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The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
Current quantum devices execute specific tasks that are hard for classical computers and have the potential to solve problems such as quantum simulation of material science and chemistry, even without error correction. For practical…
A class of non-Hermitian quadratic su(2) Hamiltonians having an anti-linear symmetry is constructed. This is achieved by analysing the possible symmetries of such systems in terms of automorphisms of the algebra. In fact, different…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…
Rydberg-atom quantum simulators are of keen interest because of their possibilities towards high-dimensional qubit architectures. Here we report three-dimensional conformation spectra of quantum-Ising Hamiltonian systems with programmed…
We show how quantum metrology protocols that seek to estimate the parameters of a Hamiltonian that exhibits a quantum phase transition can be efficiently simulated on an exponentially smaller quantum computer. Specifically, by exploiting…
We address the problem of simulating pair-interaction Hamiltonians in n node quantum networks where the subsystems have arbitrary, possibly different, dimensions. We show that any pair-interaction can be used to simulate any other by…
Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian…
The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here we present a process for obtaining the…
Quantum walks are powerful kernels in quantum computing protocols that possess strong capabilities in speeding up various simulation and optimisation tasks. One striking example is given by quantum walkers evolving on glued trees for their…
We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs. Our algorithm generates square matrices whose entries are orthogonal projections onto one-dimensional subspaces satisfying a…
Quantum walk is a useful model to simulate complex quantum systems and to build quantum algorithms; in particular, to develop spatial search algorithms on graphs, which aim to find a marked vertex as quickly as possible. Quantum walks are…
The construction of two-qubit gates appropriate for universal quantum computation is of enormous importance to quantum information processing. Building such gates is dependent on accurate knowledge of the interaction dynamics between two…
We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this…
Topologically ordered quantum matter exhibits intriguing long-range patterns of entanglement, which reveal themselves in subsystem entropies. However, measuring such entropies, which can be used to certify topological order, on large…
We present an efficient quantum circuit for block encoding pairing Hamiltonian often studied in nuclear physics. Our block encoding scheme does not require mapping the creation and annihilation operators to the Pauli operators and…
Recently a method for adiabatic quantum computation has been proposed and there has been considerable speculation about its efficiency for NP-complete problems. Heuristic arguments in its favor are based on the unproven assumption of an…
We show how one can implement any local quantum gate on specific qubits in an array of qubits by carrying adiabatically a Hamiltonian around a closed loop. We find the exact form of the loop and the Hamiltonian for implementing general one…
A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly, it has been shown that algorithmic properties of quantum walks with…
Exactly-solvable Hamiltonians that can be diagonalized using relatively simple unitary transformations are of great use in quantum computing. They can be employed for decomposition of interacting Hamiltonians either in Trotter-Suzuki…