Quantum Depth Compression via Local Dynamic Circuits

Abstract

We present Quantum Depth Compression (QDC), a general compilation framework that utilizes dynamic circuits to reduce arbitrary quantum circuits to depth linear in the number of non-Clifford gates and to grid connectivity without the need for expensive SWAP-networks. The framework consists of pushing Clifford gates to the end of the circuit, resulting in a sequence of non-Clifford Pauli-phasors followed by an all Clifford sub-circuit, both of which are then reduced to constant depth via dynamic circuits. We show that applying QDC to random Pauli-phasor circuits lowers both their depth and CNOT count compared to a standard alternative compiler.

Figures (16)

• Figure 1: Overview of QDC's steps. Compile: each blue and turquoise square represents a Clifford section $C_i$ and non-Clifford Pauli-phasor $P_i$, respectively. Push: each turquoise square and blue rectangle represents a modified Pauli-phasor $P'_i$ or combined Clifford section $C$, respectively. Synthesize: the blue square represents the synthesized Clifford section $C'$. Reduce: see Figure \ref{['fig:reduce']} below.
• Figure 2: An $n=3$ qubit example of the fourth QDC step (reduce) showing steps in time (t) of an $\text{n}\times\text{n}$ grid of qubits (gray circles). The turquoise and blue time steps represent reduced Pauli-phasor and Clifford sections, respectively. The black and gray curves represent cups/caps (Figure \ref{['fig:cup_and_cap']}) and two-qubit entangling gates, respectively.
• Figure 3: Depiction of the circuit after the compile step. Blue and turquoise rectangles represent Clifford sections and non-Clifford Pauli-phasors, respectively.
• Figure 4: Example of one iteration of the push step: the left-most Clifford section $C_i$ is pushed past the Pauli-phasor $P_i$ immediately to its right, modifying the Pauli-phasor to $P'$ in the process.
• Figure 5: A depth $d$ Clifford circuit $C$ divided in to an odd number of sub-circuits $C_1,...,C_{2n+1}$ executed in constant depth by "snaking" the circuit across $nd$ qubits via cups and caps. The required Pauli-corrections $P_2,...,P_{2n}$ may be "pushed" to the end of the Circuit resulting in a single combined correct $P$ (Equation \ref{['eq:P']}).