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Quantum Computing with the IBM Quantum Experience with the Quantum Information Software Toolkit (Qiskit) Nick Bronn Research Staff Member IBM T.J

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Quantum Computing with the IBM Quantum Experience with the Quantum Information Software Toolkit (Qiskit) Nick Bronn Research Staff Member IBM T.J Quantum Computing with the IBM Quantum Experience with the Quantum Information Software Toolkit (QISKit) Nick Bronn Research Staff Member IBM T.J. Watson Research Center ACM Poughkeepsie Monthly Meeting, January 2018 1 ©2017 IBM Corporation 25 January 2018 Overview Part 1: Quantum Computing § What, why, how § Quantum gates and circuits Part 2: Superconducting Qubits § Device properties § Control and performance Part 3: IBM Quantum Experience § Website: GUI, user guides, community § QISKit: API, SDK, Tutorials 2 ©2017 IBM Corporation 25 January 2018 Quantum computing: what, why, how 3 ©2017 IBM Corporation 25 January 2018 “Nature isn’t classical . if you want to make a simula6on of nature, you’d be:er make it quantum mechanical, and by golly it’s a wonderful problem, because it doesn’t look so easy.” – Richard Feynman, 1981 1st Conference on Physics and Computation, MIT 4 ©2017 IBM Corporation 25 January 2018 Computing with Quantum Mechanics: Features Superposion: a system’s state can be any linear combinaon of classical states …un#l it is measured, at which point it collapses to one of the classical states Example: Schrodinger’s Cat “Classical” states Quantum Normalizaon wavefuncon Entanglement: par0cles in superposi0on 1 ⎛ ⎞ ψ = ⎜ + ⎟ can develop correlaons such that 2 ⎜ ⎟ measuring just one affects them all ⎝ ⎠ Example: EPR Paradox (Einstein: “spooky Linear combinaon ac0on at a distance”) 5 ©2017 IBM Corporation 25 January 2018 Computing with Quantum Mechanics: Drawbacks 1 Decoherence: a system is gradually measured by residual interac0on with its environment, killing quantum behavior Qubit State Consequence: quantum effects observed only 0 Time in well-isolated systems (so not cats… yet) Uncertainty principle: measuring one variable (e.g. posi0on) disturbs its conjugate (e.g. momentum) Consequence: complete knowledge of an arbitrary quantum state is impossible. à “No-Cloning Theorem” 6 ©2017 IBM Corporation 25 January 2018 What does a quantum bit look like? Classical bit Physical systems: capacitor charge, transistor state, magne0c polarizaon, presence or absence of a punched hole, etc. Logical states: just 0 and 1 Mul8-bit effects: none Quantum bit (“qubit”) Physical systems: electron spins, atomic states, superconducng circuit states Logical states: |0>, |1>, superposi6ons Mul8-qubit effects: entanglement 7 ©2017 IBM Corporation 25 January 2018 Gate model quantum compung: the future Fault-Tolerant QC 8 ©2017 IBM Corporation 25 January 2018 How powerful is a quantum computer: quantum volume Quantum Volume Number of qubits (more is better) Errors (fewer is better) Connectivity (more is better) Gate set (more is better) 9 9 ©2017 IBM Corporation 25 January 2018 © 2017 IBM Corporation Quantum computing: quantum operations and circuits 10 ©2017 IBM Corporation 25 January 2018 Single-qubit gates § Gates are described by one or more Clifford group: permutes the states |​ rotations about an axis or set of axes �⟩, |​�⟩, |​+⟩, |​−⟩, |!​ ⟩, and |!​ ⟩, idenfied – Pauli X, Y, Z gates: below Z § Rotate π radians about specified axis |​�⟩ § X and Y gates equivalent to classical NOT |​−⟩ -Transform |0> to |1> and vice versa |!​ ⟩ |!​ ⟩ – Clifford gates: Y § Permute states identified at right (includes |​+⟩ Pauli gates) |​�⟩ – Arbitrary gates: X § Map any point on sphere to any other =​ | ​� ⟩+ | ​� /√⟩ �⁠ |​�⟩ |​�⟩ § Typically implemented with a small set of |​+⟩ |​−⟩ =​ − /√�⁠ well-calibrated gates, e.g. Clifford group =​ | ​� ⟩+ � | ​� /√⟩ �⁠ =​ | ​� −⟩ � | ​� ⟩/√ �⁠ plus one additional gate |!​ ⟩ |!​ ⟩ 11 ©2017 IBM Corporation 25 January 2018 Z Key single-qubit gate: Hadamard (H) X + Z |​�⟩ § Hadamard gate: rotate 180°about X+Z axis |​−⟩ – Exchanges Z and X axes – Takes classical states to equal-weighted |!​ ⟩ |!​ ⟩ superposition states and vice versa Y § |​�⟩ à |​+⟩ |​+⟩ à |​�⟩ |​+⟩ § |​�⟩ à |​−⟩ |​−⟩ à |​�⟩ X – Used in almost every quantum algorithm |​�⟩ § Performs the quantum Fourier transform of Matrix representation of Hadamard acting on |​0⟩ a single qubit – Classical Fourier transform: exchange conjugate variables describing a signal (e.g. time domain à frequency domain) – Quantum Fourier transform: exchange conjugate variables describing a state 12 ©2017 IBM Corporation 25 January 2018 Qubit measurements Measurement icon used in the IBM QX § Standard measurement in the computational basis: Ini0al state Possible outcomes – Collapses any superposition into one |0> with probability α2 of the two classical states: |​�⟩ or |​�⟩ |1> with probability β2 § Measurement in other bases: – Measurement itself is only sensitive to Z Basis change for |​�⟩ vs |​�⟩ |​�⟩ measuring in |​ – To measure in other bases, rotate first |​−⟩ +⟩ / |​−⟩ basis – Example: to distinguish |​+⟩ from |​−⟩, apply Hadamard before measuring Y |​+⟩ |​�⟩ § If state was , measure |​+⟩ § If state was |​−⟩, measure |​�⟩ X |​�⟩ 13 ©2017 IBM Corporation 25 January 2018 A simple “quantum score” § Visual representation of a series of operations Quantum Opus I performed on a quantum register (a set of qubits grouped together) § N-qubit quantum register: qubits q[0] – q[N-1] § After measurement, results stored in classical Measure in |​ Inialize Hadamard register as c[0] – c[N-1] �⟩, |​�⟩ basis § Example quantum score on 2-qubit register: – Initialize both qubits in |​�⟩ – Apply Hadamard (H) to each qubit – Measure q[0] in the |​�⟩, |​�⟩ basis – Measure q[1] in the |​+⟩, |​−⟩ basis § Results: – q[0] measurement gives either |​�⟩ or |​�⟩, each with 50% probability – q[1] measurement always gives |​�⟩ |​ § Infer that q[1] was in |​+⟩ prior to 2nd H Measure in 14 ©2017 IBM Corporation 25 January 2018 +⟩, |​−⟩ basis Multi-qubit operations § Two-qubit operations: – Controlled not (CNOT): § Classical behavior: flip target iff control is 1 Initial State Final State Entangled state! Control Q Target Q Control Q Target Q | | | | | | | | α | + β | | α | + β | – Controlled phase (CPhase) § Same idea but target qubit is flipped around the Z axis (instead of X) § Equivalent to CNOT up to single-qubit gates 15 ©2017 IBM Corporation 25 January 2018 Superconducting qubits: device properties 16 ©2017 IBM Corporation 25 January 2018 Superconducting qubit building blocks Circuit element toolbox Josephson Junction: • Weak link between two dI 1 R C L JJ = V (t) superconductors dt L • Typically Al / AlOx / Al Φ Key features: L(δ ) = 0 • non-linear inductance 2πI0 cos(δ ) • dissipationless operation L-C Oscillator: harmonic JJ-C Oscillator: anharmonic à can’t address individual transitions à individual transitions addressable ω23 = ω12 |2〉 |2〉 ω12 = ω01 |1〉 |1〉 ω01 |0〉 |0〉 Qubit 17 ©2017 IBM Corporation 25 January 2018 Qubit coupling via resonators: circuit QED (cQED) § Qubit interacts with environment via a resonator § Analogous to an atom in an optical cavity 0 Wallraff et al., Nature 431, 162 (2004) 18 ©2017 IBM Corporation 25 January 2018 Qubit Readout in cQED Create Readout pulses Resonator / Qubit Amplify, digitize, identify as 0 or 1 pulses Control pulses System Readout freq. near ωr; control freq. at ω0 I = in-phase Resonator frequency depends on qubit state Q = out-of-phase à Infer qubit state from resonator response 2χ Q Amplitude |​1⟩ |​0⟩ |​1⟩ IQ22+ mm κ |​0⟩ f θ I 90 I m I m −1 Phase (deg) |​1⟩ θχκ= 2tan( / ) −1 For 2χ =κ, θ = 90° tan(QImm / ) |​0⟩ -90 f Gambeha et al., PRA 77, 012112 (2008) fd jeffrey et al., PRL 112, 190504 (2014) 19 ©2017 IBM Corporation 25 January 2018 Magesan et al., PRL 114, 200501 (2015) IBM single-junction transmons Josephson Junction ~100 x 100 nm2 LJ ~ 20 nH CS ~ 60 fF 100 m CJ ~ 1 fF µ = To bus To bus § Patterned superconducting metal (niobium + aluminum) on silicon – Qubit capacitance dominated by shunting capacitance CS § Resonant frequency ~ 5 GHz à energy splitting ~ 20 µeV, or 240 mK à Cool in a dilution refrigerator (~ 10 mK) to reach ground state § Interactions mediated by capacitively coupled co-planar waveguide resonators (circuit QED) 20 ©2017 IBM Corporation 25 January 2018 Anatomy of a multi-qubit device Qubits: Single-juncon transmon Frequency ~ 5 GHz Anharmonicity ~ 0.3 GHz Resonators: Co-planar waveguide Frequency ~ 6 – 7 GHz Roles: Individual qubit readout Qubit coupling (“bus”) Ground plane Periodic holes prevent stray 1 mm magne0c field from hur0ng superconductor performance Corcoles et al., Nat. Commun. 6, 6979 (2015) 21 ©2017 IBM Corporation 25 January 2018 IBM Quantum Experience 22 ©2017 IBM Corporation 25 January 2018 IBM Quantum Experience (IBMQX) • Free cloud based quantum computing platform Cloud – 5-qubit quantum processor (real hardware) research.ibm.com/ibm-q/ – 20-qubit quantum simulator – 16-qubit quantum processor (access through QISKit: www.qiskit.org) IBM QX2: 5-qubit Quantum Simulator IBM QX3: 16-qubit 23 ©2017 IBM Corporation 25 January 2018 15 External Papers 24 ©2017 IBM Corporation 25 January 2018 Real Quantum Processor: Device Details • 5-qubit device – Single-junction transmons – T1 ~ T2 ~ 50 – 100 µs – 1Q gate fidelities > 99% – 2Q gate fidelities > 95% – Measurement fidelities > 93% – Connectivity: 6 CNOTs available • 16-qubit device (NEW!) – Access through QISKit API only 25 ©2017 IBM Corporation 25 January 2018 IBM QX: Web Interface § https://quantumexperience.ng.bluemix.net § Graphical composer – Compose quantum circuits using drag and drop interface – Save circuits online or as QASM text, and import later – Run circuits on real hardware and simulator 26 ©2017 IBM Corporation 25 January 2018 IBM QX: Web Interface § https://quantumexperience.ng.bluemix.net § Library – User guides for all levels (beginner, advanced,
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