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Random quantum states have various applications in quantum information science. We discover a new ensemble of quantum states that serve as an $\epsilon$-approximate state $t$-design while possessing extremely low entanglement, magic, and…
We show that any pseudoentangled state ensemble with a gap of $t$ bits of entropy requires $\Omega(t)$ non-Clifford gates to prepare. This bound is tight up to polylogarithmic factors if linear-time quantum-secure pseudorandom functions…
Since the final quantum state in the Grover search algorithm is the normalized marked quantum state from the Gram-Schmidt process, Abrams and Lloyd [1] has shown that we can generate this vector by using a non-unitary gate. Following their…
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivity, and coherence times, a quantum circuit optimization is essential to make the best use of near-term quantum devices. We…
The performance of quantum algorithms for ground-state energy estimation is directly impacted by the quality of the initial state, where quality is traditionally defined in terms of the overlap of the input state with the target state. An…
The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wavefunctions that are relevant in the behavior of the system under study. Hamiltonian symmetries are an important…
We introduce a novel deterministic quantum search algorithm that provides a practical alternative to conventional probabilistic search approaches. Our scheme eliminates the inherent uncertainty of quantum search without relying on arbitrary…
Understanding what can be learned from experiments is central to scientific progress. In this work, we use a learning-theoretic perspective to study the task of learning physical operations in a quantum machine when all operations (state…
We introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…
We present a deterministic framework for preparing an arbitrary three-qubit pure state. To leverage entanglement structure in the state-preparation task, we classify three-qubit pure states into five types with respect to a $1|2$…
We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…
The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…
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…
Most work in quantum circuit optimization has been performed in isolation from the results of quantum fault-tolerance. Here we present a polynomial-time algorithm for optimizing quantum circuits that takes the actual implementation of…
We propose an efficient protocol to fully reconstruct a set of high-fidelity quantum gates. Usually, the efficiency of reconstructing high-fidelity quantum gates is limited by the sampling noise. Our protocol is based on a perturbative…
Efficiently characterizing large quantum states and processes is a central yet notoriously challenging task in quantum information science, as conventional tomography methods typically require resources that grow exponentially with system…
Quantum computers are capable of efficiently contracting unitary tensor networks, a task that is likely to remain difficult for classical computers. For instance, networks based on matrix product states or the multi-scale entanglement…
Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from…
This work focuses on reducing the physical cost of implementing quantum algorithms when using the state-of-the-art fault-tolerant quantum error correcting codes, in particular, those for which implementing the T gate consumes vastly more…
Compact representations of fermionic Hamiltonians are necessary to perform calculations on quantum computers that lack error-correction. A fermionic system is typically defined within a subspace of fixed particle number and spin while…