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Simulation of quantum systems is expected to be one of the most important applications of quantum computing, with much of the theoretical work so far having focused on fermionic and spin-1 2 systems. Here, we instead consider encodings of d-level (i.e., qudit) quantum operators into multi-qubit operators, studying resource requirements for approximating operator exponentials by Trotterization. We primarily focus on spins and truncated bosonic operators in second quantization, observing desirable properties for approaches based on the Gray code, which to our knowledge has not been used in this context previously. After outlining a methodology for implementing an arbitrary encoding, we investigate the interplay between Hamming distances, sparsity patterns, bosonic truncation, and other properties of local operators. Finally, we obtain resource counts for five common Hamiltonian classes used in physics and chemistry, while modeling the possibility of converting between encodings within a Trotter step. The most efficient encoding choice is heavily dependent on the application and highly sensitive to d, although clear trends are present. These operation count reductions are relevant for running algorithms on near-term quantum hardware because the savings effectively decrease the required circuit depth. Results and procedures outlined in this work may be useful for simulating a broad class of Hamiltonians on qubit-based digital quantum computers.

A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer.Fast and robust quantum gates play a central role in realizing a practical quantum computer. While the robustness offers resilience to certain errors such as parameter fluctuations, the fast implementation of designated quantum gates increases computational speed, which in turn decreases environment-induced errors. A possible approach towards robust quantum computation is to implement quantum gates by means of different types of geometric phases [1][2][3][4] ; an approach known as holonomic quantum computation (HQC) [5][6][7][8][9][10] . Such geometric gates depend solely on the path of a system evolution, rather than its dynamical details.Universal quantum computation based purely on geometric means has been proposed in the adiabatic regime, resulting in a precise control of a quantum-mechanical system 7 . Despite the appealing features, the adiabatic evolution is associated with long run time, which increases the exposure to detrimental decoherence and noise. However, this drawback can be eliminated by using non-adiabatic HQC schemes based on Abelian 8,9 or non-Abelian geometric phases 10 . The latter has been developed further in refs 11-14 experimentally demonstrated in refs 15-18 and its robustness to a variety of errors has been studied in refs 19,20.Adiabatic processes can also be carried out swiftly by employing transitionless quantum driving algorithm (TQDA) if the quantum system consists of non-degenerate subspaces 21 . This is also known as adiabatic shortcut in the literature [22][23][24][25][26][27] . A key notion of TQDA is to seek a transitionless Hamiltonian so that the system evolves exactly along the same adiabatic passage of a given target Hamiltonian, but at any desired rate. This is achieved with the aid of an additional Hamiltonian that suppresses the energy level fluctuations caused by the changes in th...

Circuit quantum electrodynamics, consisting of superconducting artificial atoms coupled to on-chip resonators, represents a prime candidate to implement the scalable quantum computing architecture because of the presence of good tunability and controllability. Furthermore, recent advances have pushed the technology towards the ultrastrong coupling regime of light-matter interaction, where the qubit-resonator coupling strength reaches a considerable fraction of the resonator frequency. Here, we propose a qubit-resonator system operating in that regime, as a quantum memory device and study the storage and retrieval of quantum information in and from the Z2 parity-protected quantum memory, within experimentally feasible schemes. We are also convinced that our proposal might pave a way to realize a scalable quantum random-access memory due to its fast storage and readout performances.

Adaptive construction of ansatz circuits offers a promising route towards applicable variational quantum eigensolvers on near-term quantum hardware. Those algorithms aim to build up optimal circuits for a certain problem and ansatz circuits are adaptively constructed by selecting and adding entanglers from a predefined pool. In this work, we propose a way to construct entangler pools with reduced size by leveraging classical algorithms. Our method uses mutual information between the qubits in classically approximated ground state to rank and screen the entanglers. The density matrix renormalization group method is employed for classical precomputation in this work. We corroborate our method numerically on small molecules. Our numerical experiments show that a reduced entangler pool with a small portion of the original entangler pool can achieve same numerical accuracy. We believe that our method paves a new way for adaptive construction of ansatz circuits for variational quantum algorithms.

We propose to construct large quantum graph codes by means of superconducting circuits working at the ultrastrong coupling regime. In this physical scenario, we are able to create a cluster state between any pair of qubits within a fraction of a nanosecond. To exemplify our proposal, creation of the five-qubit and Steane codes is numerically simulated. We also provide optimal operating conditions with which the graph codes can be realized with state-of-the-art superconducting technologies.

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We provide a general description of a time-local master equation for a system coupled to a non-Markovian reservoir based on Floquet theory. This allows us to have a divisible dynamical map at discrete times, which we refer to as Floquet stroboscopic divisibility. We illustrate the theory by considering a harmonic oscillator coupled to both non-Markovian and Markovian baths. Our findings provide us with a theory for the exact calculation of spectral properties of time-local non-Markovian Liouvillian operators, and might shed light on the nature and existence of the steady state in non-Markovian dynamics.