A Brief Update on Google’s Quantum Computing Initiative HPC & Quantum, London February 5,, 2019 kkissell@google.com Confidential & Proprietary
Our Brains are Wired for Newtonian Physics Brains that recognize and anticipate behaviors of Heat, Light, Momentum, Gravity, etc. have an Evolutionary Advantage. Quantum phenomena contradict our intuition.
Quantum Phenomena Contradict Intuition Interference, “Erasure”, etc. ( ) 0 Quantum Theory Explains 1 Cleanly… ...but the Math looks Strange 1 1 1 1 i i √2 i 1 How can a Particle be √2 On Two Paths at the Same Time? 1 1 i √2 ( ) P u 1 1 i P r √2 i 1 Confidential & Proprietary
Superposed States, Superposed Information l0 〉 |0 〉 + |1 〉 ( |0 〉 +|1 〉 ) 2 = |00 〉 +|01 〉 +|10 〉 +|11 〉 l1 〉 Confidential & Proprietary
0 1 Macroscopic QM Enables New Technology Control of single quantum systems, to quantum computers 1 nm 1 μ m 1 mm H atom wavefunctions: Problem: Light is 1000x larger Large “atom” has room for complex control Confidential & Proprietary
Xmon Qubit: Direct coupling + Tunable Transmons ● Direct qubit-qubit capacitive coupling ● Turn interaction on and off with frequency Readout control “OFF” “ON” f 10 XY control Frequency Frequency f 21 Δ η Z control Coupler Qubit Qubit Coupling rate Ω zz ≈ 4ηg 2 / Δ 2 Confidential & Proprietary
Logic Built from Universal Gates Classical circuit: Quantum circuit: 1 bit NOT 1 qubit rotation 2 bit AND 2 qubit CNOT 1 Input Gates Wiring fan-out No copy 2 Input Gates (space+time ) time Confidential & Proprietary
Execution of a Quantum Simulation Confidential & Proprietary
Quantum Simulation Results, H 2 Molecule Control Qubits Confidential & Proprietary Confidential & Proprietary Office of the CTO
Space-Time Volume of a Quantum Gate Computation 2 qubit gate fidelity = 99.5% Uncorrected Gate “Circuits” Limited by Fidelity of Operations and Decoherence Times Fidelity is the Third Dimension Gate Depth Confidential & Proprietary
Which computer is probability p(k)/p err better at landing Quantum “Supremacy” samples the “Bright Spots” ? Do what classical CPUs Cannot do: index k 2 n 0 Ideal distribution probability p(k)/p err Multiple errors e -p >50 Qubits, >40 Steps 2 n 0 ordered index k Confidential & Proprietary
Toward Universal Fault-Tolerant QC Qubit error rates ~10 -2 -10 -3 per operation ● Universal QC requires ~10 -10 ● Error correction: ● Low error logical qubit made with many ○ physical qubits ● Surface code error correction: 2D array of qubits (n.n. coupling) ○ Modest error rates (1% threshold, ○ 0.1% target) Useful at 10 6 physical qubits ○ Confidential & Proprietary
9 Qubit: Good performance, Limited Scaling 9 qubit device has good performance ● Err CZ down to 0.6% ● Err SQ < 0.1% ● Err RO = 1% Limited to 1D connectivity (planar geometry) Scale-up strategy: move qubits, control to different planes Confidential & Proprietary
Bump-Bond Architecture ● Bond together two separate chips ○ Qubits → “Chip” “Chip” ○ Control → “Carrier” bumps “Carrier” ● Superconducting interconnect ● Use lossless vacuum as dielectric In 30 μm TiN Al Confidential & Proprietary
Qubits Scaling to 2D Control (chip) (substrate) Res Res Res Design must be “tileable” (control fits in qubit footprint) ● Readout resonator ● XY coupler Res Res Res ● SQUID coupler Need to shield qubits from interior wire routing Res Res Res ● Small coupling to 50Ω line will decohere qubit Res Res Res Confidential & Proprietary
“Foxtail” 22 Qubit Device “Chip” “Carrier” ● Qubits ● Readout ● XY control ● Z control Confidential & Proprietary
2D Unit Cell ● Diagonal for surface code: all “measure” qubits on same line ● Condense footprint across 2 chips ● Introduce shielded wiring between qubits ● Tile unit cell for 2D array Unit cell: Condensed, diagonal linear chain Condense Readout line rotate RO RO RO RO RO RO XYZ XYZ XYZ XYZ XYZ XYZ Unit cell designed for surface code Confidential & Proprietary
“Bristlecone” Architecture Tile 12 unit cells of 6 qubits = 72 qubits Tile for a 2D grid of n.n. coupled qubits Bonus: Looks like a pine cone! Confidential & Proprietary
“72 qubits cold in fridge” Confidential & Proprietary
Early Quantum Computing Applications Quantum Numerical Simulation Optimization Confidential & Proprietary
C’est quoi ce Cirq? Confidential & Proprietary
Cloud Quantum Computing Workflow Application Frameworks OpenFermion (chemistry) IsingFlow (optimization) TensorFlow (ML) Quantum results quantum Hardware hardware language qhl Quantum Engine results qhl Python framework for writing quantum programs Quantum results Programs Simulator Jobs Results Confidential & Proprietary
Hardware-Agnostic Languages for NISQ? Assembly languages Frameworks Hardware control Languages OpenQASM PyQuil Mix of industry tools Q# Quil QISKit and proprietary aQasm ProjectQ higher levels of abstraction Cirq is built in the belief that NISQ programming tools need to be hardware aware, not hardware agnostic. Confidential & Proprietary
is ● An open source Python framework for writing, optimizing, and running quantum programs on near term hardware. Confidential & Proprietary
Cirq Structure Confidential & Proprietary
1-bit Calculator H Measurement H This circuit executes four calculations simultaneously Confidential & Proprietary
The 1-bit Calculator in Cirq - Build a Circuit H import matplotlib.pyplot as plot from pandas import DataFrame import cirq from cirq.ops import CNOT, TOFFOLI H runs = 1000 # Create 3 gubits in a line q1 = cirq.GridQubit(0,0) q2 = cirq.GridQubit(0,1) q3 = cirq.GridQubit(0,2) # Create a circuit for the qubits circuit = cirq.Circuit.from_ops( cirq.H(q1), cirq.H(q2), # Start wiih H gates on q1 and q2 TOFFOLI(q1,q2,q3), CNOT(q1,q2), cirq.measure(q2, key='m1'), cirq.measure(q3, key='m2')) print("Circuit:") print(circuit) Circuit: (0, 0): ───H───@───@───────────── │ │ (0, 1): ───H───@───X───M('m1')─── │ (0, 2): ───────X───────M('m2')─── Confidential & Proprietary
The 1-bit Calculator in Cirq - Simulate and Sample # Instantiate a simulator and run the circuit simulator = cirq.google.XmonSimulator() result = simulator.run(circuit, repetitions=runs) summary = {'00':0, '01':0, '10':0} for m1, m2 in zip(result.measurements['m1'], result.measurements['m2']): if m1[0] and not m2[0]: summary['01'] += 1.0 / runs elif not m1[0] and m2[0]: summary['10'] += 1.0 / runs else: summary['00'] += 1.0 / runs print() print('Result:') fig = plot.figure() subplot = fig.add_subplot(111) subplot.set_xticks(range(3)) subplot.set_ylim([0, 1.0]) subplot.bar(range(3), summary.values()) _ = subplot.set_xticklabels(summary.keys()) plot.show() Confidential & Proprietary
Thanks for Your Attention! Resources: https://github.com/quantumlib/Cirq https://github.com/quantumlib/OpenFermion
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