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Quantum Reservoir Engineering (Discussion in the Quantum Coherent Control Program) IQOQI AUSTRIAN ACADEMY of SCIENCES

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Quantum Reservoir Engineering (Discussion in the Quantum Coherent Control Program) IQOQI AUSTRIAN ACADEMY of SCIENCES 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)
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