Superconducting qubits for quantum information Symposium in honor of Paul Benioff’s fundamental contributions to quantum information
Andrew N Cleland All work from UC Santa Barbara Collaboration with: J. Martinis, Argonne National M. Geller, A. Korotkov, F. Laboratory Wilhelm
Argonne National Laboratory Symposium on Quantum Computing: Beginnings to Current Frontiers May 26 2016 3:10-4 pm Quantum engineered systems
Quantum computation . Gate-based implementation of quantum algorithms (Shor, Grover) . Quantum simulation of complex systems (e.g. molecular chemistry) . Adiabatic evolution for minimization problems (e.g. traveling salesman) Quantum communication . Quantum key distribution . Quantum repeaters Quantum sensing . Detection of weak fields . Detection of small displacements . Long baseline interference Ions, Rydberg atoms, BECs Atomic defects (NV, P in Si) Semiconductor quantum dots Superconducting circuits
Argonne National Laboratory Superconducting circuits in the traditional semiconductor technology roadmap
. Materials Current focus of most . Device design research Tightly interconnected . Circuit design for engineered quantum . Interconnects devices/circuits . Board level integration . Systems integration . Packaging
Argonne National Laboratory Superconducting qubits ∝Φ
C 1 energy 2 1 magnetic flux Φ Microwave frequency circuits: 2 ⁄ ~ 5 10 GHz
• Operate at 25 mK: ≪ ⇒quantum ground state • Need anharmonicity to enable quantum control
Argonne National Laboratory Superconducting qubits ∝Φ Φ
Al Al
energy | 〉 AlOx Josephson junction: Capacitor is A very nonlinear critical to qubit magnetic flux Φ inductor performance Qubit levels | 〉 and
Qubit frequency ~ 4 6 GHz Anharmonicity at single photon level: 0.95 Can tune & by changing flux through qubit
Qubit is determined by loss mechanisms in capacitor
Argonne National Laboratory Z control Measurement: • Dispersive resonator readout • Measure change in phase of few- Coupling to photon excitation other qubits Josephson in readout junctions resonator in flux loop • Projective & accurate Transmon qubit (UCSB variant) Z rotations: Capacitance • Flux tuning varies C • Changes Josephson X and Y rotations: junctions • Microwaves at (inductance L)
Argonne National Laboratory readout waveguide
readout resonators direct (one per qubit) capacitive coupling between two control lines qubits per qubit
XY XY
Z XYZ XYZ XYZ Z
Argonne National Laboratory Argonne National Laboratory Argonne National Laboratory High fidelity quantum gates Gate Fidelity ( 0.03) X 99.92 Complete set of single qubit Y 99.92 gates needed to execute an arbitrary quantum algorithm X/2 99.93 All single qubit gates operate Y/2 99.95 with fidelity > 99.9% -X 99.92 (randomized benchmarking) -Y 99.91 Controlled Z gate (equivalent to -X/2 99.93 CNOT): -Y/2 99.95 40 ns execution time H 99.91 99.5% fidelity State preparation and I 99.95 measurement fidelity ~ 90% S (Z/2 99.92 No RB method – How do we measure these low T / error rates? not a Clifford
Argonne National Laboratory Controlled Z (CZ) gate: 10 00 01 0 0 Direct ⇒ 001 0 Other states left unchanged 000 1 capacitive coupling Avoided crossing | 〉:
A B
| 〉 Adiabatic trajectory Frequency 40 ns total duration! ⇒ | 〉 XY ZZXY Qubit A tuning
Argonne National Laboratory Benchmarking • Imperfect state preparation • Imperfect state measurement • Individual gate errors small compared to SPAM Randomized benchmarking gates 95-97% 90-95% Prepare Measure random test random test random test reset gate gate gate gate gate gate gate
Argonne National Laboratory High fidelity quantum gates Gate Fidelity ( 0.03) Complete set of single qubit X 99.92 gates needed to execute an Y 99.92 arbitrary quantum algorithm X/2 99.93 All single qubit gates operate Y/2 99.95 with fidelity > 99.9% (randomized benchmarking) -X 99.92 -Y 99.91 Controlled Z gate (equivalent to CNOT): -X/2 99.93 40 ns execution time -Y/2 99.95 99.5% fidelity H 99.91 State preparation and I 99.95 measurement fidelity ~ 90% S (Z/2 99.92 Measurement now 98% in 150 ns No RB method – T / Dominant errors due to decay not a Clifford
Argonne National Laboratory Qubit Progress inqubit (UC Santa Barbara results) Laboratory National Argonne • • • Improvements: Better circuit design Reduced electricfields Fewer imperfections Aluminum resonators on sapphire • MBE grown Al on annealed sapphire gives best performance • Intrinsic around 2 106 at low power • Film quality & substrate properties critical
Argonne National Laboratory Superconducting qubits on sapphire
• ( ) vary strongly with frequency (repeatable) • ( ) consistent with two-level states
Resonators have Q’s 3-5 times higher
Argonne National Laboratory Defects: Two-level states at GHz frequencies
SEM inspection Microwave measurement GHz-frequency two-level states become active at low temperatures Circuits primarily sensitive to electrically active TLS Reduce qubit and resonator Participation strongest for aligned dipoles in strong electric fields What are these TLS? Where do they come from? How do we minimize/eliminate them?
Argonne National Laboratory Limiting effects due to materials Two-level states Most important contributor to qubit Resonators (single step fabrication) have 3-5 times fewer TLS Origin unknown Become active at low temperatures Vary with substrate and substrate preparation Flux noise Important limiting effect on qubit No apparent effect on resonators Origin unknown Investigated since 1980s in SQUIDs Surface density of correlated magnetic dipoles (~1013/cm2)?
Argonne National Laboratory Programming a 5 qubit GHZ state CZ | 〉 Y/2 A CZ | 〉 -Y/2 Y/2 B CZ | 〉 -Y/2 Y/2 C CZ | 〉 -Y/2 Y/2 D | 〉 -Y/2 Y/2 E
2Bell 3GHZ 4GHZ 5GHZ
0.995 0.960 0.863 0.817
Argonne National Laboratory Superconducting implementation of Shor’s algorithm
Quantum processor with 4 qubits and 5 microwave resonators von Neumann architecture to factor 15 using Shor’s algorithm Achieves correct answer 48% of attempts (best possible 50%)
Argonne Lucero et al. Nature Physics (2012) National Laboratory Building perfection from imperfection: The surface code Square array of physical qubits Only nearest-neighbor coupling Data qubit: Stores computational state | 〉 Measure-X qubit: Stabilizes data qubits individual physical Measure-Z qubit: qubits Stabilizes data qubits Measure-X qubit cycle Surface code stabilizer cycle: • Qubit state reset • Hadamard gate • Multiple two-qubit CNOTs • Projective measurement Analogous stabilizer Result: eigenstate Need overall fidelity > 99.5%
Argonne National Laboratory Quantum algorithms 10 Quantum entanglement enables new problem-solving algorithms 10 . Deutsch-Jozsa: Given a black-boxSieve function 10 → 0,1 , wherespeedup is an element binary vector, determine whetherspeedup is constant or balanced. Classical algorithm needs 2 Shor 1function evaluations (worst case). (computation time) (computation Deutsch-Jozsa gets answer with one evaluation 10 (non-probabilistic). . Grover: Given a black-box function , where has possible RSA-768 values, find given . RSA-500 Classical algorithmLog needs function evaluations. Grover gets high- probability answer with ⁄ evaluations (quadratic speed-up). Makes brute-force attack on small (128Log bit) RSA (sizeencryption of problem) feasible. . Shor: Find the prime factors of the integer . Classical sieve algorithm: exp 1.9 log ⁄ log log ⁄ steps. Quantum Shor algorithm: log log log log log log steps Answer is probabilistic; assumes unlimited resources
Argonne National Laboratory Building perfection from imperfection: The surface code . Assume error rate 1/10th threshold (99.95% fidelity) Logical memory qubit from array of physical qubits 1,000 smaller error rate: ~600 physical qubits 1,000,000 smaller error rate: ~2,000 physical qubits 1,000,000,000 smaller rate: ~4,500 physical qubits Circuit to demonstrate topological CNOT: With 1,000 smaller error rate: ~1,800 physical qubits Prime factoring with Shor’s algorithm: Factor a 15 bit number (105): ~40,000,000 qubits Factor a 2000 bit number (10600): ~1,000,000,000 qubits
Argonne National Laboratory Quantum computer circuit time control | 〉 | 〉 targets | 〉 | 〉
| 〉 | 〉 What does this code do? It “purifies” | 〉 a special | 〉 state: ⁄ | 〉 | 〉 Needed for gate | 〉 | 〉 99% of a factoring | 〉 | 〉 output computer is used to | 〉purify states | 〉
Argonne National Laboratory “Gate-based” quantum computation: Challenges
Scale-up challenge: 1D to 2D qubit circuits Demonstrate full quantum error correction Fix , , errors caused by environment Demonstrate logical qubit Logical qubit state lifetime longer than physical qubit lifetime Demonstrate “large” logical qubit entanglement Demonstrate protected logical operations Logical qubit manipulations with error protection Scale-up challenge: 2D to 3D wiring interconnects Quantum simulations: Useful & interesting problems
Argonne National Laboratory Superconducting qubits for quantum information Symposium in honor of Paul Benioff’s fundamental contributions to quantum information Andrew N Cleland
Argonne National Laboratory
Argonne National Laboratory Symposium on Quantum Computing: Beginnings to Current Frontiers May 26 2016 3:10-4 pm