Related papers: Minimizing CNOT-count in quantum circuit of the ex…
Tomography has reached its practical limits in characterization of new quantum devices, and there is a need for a new means of characterizing and validating new technological advances in this field. We propose a different verification…
Quantum computing has transformative computational power to make classically intractable computing feasible. As the algorithms that achieve practical quantum advantage are beyond manual tuning, quantum circuit optimization has become…
We demonstrate that, in the case of Shor's algorithm for factoring, highly mixed states will allow efficient quantum computation, indeed factorization can be achieved efficiently with just one initial pure qubit and a supply of initally…
The promise of quantum computers hinges on the ability to scale to large system sizes, e.g., to run quantum computations consisting of more than 100 million operations fault-tolerantly. This in turn requires suppressing errors to levels…
The solving of linear systems provides a rich area to investigate the use of nearer-term, noisy, intermediate-scale quantum computers. In this work, we discuss hybrid quantum-classical algorithms for skewed linear systems for…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It…
We contribute a 2D nearest-neighbor quantum architecture for Shor's algorithm to factor an $n$-bit number in $O(\log^2(n))$ depth. Our implementation uses parallel phase estimation, constant-depth fanout and teleportation, and…
Fault-tolerant quantum error correction (QEC) is crucial for unlocking the true power of quantum computers. QEC codes use multiple physical qubits to encode a logical qubit, which is protected against errors at the physical qubit level.…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
Extracting information from quantum systems is crucial in quantum physics and information processing. Methods based on randomized measurements, like shadow estimation, show advantages in effectively achieving such tasks. However, randomized…
This work presents a generalized period decomposition approach, significantly improving the practical reliability of Shor's quantum factoring algorithm. Although Shor's algorithm theoretically enables polynomial-time integer factorization,…
Optimizing the size and depth of CNOT circuits is an active area of research in quantum computing and is particularly relevant for circuits synthesized from the Clifford + T universal gate set. Although many techniques exist for finding…
In quantum computation every unitary operation can be decomposed into quantum circuits-a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-NOT (CNOT) gates. Two measures are important when…
Among the cost metrics characterizing a quantum circuit, the $T$-count stands out as one of the most crucial as its minimization is particularly important in various areas of quantum computation such as fault-tolerant quantum computing and…
Multi-controlled single-target (MC) gates are some of the most crucial building blocks for varied quantum algorithms. How to implement them optimally is thus a pivotal question. To answer this question in an architecture-independent manner,…
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…
Current experimental quantum computing devices are limited by noise, mainly originating from entangling gates. If an efficient gate sequence for an operation is unknown, one often employs layered parameterized quantum circuits, especially…
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…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…