Related papers: High Performance Quantum Modular Multipliers
The success of quantum circuits in providing reliable outcomes for a given problem depends on the gate count and depth in near-term noisy quantum computers. Quantum circuit compilers that decompose high-level gates to native gates of the…
Superconducting qubits provide a promising approach to large-scale fault-tolerant quantum computing. However, qubit connectivity on a planar surface is typically restricted to only a few neighboring qubits. Achieving longer-range and more…
Galois field (GF) arithmetic circuits find numerous applications in communications, signal processing, and security engineering. Formal verification techniques of GF circuits are scarce and limited to circuits with known bit positions of…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
We study the implementation of quantum key distribution (QKD) systems over quantum repeater infrastructures. We particularly consider quantum repeaters with encoding and compare them with probabilistic quantum repeaters. To that end, we…
Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qu$trits$. Past work with qutrits has demonstrated only constant factor improvements, owing to the $\log_2(3)$…
Reversible computation has been proposed as a future paradigm for energy efficient computation, but so far few implementations have been realised in practice. Quantum circuits, running on quantum computers, are one construct known to be…
Quantum computing is in an era of limited resources. Current hardware lacks high fidelity gates, long coherence times, and the number of computational units required to perform meaningful computation. Contemporary quantum devices typically…
Computations with a future quantum computer will be implemented through the operations by elementary quantum gates. It is now well known that the collection of 1-bit and 2-bit quantum gates are universal for quantum computation, i.e., any…
A major obstacle to implementing Shor's quantum number-factoring algorithm is the large size of modular-exponentiation circuits. We reduce this bottleneck by customizing reversible circuits for modular multiplication to individual runs of…
Quantum algorithms for scientific computing require modules implementing fundamental functions, such as the square root, the logarithm, and others. We require algorithms that have a well-controlled numerical error, that are uniformly…
We introduce a quantum extension of dynamic programming, a fundamental computational method that efficiently solves recursive problems using memory. Our innovation lies in showing how to coherently generate recursion step unitaries by using…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
We present a quantum circuit optimization technique that takes into account the variability in error rates that is inherent across present day noisy quantum computing platforms. This method can be run post qubit routing or post-compilation,…
Hybrid quantum algorithms combine the strengths of quantum and classical computing. Many quantum algorithms, such as the variational quantum eigensolver (VQE), leverage this synergy. However, quantum circuits are executed in full, even when…
Composite pulse sequences, which produce arbitrary pre-defined rotations of a qubit on the Bloch sphere, are presented. The composite sequences contain up to 17 pulses and can compensate up to eight orders of experimental errors in the…
Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different…
We explore a method for automatically recompiling a quantum circuit A into a target circuit B, with the goal that both circuits have the same action on a specific input i.e. B|in> = A|in>. This is of particular relevance to hybrid, NISQ-era…
We observe structure in the sequences of quotients and remainders of the Euclidean algorithm with two families of inputs. Analyzing the remainders, we obtain new algorithms for computing modular inverses and representating prime numbers by…
We propose quantum devices that can realize probabilistically different projective measurements on a qubit. The desired measurement basis is selected by the quantum state of a program register. First we analyze the phase-covariant…