Demonstration of sequential processors with quantum advantage and analysis of classical performance limits

Abstract

In this paper, we theoretically and experimentally analyze sequential processors with limited communication between parts. We compare the expressivity of sequential quantum and classical processors under the same constraints. They consist of three or four modules, each of which processes local data. The modules of the quantum processor are linked through one-qubit or one-qutrit communication, while those of the classical processor communicate through one bit or one trit. For the classical processor, we prove bounds on its performance in terms of inequalities on correlations of the output with a target function. We theoretically show that the quantum processor violates these inequalities. We show this violation experimentally on a silicon photonics setup. We describe how to find the classical bound on correlations with arbitrary target function by reducing the problem to the minimization of an Ising-type spin-glass Hamiltonian. Our theory is applicable in general problems, such as the low-rank binary matrix approximation.

Figures (9)

• Figure 1: Single-qubit and single-bit sequential processors of similar structure.
• Figure 2: Example. Adding four two-bit numbers $(0,2,3,2)$ modulo 4 with a single-qubit quantum processor. The processor uses operations that rotate a qubit state vector, shown here as a thick violet arrow, between four points, indicated by thin yellow arrows, on the Bloch sphere. The added numbers can be arbitrary two-bit numbers with only one constraint that the total sum modulo 4 is either 0 or 2. For any set of two-bit numbers with the above promise, the ideal quantum processor solves the addition problem without errors.
• Figure 3: (a) Schematic of the sequential quantum processor implemented on a silicon photonic chip. The unitary gate was implemented using a heater and an Mach–Zehnder interferometer enclosed by the red dotted lines. (b) Overview of the one-qubit processor. A heralded single photon was injected into the sequential processor. (c) Overview of the one-qutrit processor. Two photons generated from attenuated laser light at the single-photon level were injected into the sequential processor. In panels (b) and (c), the circuit enclosed by the red dotted lines corresponds to a single unitary gate in each case.
• Figure 4: The histogram of the correlation function based on the data from three-module single-qubit processor experiment on silicon photonics. The blue line shows the classical limit for the correlation, which for the considered target function is equal to 0.25.
• Figure 5: The histogram of the correlation function based on the data from four-module single-qutrit processor experiment on silicon photonics. The blue line shows the classical limit for the correlation, which for the considered target function is equal to 0.375.

Theorems & Definitions (8)

• Proposition 1
• proof
• Proposition 2
• proof
• Proposition 3
• proof
• Theorem 1
• proof