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,