Quantum computing is a disruptive paradigm widely believed to be capable of solving classically intractable problems. However, the route toward full-scale quantum computers is obstructed by immense challenges associated with the scalability of the platform and the required fidelity of various components. One-way quantum computing is an appealing approach that shifts the burden from high-fidelity quantum gates and quantum memories to the generation of high-quality entangled resource states and high fidelity measurements. Cluster states are an important ingredient for one-way quantum computing, and a compact, portable, and mass producible platform for large-scale cluster states will be essential for the widespread deployment of one-way quantum computing. Here, we bridge two distinct fields---Kerr microcombs and continuous-variable
(CV) quantum information---to formulate a one-way quantum computing architecture based on programmable large-scale CV cluster states. Our scheme can accommodate hundreds of simultaneously addressable entangled optical modes multiplexed in the frequency domain and an unlimited number of sequentially addressable entangled optical modes in time domain. When combined with a source of non-Gaussian Gottesman-Kitaev-Preskill qubits, such cluster states enable universal quantum computation via homodyne detection and feedforward. This platform can be readily implemented with silicon photonics, opening a promising avenue for quantum computing at a large scale.
1. APS March Meeting 2020
*Bo-Han Wu, Rafael N. Alexander, Shuai Liu, Zheshen Zhang
Quantum Computing Architecture based on Large-scale Multi-dimensional
Continuous-Variable Cluster State in a Scalable Photonic Platform
University of Arizona
B.-H. Wu et al., arXiv:1909.05455 (2019).
*gowubohan@email.arizona.edu
2. Q. What kind of quantum computing system
can we choose ?
1/8
Quantum Computing
Factorization problem
[1]
Data searching
[2]
[1] P. Shor, in Proc 35th Annual Symp. on Found. of Comp. Sci.
[2] D. Deutsch et al., Proc. R. Society (London) A 439, 553 (1992).
3. [3]
Large scale cluster state preparation
Single qubit measurement
2/8
How ?
[3] F. Arute et al., Nature, 574, 505 (2019).
One-way quantum computing
(Measurement based)
[4,5]
[4] Y. Tokunaga, NTT Technical Review, 9, No.7 (2011).
[5] R. Raussendorf, Phys. Rev. Lett., 86, 5188 (2000).
Feedforward
4. Photo is from Akira Furusawa's group
Compatible with CMOS
technology
High scalability and portability
Robust
Q. Can we build the whole
system on a single chip ?
Nano-
photonics
Quantum
optics
3/8
[6]
[7]
[6] M. V. Larsen et al., Science, 366, 369 (2019).
[7] W. Asavanant et al., Science, 366, 373 (2019).
6. 2D CV cluster state
UMZI: unblanced Mach-Zehnder interferometer DL: delay line
[10]
[10] R. N. Alexander et al., Phys. Rev. A 94,
032327 (2016).
1D CV cluster state
(Spectral mode) (Spectral mode) × (Temporal mode)
5/8IBS: integrated beamsplitter
[9]
[9] M. Chen, et al., Phys. Rev. Lett. 112, 120505
(2014).
7. 0D cluster state
CV quantum error correction [11-13]
[11] K. Fukui et al., Phys. Rev. Lett., 119, 180507 (2017).
[12] K. Noh et al., arXiv:1908.03579 (2019).
[13] B. Q. Baragiola et al., Phys. Rev. Lett., 123, 200502 (2019).
1D cluster state
2D cluster state
6/8
3D cluster state
(Spectral mode) × (Spectral mode) ×
(Temporal mode)
a
b
c
d
3D CV cluster state
8. Intrinsic Q factor of ring resonator
reaches the order of 107.
Experimental Progress
beamsplitter
Microring resonator
Delay line
7/8
Quantum computing is a hot research topic in this couple years, because it is widely believed to solve some of the classical intractable problems.
For example, classically, it is hard to factorize a composite number which is the multiplication of two large prime numbers. Another example is the data searching. Given large number of inputs, the computation complexity increases linearly. We can take a look the time complexity of the two problems.
However, the quantum algorithm, implemented on the quantum computing system, can in principle reduce the classical time complexity significantly.
The research group in google published a paper last year to talk about sample a pseudo random number out of a million times within 200 seconds in the base of 53 superconducting qubits. This great achievement justifies the supremacy of quantum computing over the classical computing in some sense.
However, to build a universal quantum computer, the gate operation with high-fidelity is necessary but challenging.
To overcome the difficulties, there is an alternative solution called “one-way quantum computing”. In this one-way quantum computing protocol, we firstly prepare a specific type of entangled state called cluster state. Cluster state is a persistent multi-partite entangled state. Given this cluster state, we do the measurement on a single quibit. The measured quibit will be destroyed and the rest of the system is equivalently operated by a “gate operation”. Finally, we do the feedforward to make sure next gate operation shares the same basis as the previous one.
The most challenging part of they one-way quantum computing is “how to prepare high dimensional and high quality of cluster state”
In bulk optics system, there are several outstanding papers are published to generate two dimensional cluster states. The setup of free space optical system of Akira’s group is shown.
However, the scalability and mass-producibility of bulk optical system is challenging.
There are some papers published recently to talk about the methodology for generating the fundamental optical soliton in the microring resonator. The phase of spectral modes for the soliton is well locked and fields at each frequency tooth can be utilized as the local oscillators for doing the Homodyne measurement for the generated on-chip cluster state.
After generating thousands of entangled spectral modes, we follow the similar procedure to entangle different pairs of signal and idler photons by linear components like beamsplitter. In the input, we prepare two pump fields, which are two spectral modes apart. In the output, we acquire the one-rail cluster state.
To extend the dimensionality of cluster state, we introduce the integrated delay line after the output of the 1D case. The dimensionality of cluster state now involves the entanglement in both the spectral modes and the temporal modes.
We can further increase the dimensionality of the cluster state by adding two copies of the 2D structure in parallel but the pumping modes are all different. With this setup, we split the spectral dimension into two parties, f1 and f2, and therefore we acquire the 3D cluster state at the output port.
In our 3D cluster state quantum computing protocol, the input quibit is encoded in the red macronode. We do the measurement on the side grey macronodes, the equivalent gate will be operated in the other end of the red macronode.
By tuning the electrodes on the waveguide, we are able to programmably generate the multi-dimensional cluster state from 0 to 3.
To make our quantum computing system fault tolerant and universal, we can inject the non-Gaussian state GKP state at the box with star. Recently, there are a lot of papers that talks about how to use the GKP encoded quit to do the quantum error correction.
![Q. What kind of quantum computing system
can we choose ?
1/8
Quantum Computing
Factorization problem
[1]
Data searching
[2]
[1] P. Shor, in Proc 35th Annual Symp. on Found. of Comp. Sci.
[2] D. Deutsch et al., Proc. R. Society (London) A 439, 553 (1992).](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)