Related papers: Bounds on the QAC$^0$ Complexity of Approximating …
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce…
We say that collection of $n$-qudit gates is universal if there exists $N_0\geq n$ such that for every $N\geq N_0$ every $N$-qudit unitary operation can be approximated with arbitrary precision by a circuit built from gates of the…
The controlled-SWAP and controlled-controlled-NOT gates are at the heart of the original proposal of reversible classical computation by Fredkin and Toffoli. Their widespread use in quantum computation, both in the implementation of…
Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high fidelity two-qudit gates. We first describe how to implement parallel single qudit operations. It is by now well…
The progress in building quantum computers to execute quantum algorithms has recently been remarkable. Grover's search algorithm in a binary quantum system provides considerable speed-up over classical paradigm. Further, Grover's algorithm…
We prove that $poly(t) \cdot n^{1/D}$-depth local random quantum circuits with two qudit nearest-neighbor gates on a $D$-dimensional lattice with n qudits are approximate $t$-designs in various measures. These include the "monomial"…
We present a scalable set of universal gates and multiply controlled gates in a qudit basis through a bijective mapping from N qubits to qudits with D = 2^N levels via rotations in U(2). For each of the universal gates (H, CNOT, and T), as…
Since an n-qubit circuit consisting of CNOT gates can have up to $\Omega(n^2/\log{n})$ CNOT gates, it is natural to expect that $\Omega(n^2/\log{n})$ Toffoli gates are needed to apply a controlled version of such a circuit. We show that the…
We study the quantum complexity class QNC^0_f of quantum operations implementable exactly by constant-depth polynomial-size quantum circuits with unbounded fan-out gates (called QNC^0_f circuits). Our main result is that the quantum OR…
We exhibit some simple gadgets useful in designing shallow parallel circuits for quantum algorithms. We prove that any quantum circuit composed entirely of controlled-not gates or of diagonal gates can be parallelized to logarithmic depth,…
We study the realization of a Toffoli gate with superconducting qubits in a circuit-QED setup using quantum-control methods. Starting with optimized piecewise-constant control fields acting on all qubits and typical strengths of XY-type…
One of the prominent current challenges in complexity theory is the attempt to prove lower bounds for $TC^0$, the class of constant-depth, polynomial-size circuits with majority gates. Relying on the results of Williams (2013), an appealing…
An $n$-qubit quantum circuit is said to be peaked if it has an output probability that is at least inverse-polynomially large as a function of $n$. We describe a classical algorithm with quasipolynomial runtime $n^{O(\log{n})}$ that…
We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n + log log (1/epsilon)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2^n…
The quantum approximate optimization algorithm (QAOA) has been introduced as a heuristic digital quantum computing scheme to find approximate solutions of combinatorial problems with shallow circuits. We present a scheme to parallelize this…
We present a compact quantum circuit for factoring a large class of integers, including some whose classical hardness is expected to be equivalent to RSA (but not including RSA integers themselves). Most notably, we factor $n$-bit integers…
Random unitaries are a central object of study in quantum information, with applications to quantum computation, quantum many-body physics, and quantum cryptography. Recent work has constructed unitary designs and pseudorandom unitaries…
Implementing many important sub-circuits on near-term quantum devices remains a challenge due to the high levels of noise and the prohibitive depth on standard nearest-neighbour topologies. Overcoming these barriers will likely require…
Quantum circuit equivalence checking asks whether two circuits implement the same unitary. It guarantees compiler correctness and safe optimization, yet most existing approaches scale exponentially with the number of qubits or the circuit…
We prove new upper bounds on the tolerable level of noise in a quantum circuit. We consider circuits consisting of unitary k-qubit gates each of whose input wires is subject to depolarizing noise of strength p, as well as arbitrary…