Linear Optical Quantum Computation with Frequency-Comb Qubits and Passive Devices

We propose a linear optical quantum computation scheme using time-frequency degrees of freedom. In this scheme, a qubit is encoded in single-photon frequency combs, and manipulation of the qubits is performed using time-resolving detectors, beam splitters, and optical interleavers. This scheme does not require active devices such as high-speed switches and electro-optic modulators and is robust against temporal and spectral errors, which are mainly caused by the detectors’ finite resolution. We show that current technologies almost meet the requirements for fault-tolerant quantum computation.

Figure 1

Probability distributions of a time-frequency Gottesmann-Kitaev-Preskill (TFGKP) qudit in the frequency and time bases for $d=2$. The blue and orange lines in the frequency and time basis represent $|{\tilde{0}}_{f/t}⟩$ and $|{\tilde{1}}_{f/t}⟩$, respectively.

Figure 2

Graphical representation of $2:2$ optical interleaver (OI). Orange and blue spectral peaks represent $|{\tilde{0}}_f⟩$ and $|{\tilde{1}}_f⟩$, respectively.

Figure 3

Concrete setups for quantum operations. All detectors, beam splitters (BSs), and OIs are time-resolving detectors, $50:50$ BSs, and $2:2$ OIs, respectively. (a) Measurement in the $\cos (\theta /2)X+\sin (\theta /2)Y$ basis. $\theta$ is adjustable by changing the relative lengths between the two arms. (b) Bell-state generation, which succeeds when detectors detect two photons in different states. The OI enclosed by the dotted lines denotes a feed-forward operation required in $1/3$ of the success cases. Its total success probability is $3/16$. (c) Type-I fusion gate, which succeeds when a detector detects a photon with a probability $1/2$. (d) Type-II’ fusion gate, which succeeds when a detector or detectors detect $|0⟩$ and $|1⟩$ with a probability of $1/2$. (e) Type-I’ fusion gate, which succeeds when a detector detects a photon with a probability of $1/4$.