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Quantum noise is a central challenge in quantum computing across many applications. Extensive work has examined how qubits couple to their environment, leading to decoherence and relaxation, which is irreversible. Current studies focus on…
This paper introduces an algorithm designed to approximate quantum transformation matrix with a restricted number of gates by using the block decomposition technique. Addressing challenges posed by numerous gates in handling large qubit…
The conventional circuit paradigm, utilizing a limited number of gates to construct arbitrary quantum circuits, is hindered by significant noise overhead. For instance, the standard gate paradigm employs two CNOT gates for the partial…
The synthesis approaches for quantum circuits typically aim at minimizing the number of lines or gates. Given the tight restrictions on those logical resources in physical implementations, we propose to view the problem fundamentally…
Variational quantum algorithms constitute one of the most widespread methods for using current noisy quantum computers. However, it is unknown if these heuristic algorithms provide any quantum-computational speedup, although we cannot…
Simulating noisy quantum circuits is vital in designing and verifying quantum algorithms in the current NISQ (Noisy Intermediate-Scale Quantum) era, where quantum noise is unavoidable. However, it is much more inefficient than the classical…
During the noisy intermediate-scale quantum (NISQ) era, it is important to optimize the quantum circuits in circuit depth and gate count, especially entanglement gates, including the CNOT gate. Among all the unitary operators, diagonal…
We study optimal synthesis of Clifford circuits, and apply the results to peep-hole optimization of quantum circuits. We report optimal circuits for all Clifford operations with up to four inputs. We perform peep-hole optimization of…
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
Fastness and robustness are both critical in the implementation of high-fidelity gates for quantum computation, but in practice, a trade-off has to be made between them. In this paper, we investigate the underlying robust time-optimal…
Despite significant progress in quantum computing in recent years, executing quantum circuits for practical problems remains challenging due to error-prone quantum hardware. Hence, quantum error correction becomes essential but induces…
Recent work has explored using the stabilizer formalism to classically simulate quantum circuits containing a few non-Clifford gates. The computational cost of such methods is directly related to the notion of stabilizer rank, which for a…
IBM has made several quantum computers available to researchers around the world via cloud services. Two architectures with five qubits, one with 16, and one with 20 qubits are available to run experiments. The IBM architectures implement…
The performance requirements for fault-tolerant quantum computing are very stringent. Qubits must be manipulated, coupled, and measured with error rates well below 1%. For semiconductor implementations, silicon quantum dot spin qubits have…
Fault-tolerant quantum computation (FTQC) is essential to implement quantum algorithms in a noise-resilient way, and thus to enjoy advantages of quantum computers even with presence of noise. In FTQC, a quantum circuit is decomposed into…
CNOT optimization plays a significant role in noise reduction for Quantum Circuits. Several heuristic and exact approaches exist for CNOT optimization. In this paper, we investigate more complicated variations of optimal synthesis by…
Classical simulation of noisy quantum circuits is essential for understanding quantum computing experiments. It enables scalable error characterization, analysis of how noise impacts quantum algorithms, and optimized implementations of…
We show the applicability of the Cartan decomposition of Lie algebras to quantum circuits. This approach can be used to synthesize circuits that can efficiently implement any desired unitary operation. Our method finds explicit quantum…
This thesis deals with a series of quantum computer implementation issues from the Kane 31P in 28Si architecture to Shor's integer factoring algorithm and beyond. The discussion begins with simulations of the adiabatic Kane CNOT and readout…
In this paper, we study the close relationship between Reed-Muller codes and single-qubit phase gates from the perspective of $T$-count optimization. We prove that minimizing the number of $T$ gates in an $n$-qubit quantum circuit over CNOT…