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Simulating the dynamics of electrons and other fermionic particles in quantum chemistry, materials science, and high-energy physics is one of the most promising applications of fault-tolerant quantum computers. However, the overhead in…
We use our Clifford algebra technique, that is nilpotents and projectors which are binomials of the Clifford algebra objects $\gamma^a$ with the property $\{\gamma^a,\gamma^b\}_+ = 2 \eta^{ab}$, for representing quantum gates and quantum…
We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves $\varepsilon$-approximations using circuits of length $O(\log(1/\varepsilon))$, which is…
Compared to general quantum states, the sparse states arise more frequently in the field of quantum computation. In this work, we consider the preparation for $n$-qubit sparse quantum states with $s$ non-zero amplitudes and propose two…
We present an explicit quantum circuit that prepares an arbitrary $U(1)$-eigenstate on a quantum computer, including the exact eigenstates of the spin-1/2 XXZ quantum spin chain with either open or closed boundary conditions. The algorithm…
We study the resources required to achieve universal quantum computing via the gate sets that provide the fundamental instructions from which quantum algorithms are built. While single-gate universal sets are known, they rely on precisely…
We consider the task of deciding whether an unknown qubit state falls in a prescribed neighborhood of a reference state. We assume that several copies of the unknown state are given and apply a unitary operation pairwise on them combined…
Efficiently estimating fermionic Hamiltonian expectation values is vital for simulating various physical systems. Classical shadow (CS) algorithms offer a solution by reducing the number of quantum state copies needed, but noise in quantum…
The random purification channel maps n copies of any mixed quantum state to n copies of a random purification of the state. We generalize this construction to arbitrary symmetries: for any group G of unitaries, we construct a quantum…
Quantum state preparation is an important subroutine for quantum computing. We show that any $n$-qubit quantum state can be prepared with a $\Theta(n)$-depth circuit using only single- and two-qubit gates, although with a cost of an…
Tensor network states and specifically matrix-product states have proven to be a powerful tool for simulating ground states of strongly correlated spin models. Recently, they have also been applied to interacting fermionic problems,…
Methods of processing quantum data become more important as quantum computing devices improve their quality towards fault tolerant universal quantum computers. These methods include discrimination and filtering of quantum states given as an…
Quantum algorithms for linear systems produce the solution state $A^{-1}|b\rangle$ by querying two oracles: $O_A$ that block encodes the coefficient matrix and $O_b$ that prepares the initial state. We present a quantum linear system…
For universal quantum computation, a major challenge to overcome for practical implementation is the large amount of resources required for fault-tolerant quantum information processing. An important aspect is implementing arbitrary unitary…
While Clifford operations are relatively easy to implement in fault-tolerant quantum computers,continuous rotation gates remain a significant bottleneck in typical quantum algorithms. In this work, we ask the question: "What is the most…
We aim to establish a scalable scheme for characterising diagonal non-Clifford gates for single- and multi-qudit systems; \(d\) is a prime-power integer. By employing cyclic operators and a qudit T gate, we generalise the dihedral…
As experimental platforms for quantum information processing continue to mature, characterization of the quality of unitary gates that can be applied to their quantum bits (qubits) becomes essential. Eventually, the quality must be…
The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven…
In quantum computation every unitary operation can be decomposed into quantum circuits-a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-NOT (CNOT) gates. Two measures are important when…
In this article we study the possibilities of recovering the structure of port-Hamiltonian systems starting from ``unlabelled'' ordinary differential equations describing mechanical systems. The algorithm we suggest solves the problem in…