Related papers: Bounds on the QAC$^0$ Complexity of Approximating …
Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…
We first show how to construct an O(n)-depth O(n)-size quantum circuit for addition of two n-bit binary numbers with no ancillary qubits. The exact size is 7n-6, which is smaller than that of any other quantum circuit ever constructed for…
Quantum Error Correction (QEC) is the cornerstone of practical Fault-Tolerant Quantum Computing (FTQC), but incurs enormous resource overheads. Circuits must decompose into Clifford+T gates, and the non-transversal T gates demand costly…
Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type…
Equivalence checking of quantum circuits is an essential element in quantum program compilation, in which a quantum program can be synthesized into different quantum circuits that may vary in the number of qubits, initialization…
Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising quantum algorithms for the Noisy Intermediate-Scale Quantum (NISQ) era. Quantifying the performance of QAOA in the near-term regime is of utmost importance. We…
We introduce the parity-unfolded architecture, a fault-tolerant quantum computing scheme that relies on direct preparation and teleportation of small-angle rotations $ Z^{1/2^{k}}$ rather than approximating them with the conventional…
We show that any quantum circuit of treewidth $t$, built from $r$-qubit gates, requires at least $\Omega(\frac{n^{2}}{2^{O(r\cdot t)}\cdot \log^4 n})$ gates to compute the element distinctness function. Our result generalizes a…
In principle a 1D array of nearest-neighbour linked qubits is compatible with fault tolerant quantum computing. However such a restricted topology necessitates a large overhead for shuffling qubits and consequently the fault tolerance…
In Exact Quantum Query model, almost all of the Boolean functions for which non-trivial query algorithms exist are symmetric in nature. The most well known techniques in this domain exploit parity decision trees, in which the parity of two…
While a Quantum Approximate Optimization Algorithm (QAOA) is intended to provide a quantum advantage in finding approximate solutions to combinatorial optimization problems, noise in the system is a hurdle in exploiting its full potential.…
We present QEst, a procedure to systematically generate approximations for quantum circuits to reduce their CNOT gate count. Our approach employs circuit partitioning for scalability with procedures to 1) reduce circuit length using…
In the current NISQ (Noisy Intermediate-Scale Quantum) era, simulating and verifying noisy quantum circuits is crucial but faces challenges such as quantum state explosion and complex noise representations, constraining simulation and…
It has been shown that, for even $n$, evolving $n$ qubits according to a Hamiltonian that is the sum of pairwise interactions between the particles, can be used to exactly implement an $(n+1)$-qubit fanout gate using a particular…
Quantum unitaries of the form $\Sigma_{c}\ket{c}\bra{c}\otimes U_{c}$ are ubiquitous in quantum algorithms. This class encompasses not only standard uniformly controlled gates (UCGs) but also a wide range of circuits with uniformly…
We use a random search technique to find quantum gate sequences that implement perfect quantum state preparation or unitary operator synthesis with arbitrary targets. This approach is based on the recent discovery that there is a large…
We study the achievements of quantum circuits comprised of several one- and two-qubit gates. Quantum process matrices are determined for the basic one- and two-qubit gate operations and concatenated to yield the process matrix of the…
Designing noisy-resilience quantum algorithms is indispensable for practical applications on Noisy Intermediate-Scale Quantum~(NISQ) devices. Here we propose a quantum approximate optimization algorithm~(QAOA) with a very shallow circuit,…
We present two protocols for classical verification of quantum depth. Our protocols allow a purely classical verifier to distinguish devices with different quantum circuit depths even in the presence of classical computation. We show that a…
Quantum Error Correction (QEC), combined with magic state distillation, ensures fault tolerance in large-scale quantum computation. To apply QEC, a circuit must first be transformed into a non-Clifford (or T) gate set. T-depth, the number…