Simulating quantum systems is one of the most important potential applications of quantum computers. The high-level circuit defining the simulation needs to be compiled into one that complies with hardware limitations such as qubit architecture (connectivity) and instruction (gate) set. General-purpose quantum compilers work at the gate level and have little knowledge of the mathematical properties of quantum applications, missing further optimization opportunities. Existing application-specific compilers only apply advanced optimizations in the scheduling procedure and are restricted to the CNOT or CZ gate set. In this work, we develop a compiler, named 2QAN, to optimize quantum circuits for 2-local qubit Hamiltonian simulation problems, a framework which includes the important quantum approximate optimization algorithm (QAOA). In particular, we exploit the flexibility of permuting different operators in the Hamiltonian (no matter whether they commute) and propose permutation-aware techniques for qubit routing, gate optimization and scheduling to minimize compilation overhead. 2QAN can target different architectures and different instruction sets. Compilation results on four applications (up to 50 qubits) and three quantum computers (namely, Google Sycamore, IBMQ Montreal and Rigetti Aspen) show that 2QAN outperforms state-of-the-art general-purpose compilers and application-specific compilers. Specifically, 2QAN can reduce the number of inserted SWAP gates by 11.5X, reduce overhead in hardware gate count by 68.5X, and reduce overhead in circuit depth by 21X. Experimental results on the Montreal device demonstrate that benchmarks compiled by 2QAN achieve the highest fidelity.

In a fault tolerant quantum computer, quantum codes are expected to serve the conflicting purposes of protecting quantum information while also allowing that information to be manipulated by fault-tolerant gates. We introduce a new technique for placing limitations on such gates, and apply this technique to a class of quantum codes known as hypergraph product codes contained within the vertical sector. These codes are constructed from input which is a pair of classical linear codes, and generalize the Kitaev surface code which is the hypergraph product of classical repetition codes. We provide a necessary condition on these input codes, under which the resulting hypergraph product code has transversal gates limited to the Clifford group. We conjecture that this condition is satisfied by all$[n,k,d]$Gallagher codes with$d\ge 3$and$k\le n/2$. This work is a generalization of an argument due to Bravyi and König, and we also conjecture this is a refinement of the recent notion of disjointness due to Jochym-O’Connoret al.

Near-term quantum computing (QC) systems have limited qubit counts, high gate (instruction) error rates, and typically support a minimal instruction set having one type of two-qubit gate (2Q). To reduce program instruction counts and improve application expressivity, vendors have proposed, and shown proof-of-concept demonstrations of richer instruction sets such as XY gates (Rigetti) and fSim gates (Google). These instruction sets comprise of families of 2Q gate types parameterized by continuous qubit rotation angles. That is, it allows a large set of different physical operations to be realized on the qubits, based on the input angles. However, having such a large number of gate types is problematic because each gate type has to be calibrated periodically, across the full system, to obtain high fidelity implementations. This results in substantial recurring calibration overheads even on current systems which use only a few gate types. Our work aims to navigate this tradeoff between application expressivity and calibration overhead, and identify what instructions vendors should implement to get the best expressivity with acceptable calibration time.Studying this tradeoff is challenging because of the diversity in QC application requirements, the need to optimize applications for widely different hardware gate types and noise variations across gate types. Therefore, our work develops NuOp, a flexible compilation pass based on numerical optimization, to efficiently decompose application operations into arbitrary hardware gate types. Using NuOp and four important quantum applications, we study the instruction set proposals of Rigetti and Google, with realistic noise simulations and a calibration model. Our experiments show that implementing 4-8 types of 2Q gates is sufficient to attain nearly the same expressivity as a full continuous gate family, while reducing the calibration overhead by two orders of magnitude. With several vendors proposing rich gate families as means to higher fidelity, our work has potential to provide valuable instruction set design guidance for near-term QC systems.