IBM quantum experience: Experimental implementations, scope, and limitations

Transcription

1 IBM quantum experience: Experimental implementations, scope, and limitations

2 Plan of the talk IBM Quantum Experience Introduction IBM GUI Building blocks for IBM quantum computing Implementations of various QIP tasks Limitations and scope Initialization Quantum gates Measurement Reversible logic Quantum teleportation Error correction

3 Plan of the talk IBM Quantum Experience Introduction IBM GUI Building blocks for IBM quantum computing Implementations of various QIP tasks Limitations and scope Initialization Quantum gates Measurement Reversible logic Quantum teleportation Error correction

4 Quantum information processors Quantum information processor (QIP) DiVincenzo s criteria Initialization ψ = a 0 + b 1 Quantum Gates ψ = U k U K-1 U 1 ψ Measurement A = ψ A ψ Superposition: Makes quantum processors more capable than classical computers in certain tasks Nuclear spins: NMR Josephson qubits: SQUID (IBM quantum computer) Photons: Linear optics Ion trap NV and P vacancy systems: Solid state spins etc.

5 Plan of the talk IBM Quantum Experience Introduction IBM GUI Building blocks for IBM quantum computing Implementations of various QIP tasks Limitations and scope Initialization Quantum gates Measurement Reversible logic Quantum teleportation Error correction

6 Introduction: User platform for IBM quantum computer Retrieved from

7 Schematic diagram of architecture Retrieved from

8 Plan of the talk IBM Quantum Experience Introduction IBM GUI Building blocks for IBM quantum computing Implementations of various QIP tasks Limitations and scope Initialization Quantum gates Measurement Reversible logic Quantum teleportation Error correction

9 Initialization Single qubit state ψ = α 0 + β 1 α = 0.923, β= Entangled state ψ = α ( )+β ( ) α = 0.612, β=

10 Quantum Gates Clifford Gate library H S S id X Y Z Hadamard Phase gate (π/2) Pauli Gates Phase Gate (π/8) T T Universal Gate library C-NOT Some more physical Gates (Helps in preparation of complex states) U1 U2 U / > ( 0 + e iφ 1 )/ 2 ( )/ > α 0 +βe (iφ) 1 here α = cos(λ/2)e (i λ/2), β = sin(λ/2)e (-i λ/2)

11 Measurement in IBM quantum computer Measurement in Z basis Z M z M z 0 1 Measurement in X basis M x Mx X = H / / 2 Measurement in Y basis P i = M 1 E 1 + M 2 E 2 = 1 [ 1 + ( x x + Y y + Z z ) ] 2 = Y = S H Density matrix tomography (single qubit) M y M y 0 +i 1 / 2 0 -i 1 / 2

12 Some useful control operations Reverse C-NOT = Control-H H = Control-P P = C C P- Pauli Operator C- Clifford Gate

13 Some more Gates Toffoli = Swap Gates =

14 Plan of the talk IBM Quantum Experience Introduction IBM GUI Building blocks for IBM quantum computing Implementations of various QIP tasks Limitations and scope Initialization Quantum gates Measurement Quantum teleportation Reversible logic Error correction

15 Quantum teleportation Single qubit state teleportation ψ Measurement by Alice on her qubits Quantum channel φ + Classical communication Reconstructed single qubit state ψ Application of unitaries by Bob on his qubit Multi-qubit state teleportation ψ = i α i x i where x i is a basis element of N-qubit basis {X i }. Arbitrary N qubit state : N pair of Bell state are required ψ Possibility of optimizing channel size: Size depends on Number of unknowns Teleporting a m-unknown N qubit state of type ψ = i α i x i by using optimal channel size Choudhury et al., IJTP (2016): 1-7; 4-qubit cluster state; ( ( ) Li et. al, IJTP 55 (2016): ; Four qubit cluster state;

16 Quantum teleportation Example: Teleporting an N qubit state with two unknowns. Step1: Step2: Step3: Standard method for teleporting a single qubit arbitrary state U N qubit state with two unknowns!! ( ( ) Two Bell states One Bell states

17 Quantum teleportation Circuit for Implementation of protocol on IBM quantum computer α = 0.612, β= Initial state Reconstructed state ψ = 0.621( ) ( ) ψ = 0.633( ) ( )

18 Implementation of reversible circuit on IBM quantum computer (1) Arithmetic 4:1 reversible multiplexer (2) Half adder (2) In: 111 0/p: 110 Retrived from: reversible logic benchmark pagehttp://webhome.cs.uvic.ca/dmaslov/

19 Implementation of reversible circuit on IBM quantum computer (1) Hamming optimal coding function (2) To find primes upto 3 binary digits (1) (2) Retrived from: Reversible logic benchmark page,

20 Error correction A simple code for detecting bit-flip error α 0 + β a1 0 a2 ψ = α 0 + β 1 X 3 1 α β a1 0 a2 0 2 Correction α β a1 0 a 0 0 Measure 3 S qubit 1 S qubit 2 S qubit 3 A1 A2 F N N F N N F N F F N N F N F α β a1 0 a2 4 α β 011 ) 10 a Elements of quantum information and quantum communication, Anirban Pathak, Taylor & Francis (2013).

21 Error correction A simple code for detecting phase-flip error α β 111 H 123 ψ = α 0 + β H H H X 2 H H H 3 4 Correction α β a1 0 a2 2 α β a1 0 a2 H 123 Measure α β a1 0 a2 3 4 Phase flip error can be encoded in diagonal basis as bit flip error. α β a Elements of quantum information and quantum communication, Anirban Pathak, Taylor & Francis (2013)

22 Error correction IBM experiment for detecting bit-flip error Bit flip detected and corrected!!

23 Plan of the talk IBM Quantum Experience Introduction IBM GUI Building blocks for IBM quantum computing Implementations of various QIP tasks Limitations and scope Initialization Quantum gates Measurement Reversible logic Quantum teleportation Error correction

24 Limitations and scope Decoherence and Gate errors: T1, T2 relaxation times are very short compare to already reported qubit systems in same architecture. A brief detail is following. Low fidelity of gates: for C-NOT Unavailability of all coupled qubits: Restricts direct application of C-NOT gate between arbitrary qubits. Swap operations: This limitation can be handled up to an extent only if circuit to be implemented has less complexity. Otherwise results in a drastic loss of fidelity. Example: Fredkin gate

25 Limitations and scope Results Restricted number of gates: Currently we can not apply more than forty gates in each line. Dead end after measurement: Limits feed back applications. Unavailability of shaped pulses. It provides a decent platform for application of various QIP tasks on small scale registers and hence provides a chance to test theoretical models. Its open access to the young minds will speed-up evolution of quantum technologies.

26 Entanglement assisted metrology Detecting state of single spin with the help of an ensemble of spins X P. Cappellaro et al., PRL, 2005

27 Group members and project collaborators Principal investigator To all of you for your attention and time.