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Implementation of Cross-Resonance System for Universal Quantum Computing 1215047 S. Shirai Department of Physics, Tokyo University of Science. Center of Emergent Matter Science, RIKEN. Introduction Cross-Resonance Gate Fabricated Sample Experimental Result Conclusion and Future Work Universal quantum computing Theory of circuit QED g Cavity + Two level system ωσ z /2 ω r a a Resonator1 Q1 Resonator + SC qubit "cavity" QED "circuit" QED g n=0 n=1 n=2 n=3 n=0 n=1 n=2 n=3 Harmonic oscillator Transmon (Charge qubit) L C C Josephson Junction Cavity Quantum electrodynamics (cavity QED) is the study of the interaction between light and atom. The case of a single 2-level atom in the cavity is mathematically described by the Jaynes- Cummings model. On the other hand, by using the macroscopic quantum effect appearing in the superconductor, it is possible to construct a system of cavity QED by the solid element. Such a system is called a "circuit QED" system. Jaynes-Cummings Hamiltonian : Superconducting Qubit AlOx SC(Al) SC(Al) AlOx SC(Al) SC(Al) Josephson Junction Qubit Subspace Tunability Noise sorce Bus Resonator1 Resonator2 Q1 Q2 ω 2 (=Q2 frequency) J g 2 g 1 fast oscillating term When the time evolution by microwave irradiation of the system is sufficiently long, the effect of the vibration term is reduced. =A(t) Time evolution for CNOT 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 0 Output Input CNOT gate ''Control bit'' "Target bit" Bit flip Bit flip When the value of the control bit is 1, the gate that inverts the value of the target bit is called "Controled-NOT gate" (Simply, CNOT). Pulsed spectroscopy CNOT=[ZI] -1/2 [ZX] 1/2 [IX] -1/2 ref. 10.1103/PhysRevB.81.134507 We get CNOT by combining with one qubit gates. time Δt=10ns Qubit Drive Probe τ tp~2us Ω R time Δt=10ns Qubit Drive Probe td~4us tp~2us τ [ns] τ [ns] Qubit2 Qubit2 Qubit2 Qubit1 2J~40MHz Rabi oscillation Fitting function : τ R ~448 ns τ R ~1032 ns The sample could not work in the regime of CR gate. However, I could confirm the existence of coupling between qubits. Next time, I would like to fabricate the qubits with better coherence time in CR gate regime. Acknowledgment This work supported by JST CREST Grant Number JPMJCR1676, Japan. fig. truth table 500 μm fig.1 example of quantum circuit According to the Solovay-Kitaev theorem, arbitrary N-qubit unitary operators can be approximated with ''universal gate set''.{S, H, T, CNOT} is one of universal set. CNOT gate is so-called two-qubit entangling gate. It is difficult to realize two-qubit gates compared to one-qubit gates. So, implementing a precise 2-qubit gate is one of the big challenges. fig. SQUID Φ I I fig. Cross-Resonance system Resonator + SC qubit are smallest set of cQED system. The above system Hamiltonian can be written as bellow. After performing the two-level approximation, unitary transformation and perturbative expantion are performed and the following interaction Hamiltonian is obtained while irradiating microwaves from the outside under the condition of {| J / ω1-ω2 | << 1}. Cross-Resonance interaction fig. Potential energy and circuit fig. Two qubits(red) coupled circuit via a central resonator(green). Time evolution by H(t) : Procedure : 1. Irradiate the microwave for a long time. 2. The state of the qubit becomes classical mixed state by the microwave. 3. The resonance frequency of the resonator varies according to the state of the qubit. 4. The change in the reflection signal of the resonator due to the change of the resonance frequency is read by VNA. f q1 ~6.866, f q2 ~6.886 GHz J~20MHz Procedure : 1. Irradiate the microwave pulse to the qubit. 2. Read the state of the qubit through the resonator. 3. Repeat steps 1 and 2 while changing irradiation time of microwave pulse. 500 nm Josephson Junction R e s o n a t o r 1 R e s o n a t o r 2 Q 1 Q 2 C o u p l i n g R e s o n a t o r

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Implementation of Cross-Resonance System for Universal Quantum Computing

1215047 S. ShiraiDepartment of Physics, Tokyo University of Science. Center of Emergent Matter Science, RIKEN.

Introduction

Cross-Resonance Gate

Fabricated Sample

Experimental Result

Conclusion and Future Work

Universal quantum computing

Theory of circuit QED

g

Cavity + Two level system

ωσz/2

ωra†a

Resonator1Q1

Resonator + SC qubit

"cavity" QED "circuit" QED

g

n=0

n=1

n=2

n=3

n=0

n=1

n=2n=3

Harmonic oscillator Transmon (Charge qubit)

LC C JosephsonJunction

Cavity Quantum electrodynamics (cavity QED) is the study of the interaction between light and atom. The case of a single 2-level atom in the cavity is mathematically described by the Jaynes-Cummings model. On the other hand, by using the macroscopic quantum effect appearing in the superconductor, it is possible to construct a system of cavity QED by the solid element. Such a system is called a "circuit QED" system.

Jaynes-Cummings Hamiltonian :

Superconducting QubitAlOxSC(Al) SC(Al)

AlOxSC(Al) SC(Al)

JosephsonJunction

QubitSubspace

・Tunability・Noise sorce

BusResonator1 Resonator2Q1 Q2

ω2(=Q2 frequency)

J g2g1

fast oscillating term

When the time evolution by microwave irradiation of the system is sufficiently long, the effect of the vibration term is reduced.

=A(t)

Time evolution for CNOT0

0011

101 1

0110

010OutputInput CNOT gate''Control bit''

"Target bit"

Bit flip

Bit flip

When the value of the control bit is 1, the gate that inverts the value

of the target bit is called "Controled-NOT gate" (Simply, CNOT).

Pulsed spectroscopy

CNOT=[ZI]-1/2[ZX]1/2[IX]-1/2

ref. 10.1103/PhysRevB.81.134507

We get CNOT by combining with one qubit gates.

time

Δt=10ns

Qubit Drive

Probe

τ

tp~2us

ΩR

time

Δt=10ns

Qubit Drive

Probe

td~4us

tp~2us

τ [ns] τ [ns]

Qubit2

Qubit2

Qubit2Qubit1

2J~40MHz

Rabi oscillation

Fitting function :

τR~448 ns τR~1032 ns

The sample could not work in the regime of CR gate. However, I could confirm the existence of coupling between qubits. Next time, I would like to fabricate the qubits with better coherence time in CR gate regime.

AcknowledgmentThis work supported by JST CREST Grant Number JPMJCR1676, Japan.

fig. truth table

500 μm

fig.1 example of quantum circuit

According to the Solovay-Kitaev theorem, arbitrary N-qubit unitary operators can be approximated with ''universal gate set''.{S, H, T, CNOT} is one of universal set.CNOT gate is so-called two-qubit entangling gate. It is difficult to realize two-qubit gates compared to one-qubit gates. So, implementing a precise 2-qubit gate is one of the big challenges.

fig. SQUID

ΦI I

fig. Cross-Resonance system

Resonator + SC qubit are smallest set of cQED system. The above system Hamiltonian can be written as bellow.

After performing the two-level approximation, unitary transformation and perturbative expantion are performed and the following interaction Hamiltonian is obtained while irradiating microwaves from the outside under the condition of {| J / ω1-ω2 | << 1}.

Cross-Resonance interaction

fig. Potential energy and circuit

fig. Two qubits(red) coupled circuit via a central resonator(green).

Time evolution by H(t) :

Procedure : 1. Irradiate the microwave for a long time. 2. The state of the qubit becomes classical mixed state by the microwave.3. The resonance frequency of the resonator varies according to the state of the qubit.4. The change in the reflection signal of the resonator due to the change of the resonance frequency is read by VNA.

fq1~6.866, fq2~6.886 GHzJ~20MHz

Procedure : 1. Irradiate the microwave pulse to the qubit.2. Read the state of the qubit through the resonator.3. Repeat steps 1 and 2 while changing irradiation time of microwave pulse.

500 nm

Josephson Junction

Resonator1 Resonator2

Q1

Q2

CouplingResonator