Josephson Flux Qubits in Charge-Phase Regime D-Wave Systems Inc. THE QUANTUM COMPUTING COMPANYTM Josephson Flux Qubits in Charge-Phase Regime M. H. S. Amin D-Wave Systems Inc., Vancouver, Canada Thanks to: P. Echternach (JPL) M. Grajcar (IPHT/Comenius) E. Il’ichev (IPHT) M. Kenyon (JPL) A. Kleinsasser (JPL) A. Maassen van den Brink (D-Wave) G. Rose (D-Wave) A. Shnirman (Kalsruhe) A. Smirnov (D-Wave) A. Zagoskin (D-Wave)

Charge Qubit vs Flux Qubit r = EC /EJ Flux qubits: r <<1 Charge qubits: r >>1 10-2 10-1 10 Il’ichev et al. Van der Wal et al. Nakamura et al. Guillaume et al. Pashkin et al. Duty et al. Chiorescu et al. r Vion et al. Large sensitivity to flux noise Large sensitivity to charge noise Charge-phase regime; The most Interesting

Decoherence Time t t ~ ? Charge qubit Charge-phase regime Saclay: t ~ 500 ns NEC/Chalmers/JPL: t ~ 5 ns 3JJ flux qubit Delft: t ~ 100 ns D-Wave/IPHT: t ~ 2.5 ms Phase-charge regime t ~ ?

Problems with Flux Qubits 1. Single shot readout difficult D-Wave/IPHT: t ~ 2.5 ms -Characterization technique, not readout Delft/MIT: t ~ 100 ns -Requires large L; Large coupling to magnetic environment -DC-SQUID is dissipative

Problems with Flux Qubits 1. Single shot readout difficult 2. Exponential dependence of D on qubit parameters 3. Controllable coupling difficult 4. Large sensitivity to flux noise

Why Charge-Phase Regime? The effects of both charge and flux noise can be minimized Readout can be easily switched on and off Two degrees of freedom (instead of one) are available for e.g. coupling and readout Smaller sensitivity to system parameters

Phase can be used for readout Quantronium Qubit |n |n+1 E |1 EJ |0 ng 1/2 |0 = 2-1/2 ( |n + |n+1) + . . . Qubit States: |1 = 2-1/2 ( |n - |n+1) + . . . Uncertainty in Charge  Localization of phase Phase can be used for readout

Quantronium Qubit persistent currents: F0 i1 i0 ¶ 2p E i = ¶ d E01 j j F0 ¶ d Magic point E01 ( @ Ng = 1/2 ) i0 i1 d/2p current (nA) 2 1 - d/2p 2 1 ng 2 1 2 1 - 4 1 - 4 1 2 1

Dual of Quantronium What charge? Flux qubit: D |R |L E Energy Levels 1/2 Fe/ F0 Uncertainty in phase  Localization of charge What charge?

Aharonov-Casher Effect Aharonov-Bohm effect: e F Interference F Example: DC-SQUID

Aharonov-Casher Effect Q Interference

Aharonov-Casher Effect J.R. Friedman and D.A. Averin, PRL (2002). t1 t1 Cg F Vg t2 t2  Two paths for flux to tunnel  Interference Quasicharge Island Voltage: Island Charge: State Dependent

Two Josephson Junction Qubit Cg Q Vg To charge/voltage detector F Coupling can be switched off during the operation  Large energy derivatives  Large coupling to background charges Problems:  Large flux  Large coupling to magnetic environment

Three Josephson Junction Qubit h = t2 /t1 t1 t2 T.P. Orlando et al. PRB 60, 15398 (1999)  Small flux, small coupling to environment  Two islands available for coupling

Energy Eigenstates Hamiltonian:

Energy Eigenstates Effective Hamiltonian:

Energy Eigenstates Effective Hamiltonian: Eigenenergies: r = EC /EJ h = t2 /t1 nA (=VgACg/2e)

Energy Eigenstates Effective Hamiltonian: Eigenenergies: r = EC /EJ h = t2 /t1 nA (=VgACg/2e)

Island Voltages No Coupling Magic Point: nA = nB = f = 0  VA = VB = 0 At f = Fx/F0-1/2 = 0: Magic Point: nA = nB = f = 0  VA = VB = 0 No Coupling

Island Voltages No Coupling Magic Point: nA = nB = f = 0  VA = VB = 0 At f = Fx/F0-1/2 = 0: Magic Point: nA = nB = f = 0  VA = VB = 0 No Coupling Charge/flux fluctuations affect decoherence only in the 2nd order

Island Voltages No Coupling Directional Coupling  VA = Max , VB = 0 At f = Fx/F0-1/2 = 0: Magic Point: nA = nB = f = 0  VA = VB = 0 No Coupling Coupled regime:  VA = Max , VB = 0 Directional Coupling

Small sensitivity to system parameters at large r (= EC /EJ) Some Numerics Small sensitivity to system parameters at large r (= EC /EJ)

Readout Scheme Off: Vg = 0 during the operations Switchable Readout: Sensitive charge (voltage) detector Off: Vg = 0 during the operations On: Vg = e/2Cg at the time of readout

Qubits are coupled only if Two Qubit Coupling Switchable Coupling: Qubits are coupled only if V(1)gB  0 and V(2)gA  0.

Can couple every two qubits Multi-Qubit Coupling Coupling via a bus island: Can couple every two qubits

Multi-Qubit Coupling Nearest neighbors coupling:

QA large enough to be measured by rf-SET Suggested Parameters EC / EJ = 0.1, a = 0.8, Cg = 0.1 C D  5.6 GHz, h  0.13 Island Voltage: VA  3.7 mV Island Charge: QA  0.2e QA large enough to be measured by rf-SET

Comparison with Other Qubits 3JJ flux qubit: Charge-phase qubit: Needs finite L for readout L can be small; Small coupling to magnetic environment

Comparison with Other Qubits 3JJ flux qubit: Charge-phase qubit: Needs finite L for readout L can be small; Small coupling to magnetic environment D exponentially depends on parameters Significantly smaller parameter dependence

Comparison with Other Qubits 3JJ flux qubit: Charge-phase qubit: Needs finite L for readout L can be small; Small coupling to magnetic environment D exponentially depends on parameters Significantly smaller parameter dependence EJ/D0 ~ 350 EJ/D0 ~ 10 ~3 orders of magnitude smaller kf ; smaller effect of flux fluctuations

Comparison with Other Qubits Quantronium qubit: Charge-phase qubit: kC ~ 1.3, CS ~ 5 fF kC ~ 1.8, CS ~ 8 fF Same sensitivity to background charge noise

Comparison with Other Qubits Quantronium qubit: Charge-phase qubit: kC ~ 1.3, CS ~ 5 fF kC ~ 1.8, CS ~ 8 fF Same sensitivity to background charge noise E1 E0 E2 E3 En E10 E21 Anharmonicity: A = (E21- E10 )/ E10 Harmonic oscillator: A = 0 Ideal qubit: A = 

Comparison with Other Qubits Quantronium qubit: Charge-phase qubit: kC ~ 1.3, CS ~ 5 fF kC ~ 1.8, CS ~ 8 fF Same sensitivity to background charge noise A = 0.2 A = 1.7 ~10 times better anharmonicity

Conclusion -Operation in charge-phase regime is possible and desirable for flux qubits -Single shot readout possible with no effect on other qubits -Controlled coupling to other qubits easily achievable Compared to the 3JJ qubit -Three orders of magnitude less sensitive to flux fluctuations -Smaller L, i.e. smaller coupling to the magnetic environment -One order of magnitude less sensitive to system parameters Compared to the quantronium: - Same sensitivity to the background charge fluctuations - 10 times larger anharmonicity

Conclusion -Operation in charge-phase regime is possible and desirable for flux qubits -Single shot readout possible with no effect on other qubits -Controlled coupling to other qubits easily achievable Compared to the 3JJ qubit -Three orders of magnitude less sensitive to flux fluctuations -Smaller L, i.e. smaller coupling to the magnetic environment -One order of magnitude less sensitive to system parameters Compared to the quantronium: - Same sensitivity to the background charge fluctuations - 10 times larger anharmonicity

Conclusion -Operation in charge-phase regime is possible and desirable for flux qubits -Single shot readout possible with no effect on other qubits -Controlled coupling to other qubits easily achievable Compared to the 3JJ qubit -Three orders of magnitude less sensitive to flux fluctuations -Smaller L, i.e. smaller coupling to the magnetic environment -One order of magnitude less sensitive to system parameters Compared to the quantronium: - Same sensitivity to the background charge fluctuations - 10 times larger anharmonicity

Conclusion -Operation in charge-phase regime is possible and desirable for flux qubits -Single shot readout possible with no effect on other qubits -Controlled coupling to other qubits easily achievable Compared to the 3JJ qubit -Three orders of magnitude less sensitive to the flux fluctuations -Smaller L, i.e. smaller coupling to the magnetic environment -One order of magnitude less sensitive to system parameters Compared to the quantronium: - Same sensitivity to the background charge fluctuations - 10 times larger anharmonicity

Conclusion -Operation in charge-phase regime is possible and desirable for flux qubits -Single shot readout possible with no effect on other qubits -Controlled coupling to other qubits easily achievable Compared to the 3JJ qubit -Three orders of magnitude less sensitive to flux fluctuations -Smaller L, i.e. smaller coupling to the magnetic environment -One order of magnitude less sensitive to system parameters Compared to the quantronium: - Same sensitivity to the background charge fluctuations - 10 times larger anharmonicity

Conclusion -Operation in charge-phase regime is possible and desirable for flux qubits -Single shot readout possible with no effect on other qubits -Controlled coupling to other qubits easily achievable Compared to the 3JJ qubit -Three orders of magnitude less sensitive to flux fluctuations -Smaller L, i.e. smaller coupling to the magnetic environment -One order of magnitude less sensitive to system parameters Compared to the quantronium: - Same sensitivity to the background charge fluctuations - 10 times larger anharmonicity