Related papers: Fast Quantum Modular Exponentiation
Increasing quantum circuit fidelity requires an efficient instruction set to avoid errors from decoherence. The choice of a two-qubit (2Q) hardware basis gate depends on a quantum modulator's native Hamiltonian interactions and applied…
Here we describe an approach for simulating electronic structure on quantum computers with significantly lower asymptotic complexity than prior work. The approach uses a real-space first-quantised representation of the molecular Hamiltonian…
The development of fault-tolerant quantum computers (FTQCs) is receiving increasing attention within the quantum computing community. Like conventional digital computers, FTQCs, which utilize error correction and millions of physical…
Modular quantum computing provides a scalable approach to overcome the limitations of monolithic quantum architectures by interconnecting multiple Quantum Processing Units (QPUs) through a quantum network. In this work, we explore and…
The computational power of a quantum computer is limited by the number of qubits available for information processing. Increasing this number within a single device is difficult; it is widely accepted that distributed modular architectures…
Quantum computers promise to perform certain computations exponentially faster than any classical device. Precise control over their physical implementation and proper shielding from unwanted interactions with the environment become more…
Quantum technology has the potential to revolutionize how we acquire and process experimental data to learn about the physical world. An experimental setup that transduces data from a physical system to a stable quantum memory, and…
Blockmodeling of a given problem represented by an $N\times N$ adjacency matrix can be found by swapping rows and columns of the matrix (i.e. multiplying matrix from left and right by a permutation matrix). Although classical matrix…
Quantum arithmetic circuits have practical applications in various quantum algorithms. In this paper, we address quantum addition on 2-dimensional nearest-neighbor architectures based on the work presented by Choi and Van Meter (JETC 2012).…
The design space of current quantum computers is expansive with no obvious winning solution. This leaves practitioners with a clear question: "What is the optimal system configuration to run an algorithm?". This paper explores hardware…
In general, a quantum circuit is constructed with elementary gates, such as one-qubit gates and CNOT gates. It is possible, however, to speed up the execution time of a given circuit by merging those elementary gates together into larger…
I discuss how to perform fault-tolerant quantum computation with concatenated codes using local gates in small numbers of dimensions. I show that a threshold result still exists in three, two, or one dimensions when next-to-nearest-neighbor…
Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
Quantum computers with tens to hundreds of noisy qubits are being developed today. To be useful for real-world applications, we believe that these near-term systems cannot simply be scaled-down non-error-corrected versions of future…
We consider how to optimize memory use and computation time in operating a quantum computer. In particular, we estimate the number of memory qubits and the number of operations required to perform factorization, using the algorithm…
In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large…
In an ordinary quantum algorithm the gates are applied in a fixed order on the systems. The introduction of indefinite causal structures allows to relax this constraint and control the order of the gates with an additional quantum state. It…
We give an $O(N\cdot \log N\cdot 2^{O(\log^*N)})$ algorithm for multiplying two $N$-bit integers that improves the $O(N\cdot \log N\cdot \log\log N)$ algorithm by Sch\"{o}nhage-Strassen. Both these algorithms use modular arithmetic.…
We show that the algorithmic complexity of any classical algorithm written in a Turing-complete programming language polynomially bounds the number of quantum bits that are required to run and even symbolically execute the algorithm on a…