Circuit synthesis of multi-controlled gates is crucial for qudit ( $d$ -level) quantum computing. This paper presents efficient synthesis schemes that reduce the elementary gate count for multi-controlled single-qudit gates. For synthesizing general $(n-1)$ -controlled unitaries on $n$ qudits, we reduce the controlled-increment (CINC) and generalized controlled- $X$ (GCX) gate counts to $O(n^2)$ , improving upon existing $O(n^{2+\log_2 d})$ CINC and $O(n^3)$ GCX bounds. For $(n-1)$ -controlled special unitaries, this complexity is further reduced to $O(n)$ . Furthermore, we present a method for approximately synthesizing multi-controlled unitary gates with a linear complexity in the number of control qudits. By utilizing the proposed circuit, we present qudit-based circuit constructions for isometries and quantum channels from $n$ to $m$ qudits. Moreover, for the first time, we present a circuit synthesis scheme for single-controlled gates using SUM gates and single-qudit gates when $d$ is prime. This enables all CINC-based circuits for various quantum operations to be converted into SUM-gate circuits while preserving the same asymptotic complexity. Finally, we establish a theoretical lower bound on the number of SUM and CINC gates required to synthesize general $n$ -qudit unitaries.Circuit synthesis of multi-controlled gates is crucial for qudit ($d$-level) quantum computing. This paper presents efficient synthesis schemes that reduce the elementary gate count for multi-controlled single-qudit gates. For synthesizing general $(n-1)$-controlled unitaries on $n$ qudits, we reduce the controlled-increment (CINC) and generalized controlled-$X$ (GCX) gate counts to $O(n^2)$, improving upon existing $O(n^{2+\log_2 d})$ CINC and $O(n^3)$ GCX bounds. For $(n-1)$-controlled special unitaries, this complexity is further reduced to $O(n)$. Furthermore, we present a method for approximately synthesizing multi-controlled unitary gates with a linear complexity in the number of control qudits. By utilizing the proposed circuit, we present qudit-based circuit constructions for isometries and quantum channels from $n$ to $m$ qudits. Moreover, for the first time, we present a circuit synthesis scheme for single-controlled gates using SUM gates and single-qudit gates when $d$ is prime. This enables all CINC-based circuits for various quantum operations to be converted into SUM-gate circuits while preserving the same asymptotic complexity. Finally, we establish a theoretical lower bound on the number of SUM and CINC gates required to synthesize general $n$-qudit unitaries.

quant-pharXiv:2607.08200Jul 10, 20260 citations

Quantum Circuit Synthesis using a New Quantum Logic Gate Library of NCV Quantum Gates

Zhiqiang Li, Sai Chen, Xiaoyu Song B +3 more

International Journal of Theoretical PhysicsDec 13, 201610 citations

Synthesis of Quantum Circuits

Philipp Niemann, Robert Wille

SpringerBriefs in physicsJan 1, 20170 citations

qTask: Task-parallel Quantum Circuit Simulation with Incrementality

Tsung‐Wei Huang

Incremental quantum circuit simulation has emerged as an important tool for simulation-driven quantum applications, such as circuit synthesis, verification, and analysis. When a small portion of the circuit is modified, the simulator must incrementally update state amplitudes for reasonable turnaround time and productivity. However, this type of incrementality has been largely ignored by existing research. To fill this gap, we introduce a new incremental quantum circuit simulator called qTask. qTask leverages a task-parallel decomposition strategy to explore both inter- and intra-gate operation parallelisms from partitioned data blocks. Our partitioning strategy effectively narrows down incremental update to a small set of partitions affected by circuit modifiers. We have demonstrated the promising performance of qTask on QASMBench benchmarks. Compared to two state-of-the-art simulators, Qulacs and Qiskit, qTask is respectively 1.46 × and 1.71× faster for full simulation and 5.77× and 9.76× faster for incremental simulation.Incremental quantum circuit simulation has emerged as an important tool for simulation-driven quantum applications, such as circuit synthesis, verification, and analysis. When a small portion of the circuit is modified, the simulator must incrementally update state amplitudes for reasonable turnaround time and productivity. However, this type of incrementality has been largely ignored by existing research. To fill this gap, we introduce a new incremental quantum circuit simulator called qTask. qTask leverages a task-parallel decomposition strategy to explore both inter- and intra-gate operation parallelisms from partitioned data blocks. Our partitioning strategy effectively narrows down incremental update to a small set of partitions affected by circuit modifiers. We have demonstrated the promising performance of qTask on QASMBench benchmarks. Compared to two state-of-the-art simulators, Qulacs and Qiskit, qTask is respectively 1.46 × and 1.71× faster for full simulation and 5.77× and 9.76× faster for incremental simulation.

arXiv:2210.01076IEEE International Parallel and Distributed Processing Symposium (IPDPS)May 1, 202321 citations

Circuit synthesis of multi-controlled gates is crucial for qudit (

d

-level) quantum computing. This paper presents efficient synthesis schemes that reduce the elementary gate count for multi-controlled single-qudit gates. For synthesizing general

(n-1)

-controlled unitaries on

n

qudits, we reduce the controlled-increment (CINC) and generalized controlled-

X

(GCX) gate counts to

O(n^2)

, improving upon existing

O(n^{2+\log_2 d})

CINC and

O(n^3)

GCX bounds. For

(n-1)

-controlled special unitaries, this complexity is further reduced to

O(n)

. Furthermore, we present a method for approximately synthesizing multi-controlled unitary gates with a linear complexity in the number of control qudits. By utilizing the proposed circuit, we present qudit-based circuit constructions for isometries and quantum channels from

n

m

qudits. Moreover, for the first time, we present a circuit synthesis scheme for single-controlled gates using SUM gates and single-qudit gates when

d

is prime. This enables all CINC-based circuits for various quantum operations to be converted into SUM-gate circuits while preserving the same asymptotic complexity. Finally, we establish a theoretical lower bound on the number of SUM and CINC gates required to synthesize general

n

-qudit unitaries.