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Quantum noise in real-world devices poses a significant challenge in achieving practical quantum advantage, since accurately compiled and executed circuits are typically deep and highly susceptible to decoherence. To facilitate the…
Given a universal gate set on two qubits, it is well known that applying random gates from the set to random pairs of qubits will eventually yield an approximately Haar-distributed unitary. However, this requires exponential time. We show…
Reducing the number of non-Clifford quantum gates present in a circuit is an important task for efficiently implementing quantum computations, especially in the fault-tolerant regime. We present a new method for reducing the number of…
We propose a novel technique for optimizing a modular fault-tolerant quantum computing architecture, taking into account any desired space-time trade-offs between the number of physical qubits and the fault-tolerant execution time of a…
In 2021, Broadbent and Kazmi developed a gate-teleportation-based protocol for computational indistinguishability obfuscation of quantum circuits. This protocol is efficient for Clifford+T circuits with logarithmically many T-gates, where…
We consider a quantum polynomial-time algorithm which solves the discrete logarithm problem for points on elliptic curves over $GF(2^m)$. We improve over earlier algorithms by constructing an efficient circuit for multiplying elements of…
We give a quantum approximation scheme (i.e., $(1 + \varepsilon)$-approximation for every $\varepsilon > 0$) for the classical $k$-means clustering problem in the QRAM model with a running time that has only polylogarithmic dependence on…
Pauli-based computation (PBC) is driven by a sequence of adaptively chosen, non-destructive measurements of Pauli observables. Any quantum circuit written in terms of the Clifford+$T$ gate set and having $t$ $T$ gates can be compiled into a…
Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available,…
The Clifford group is a finite subgroup of the unitary group generated by the Hadamard, the CNOT, and the Phase gates. This group plays a prominent role in quantum error correction, randomized benchmarking protocols, and the study of…
Any technology requires precise benchmarking of its components, and the quantum technologies are no exception. Randomized benchmarking allows for the relatively resource economical estimation of the average gate fidelity of quantum gates…
Any unitary operation in quantum information processing can be implemented via a sequence of simpler steps - quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, seeking for…
Quantum computing has garnered attention for its potential to solve complex computational problems with considerable speedup. Despite notable advancements in the field, achieving meaningful scalability and noise control in quantum hardware…
A milestone in the field of quantum computing will be solving problems in quantum chemistry and materials faster than state-of-the-art classical methods. The current understanding is that achieving quantum advantage in this area will…
Von Neumann's classic "multiplexing" method is unique in achieving high-threshold fault-tolerant classical computation (FTCC), but has several significant barriers to implementation: i) the extremely complex circuits required by randomized…
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,…
Surface code based quantum computers show great promise for fault-tolerant quantum computing, but most architectures needlessly increase the spacetime volume of a computation due to qubits sitting idly during a computation. Active volume…
Solving problems related to planning and operations of large-scale power systems is challenging on classical computers due to their inherent nature as mixed-integer and nonlinear problems. Quantum computing provides new avenues to approach…
This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: -- On Universal Turing Machines, a program's time complexity should be characterized as:…
A general quantum circuit can be simulated classically in exponential time. If it has a planar layout, then a tensor-network contraction algorithm due to Markov and Shi has a runtime exponential in the square root of its size, or more…