Hardware-efficient and fast three-qubit gate in superconducting quantum circuits

doi:10.1007/s11467-024-1405-8

Front. Phys.

2024, Vol. 19

Issue (5) : 51205 https://doi.org/10.1007/s11467-024-1405-8

Hardware-efficient and fast three-qubit gate in superconducting quantum circuits

Xiao-Le Li^1,², Ziyu Tao^2,³, Kangyuan Yi^2,³, Kai Luo^2,³, Libo Zhang^3,⁴, Yuxuan Zhou^2,³, Song Liu^3,^4,⁵, Tongxing Yan^3,^4,⁵(

), Yuanzhen Chen^2,^3,⁵(

), Dapeng Yu^2,^3,^4,⁵

¹. Department of Physics, Harbin Institute of Technology, Harbin 150001, China
². Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
³. Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
⁴. Shenzhen International Quantum Academy (SIQA), Shenzhen 518048, China
⁵. Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China

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Abstract

While the common practice of decomposing general quantum algorithms into a collection of single- and two-qubit gates is conceptually simple, in many cases it is possible to have more efficient solutions where quantum gates engaging multiple qubits are used. In the noisy intermediate-scale quantum (NISQ) era where a universal error correction is still unavailable, this strategy is particularly appealing since it can significantly reduce the computational resources required for executing quantum algorithms. In this work, we experimentally investigate a three-qubit Controlled-CPHASE-SWAP (CCZS) gate on superconducting quantum circuits. By exploiting the higher energy levels of superconducting qubits, we are able to realize a Fredkin-like CCZS gate with a duration of 40 ns, which is comparable to typical single- and two-qubit gates realized on the same platform. By performing quantum process tomography for the two target qubits, we obtain a process fidelity of $86.0 %$ and $81.1 %$ for the control qubit being prepared in $| 0 ⟩$ and $| 1 ⟩$ , respectively. We also show that our scheme can be readily extended to realize a general CCZS gate with an arbitrary swap angle. The results reported here provide valuable additions to the toolbox for achieving large-scale hardware-efficient quantum circuits.

Keywords quantum computation quantum gate superconducting circuit

Corresponding Author(s): Tongxing Yan,Yuanzhen Chen

About author:

Issue Date: 14 May 2024

Cite this article:

Xiao-Le Li,Ziyu Tao,Kangyuan Yi, et al. Hardware-efficient and fast three-qubit gate in superconducting quantum circuits[J]. Front. Phys. , 2024, 19(5): 51205.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-024-1405-8
https://academic.hep.com.cn/fop/EN/Y2024/V19/I5/51205

Fig.1 Schematics of the superconducting qubits and circuit diagram used in this work for a Controlled-CPHASE-SWAP (CCZS) gate. (a) Sketch of the device with three transmon qubits of tunable frequencies. Eeach qubit contains a SQUID (superconducting quantum interference device) ring whose magnetic flux can be varied by a current flowing on a on-chip flux line nearby (not shown), which in turn changes the qubit’s frequency. Each qubit is equipped with its own flux line, control line, and readout resonator (not shown) as widely used in the transmon-based superconducting quantum circuits. Adjacent qubits are coupled and share a common feedline for dispersive readout. (b) Schematics of our scheme decomposing a Fredkin-like CCZS gate into a sequence of three iSWAP operations (marked as ×) between adjacent qubits. Each iSWAP operation represents a coherent

π

rotation realized by tuning the

| 11 ?

state of the involved two qubits into resonance with the

| 20 ?

state. The overall operation is then a Fredkin-like CCZS gate: a controlled-iSWAP operation between two target qubits

Q B

and

Q C

upon the status of the control qubit

Q A

. If

Q A

is in its excited states (·), an controlled-iSWAP occurs between

Q B

and

Q C

. (c) Pulse sequence for benchmarking the CCZS gate. Single-qubit gates, marked as

R

, are used for preparing different initial states and rotating the three-qubit state for projection measurements.

Initial state	After first $U A B (π)$	After $U A C (π)$	After last $U A B (π)$

$\| 000 ?$	$\| 000 ?$	$\| 000 ?$	$\| 000 ?$
$\| 001 ?$	$\| 001 ?$	$\| 001 ?$	$\| 001 ?$
$\| 010 ?$	$\| 010 ?$	$\| 010 ?$	$\| 010 ?$
$\| 011 ?$	$\| 011 ?$	$\| 011 ?$	$\| 011 ?$
$\| 100 ?$	$\| 100 ?$	$\| 100 ?$	$\| 100 ?$
$\| 101 ?$	$\| 101 ?$	$? i \| 200 ?$	$? \| 110 ?$
$\| 110 ?$	$? i \| 200 ?$	$? \| 101 ?$	$? \| 101 ?$
$\| 111 ?$	$? i \| 201 ?$	$? i \| 201 ?$	$? \| 111 ?$

Tab.1 List of states after each step of the iSWAP gate.

Fig.2 Measured truth table for our three-qubit CCZS gate. This truth table is to be compared with

U F

in Eq. (2). The truth table fidelity is calculated as

F = (1 / 8) T r (| U e x p | ? | U F |) =

91.2 %

Fig.3 Experimental (left column) and ideal (right column) quantum process tomography matrices

χ e x p

and

χ i d e a l

for the two target qubits. The control qubit

Q A

is prepared in (a)

| 0 ?

and (b)

| 1 ?

, respectively.

Fig.4 Generation and benchmarking of a three-qubit GHZ state using our Fredkin-like CCZS gate. (a) The measured populations associated with the state of

cos ? (θ / 4) | 001 ? ?

sin ? (θ / 4) | 110 ?

when a CCZS gate is applied to a direct product state of

cos ? (θ / 4) | 001 ? ? sin ? (θ / 4) | 101 ?

. When

θ = π

, the GHZ state

12 (| 001 ? + | 110 ?)

is produced. (b?e) The reconstructed density matrix for the GHZ state

12 (| 001 ? + | 110 ?)

using QST. (b) and (c) are real and imaginary parts for the case of applying the CCZS to generate the GHZ state, respectively. (d) and (e) are real and imaginary parts for the case of using traditional CZ gate and single-qubit gates, respectively.

Fig.5 Demonstration of a controlled three-qubit iSWAP operation with an arbitrary angle. The populations of the

| 101 ?

state (blue dots) and

| 110 ?

state (red triangles) are measured as a function of

θ A C

U F (θ A C) = U A B (π)

U A C (θ A C) U A B (π)

. When

θ A C = π

| 101 ?

is completely transferred into

| 110 ?

. Lines are a guide to the eye representing the theoretical prediction without decoherence and leakage errors.

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