General-Purpose Quantum Circuit Simulator with Projected Entangled-Pair States and the Quantum Supremacy Frontier

Recent advances on quantum computing hardware have pushed quantum computing to the verge of quantum supremacy. Here, we bring together many-body quantum physics and quantum computing by using a method for strongly interacting two-dimensional systems, the projected entangled-pair states, to realize an effective general-purpose simulator of quantum algorithms. The classical computing complexity of this simulator is directly related to the entanglement generation of the underlying quantum circuit rather than the number of qubits or gate operations. We apply our method to study random quantum circuits, which allows us to quantify precisely the memory usage and the time requirements of random quantum circuits. We demonstrate our method by computing one amplitude for a $7\times 7$ lattice of qubits with depth ($1+40+1$) on the Tianhe-2 supercomputer.

Figure 1

(a) PEPS on a $5\times 5$ lattice, each qubit of the lattice is represented with a rank-5 tensor ${[{\mathbf{A}}_n^{{\sigma }_n}]}_{l,r,u,d}$, where ${\sigma }_n=0$, 1 labels the physical dimension and $l$, $r$, $u$, $d$ label the auxiliary dimensions which connect ${[{\mathbf{A}}_n^{{\sigma }_n}]}_{l,r,u,d}$ to the tensors on the neighboring sites. (b) Single-qubit gate operation on the PEPS. (c) Two-qubit gate operation on PEPS. (d) Overlapping of two PEPSs by contraction of all the physical dimensions of the two PEPSs and all the auxiliary dimensions inside each PEPS.

Figure 2

The blue circles show the log transformed probabilities from calculating 10 000 amplitudes, while the red line is the log transformed Porter-Thomas distribution. The circuit size is $8\times 8$ with a depth ($1+25+1$).