 Bell State Pumping • Bell States two spins / qubits Z1Z2 1 1 1 Ψ− = ( 01 + 10 ) + ° | ⇥2 | | + + 1 1 Φ Φ+ = ( 00 11 ) + | ⇥ ⇤2 | ⇥| ⇥ X1X2 1 1 Φ− − Φ− = ( 01 10 ) ° | ⇥ ⇤2 | ⇥| ⇥ 1 Ψ+ = ( 00 + 11 ) Bell states as eigenstates of (commuting) | ⇥2 | | stabilizer operators X1X2 and Z1Z2 Goal: Bell state pumping Ω(t) ™⌅ ™⌅ • ⌅ | ⇤⇥ | + + + + Φ 2 Φ x 1 z1z2 x Φ− − Φ− − − quantum jump c1 X1(1 Z1Z2) c2 Z1(1 X1X2) operators = + = + 9 Tuesday, March 12, 13 Bell State Pumping • Bell States two spins / qubits Z1Z2 1 1 1 Ψ− = ( 01 + 10 ) + ° | ⇥2 | | + + 1 1 Φ Φ+ = ( 00 11 ) + | ⇥ ⇤2 | ⇥| ⇥ X1X2 1 1 Φ− − Φ− = ( 01 10 ) ° | ⇥ ⇤2 | ⇥| ⇥ 1 Ψ+ = ( 00 + 11 ) Bell states as eigenstates of (commuting) | ⇥2 | | stabilizer operators X1X2 and Z1Z2 Goal: Bell state pumping Ω(t) ™⌅ ™⌅ • ⌅ | ⇤⇥ | + + + + Φ 2 Φ x 1 z1z2 x Φ− − Φ− − − quantum jump c1 X1(1 Z1Z2) c2 Z1(1 X1X2) 3-particle operators ☹ operators = + = + 9 Tuesday, March 12, 13 40 + P Ca Ions confined in 1/2 a string by a Paul trap D5/2 Detec-on Quantum 0 bit | Manipulaon S 1 1/2 | Innsbruck ion trap Tuesday, March 12, 13 Quantum operations on Innsbruck ion-trap quantum computer Individual light-shift gates (0) (1) (2) σz , σz , σz Collective spin flips S , S x y + + ... + Mølmer-Sørensen gate 2 (0) (1) (1) (2) (0) (2) Sx = σx σx + σx σx + σx σx σ(0)σ(2) (0) (1) x x σx σx (1) (2) σx σx ... 14-qubit entanglement, T. Monz et al. PRL (2011) talk U6.4 Tuesday, March 12, 13 Quantum operations on Innsbruck ion-trap quantum computer Individual light-shift gates (0) (1) (2)