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In recent years, significant progress has been made in the field of state transfer in spin chains, with the aim of achieving perfect state transfer for quantum information processing applications. Previous research has mainly focused on manipulating inter-site couplings within spin chains; here, we investigate in detail the potential of modifying on-site energies to facilitate precise quantum information transfer. Our findings demonstrate that through targeted adjustments to the diagonal elements of the XY Hamiltonian and leveraging a genetic algorithm, quasi-perfect state transfer can be achieved with careful consideration of the system's spectral characteristics. This investigation into on-site energies offers an alternative approach for achieving high-fidelity state transfer, especially in cases where manipulation of inter-site couplings may be impractical. This study thus represents a significant advancement towards unlocking the diverse applications of spin chains within practical quantum information systems., Comment: 11 pages, 8 figures, 3 tables

In recent years, analog quantum simulators have reached unprecedented quality, both in qubit numbers and coherence times. Most of these simulators natively implement Ising-type Hamiltonians, which limits the class of models that can be simulated efficiently. We propose a method to overcome this limitation and simulate the time-evolution of a large class of spinless fermionic systems in 1D using simple Ising-type Hamiltonians with local transverse fields. Our method is based on domain wall encoding, which is implemented via strong (anti-)ferromagnetic couplings $|J|$. We show that in the limit of strong $|J|$, the domain walls behave like spinless fermions in 1D. The Ising Hamiltonians are one-dimensional chains with nearest-neighbor and, optionally, next-nearest-neighbor interactions. As a proof-of-concept, we perform numerical simulations of various 1D-fermionic systems using domain wall evolution and accurately reproduce the systems' properties, such as topological edge states, Anderson localization, quantum chaotic time evolution and time-reversal symmetry breaking via Floquet-engineering. Our approach makes the simulation of a large class of fermionic many-body systems feasible on analogue quantum hardware that natively implements Ising-type Hamiltonians with transverse fields., Comment: 25 pages, 13 figures; minor changes for improved error estimation and comparison to Trotterization

Achieving dense connectivities is a challenge for most quantum computing platforms today, and a particularly crucial one for the case of quantum annealing applications. In this context, we present a scalable architecture for quantum annealers described by a hardware graph of degree $d=3$ and containing exclusively 2-local interactions to realize Ising models of arbitrary dimension. By describing the problem graph in terms of triangles, we derive this resource-efficient configuration based on logical chains of qubits. We also devise strategies to address the challenges of scaling this architecture, identifying driver Hamiltonians more suited to the symmetries of the logical solution space. We thus show a promising new route to scale up devices dedicated to classical optimization tasks within the quantum annealing paradigm., Comment: Minor corrections that don't modify the results (typos, better fitting function), added Appendix and changed the definition of reference variable $\beta$ in the driver discussion in order to improve the presentation of the results. This induced changes to the appearance of Figure 2. 5 pages, 2 figures

We propose a novel Reinforcement Learning (RL) method for optimizing quantum circuits using graph-theoretic simplification rules of ZX-diagrams. The agent, trained using the Proximal Policy Optimization (PPO) algorithm, employs Graph Neural Networks to approximate the policy and value functions. We demonstrate the capacity of our approach by comparing it against the best performing ZX-Calculus-based algorithm for the problem in hand. After training on small Clifford+T circuits of 5-qubits and few tenths of gates, the agent consistently improves the state-of-the-art for this type of circuits, for at least up to 80-qubit and 2100 gates, whilst remaining competitive in terms of computational performance. Additionally, we illustrate its versatility by targeting both total and two-qubit gate count reduction, conveying the potential of tailoring its reward function to the specific characteristics of each hardware backend. Our approach is ready to be used as a valuable tool for the implementation of quantum algorithms in the near-term intermediate-scale range (NISQ)., Comment: 18 pages, 10 figures

Spin network systems can be used to achieve quantum state transfer with high fidelity and to generate entanglement. A new approach to design spin-chain-based spin network systems, for shortrange quantum information processing and phase-sensing, has been proposed recently in [1]. In this paper, we investigate the scalability of such systems, by designing larger spin network systems that can be used for longer-range quantum information tasks, such as connecting together quantum processors. Furthermore, we present more complex spin network designs, which can produce different types of entangled states. Simulations of disorder effects show that even such larger spin network systems are robust against realistic levels of disorder., Comment: 19 pages, 25 figures

In the context of adiabatic quantum computation (AQC), it has been argued that first-order quantum phase transitions (QPTs) due to localisation phenomena cause AQC to fail by exponentially decreasing the minimal spectral gap of the Hamiltonian along the annealing path as a function of the qubit number. The vanishing of the spectral gap is often linked to the localisation of the ground state in a local minimum, requiring the system to tunnel into the global minimum at a later stage of the annealing. Recent methods have been proposed to avoid this phenomenon by carefully designing the involved Hamiltonians. However, it remains a challenge to formulate a comprehensive theory of the effect of the various parameters and the conditions under which QPTs make the AQC algorithm fail. Equipped with concepts from graph theory, in this work we link graph quantities associated to the Hamiltonians along the annealing path with the occurrence of QPTs. These links allow us to derive bounds on the location of the minimal spectral gap along the annealing path, augmenting the toolbox for the analysis of strategies to improve the runtime of AQC algorithms., Comment: 14 pages, 7 figures

In the computational model of quantum annealing, the size of the minimum gap between the ground state and the first excited state of the system is of particular importance, since it is inversely proportional to the running time of the algorithm. Thus, it is desirable to keep the gap as large as possible during the annealing process, since it allows the computation to remain under the protection of the adiabatic theorem while staying efficient. We propose steered quantum annealing as a new method to enlarge the gap throughout the process, in the case of diagonal final Hamiltonians, based on the exploitation of some assumptions we can make about the particular problem instance. In order to introduce this information, we propose beginning the anneal from a biased Hamiltonian that incorporates reliable assumptions about the final ground state. Our simulations show that this method yields a larger average gap throughout the whole computation, which results in an increased robustness of the overall annealing process., Comment: 9 pages, 7 figures

Spin chains can be used to describe a wide range of platforms for quantum computation and quantum information. They enable the understanding, demonstration, and modeling of numerous useful phenomena, such as high fidelity transfer of quantum states, creation and distribution of entanglement, and creation of resources for measurement-based quantum processing. In this paper, a more complex spin system, a 2D spin network (SN) engineered by applying suitable unitaries to two uncoupled spin chains, is studied. Considering only the single-excitation subspace of the SN, it is demonstrated that the system can be operated as a router, directing information through the SN. It is also shown that it can serve to generate maximally entangled states between two sites. Furthermore, it is illustrated that this SN system can be used as a sensor device able to determine an unknown phase applied to a system spin. A detailed modeling investigation of the effects of static disorder in the system shows that this system is robust against different types of disorder., Comment: An erratum has been published for the journal paper. This updated arXiv version presents the corrected version of the published paper. The main conclusions of the paper are not affected by this correction

Today's quantum processors composed of fifty or more qubits have allowed us to enter a computational era where the output results are not easily simulatable on the world's biggest supercomputers. What we have not seen yet, however, is whether or not such quantum complexity can be ever useful for any practical applications. A fundamental question behind this lies in the non-trivial relation between the complexity and its computational power. If we find a clue for how and what quantum complexity could boost the computational power, we might be able to directly utilize the quantum complexity to design quantum computation even with the presence of noise and errors. In this work we introduce a new reservoir computational model for pattern recognition showing a quantum advantage utilizing scale-free networks. This new scheme allows us to utilize the complexity inherent in the scale-free networks, meaning we do not require programing nor optimization of the quantum layer even for other computational tasks. The simplicity in our approach illustrates the computational power in quantum complexity as well as provide new applications for such processors., Comment: 8 pages, 5 figures

A quantum phase of matter can be understood from the symmetry of the system's Hamiltonian. The system symmetry along the time axis has been proposed to show a new phase of matter referred as discrete-time crystals (DTCs). A DTC is a quantum phase of matter in non-equilibrium systems, and it is also intimately related to the symmetry of the initial state. DTCs that are stable in isolated systems are not necessarily resilient to the influence from the external reservoir. In this paper, we discuss the dynamics of the DTCs under the influence of an environment. Specifically, we consider a non-trivial situation in which the initial state is prepared to partly preserve the symmetry of the Liouvillian. Our analysis shows that the entire system evolves towards a DTC phase and is stabilised by the effect of dephasing. Our results provide a new understanding of quantum phases emerging from the competition between the coherent and incoherent dynamics in dissipative non-equilibrium quantum systems., Comment: 9 pages, 6 Figures. Comments are welcom

Crystals form regular and robust structures that under extreme conditions can melt and recrystallize into different arrangements in a process that is called crystal metamorphism. While crystals exist due to the breaking of a continuous translation symmetry in space, it has recently been proposed that discrete crystalline order can also emerge in time and give raise to a novel phase of matter named discrete time crystal (DTC). In this paper, we join these two ideas and propose a model for quantum metamorphism between two DTCs of different periodicity, a 2T and 4T-DTC. In our model the conditions for metamorphism come from the modulation of perturbative terms in the 4T-DTC Hamiltonian that gradually melt its structure and transform it into a 2T-DTC. This process is studied in detail from the viewpoint of manybody physics of periodically driven systems. We also propose a protocol to experimentally observe quantum metamorphism using current quantum technology., Comment: 10 pages, 7 figures

As Noisy Intermediate-Scale Quantum (NISQ) devices grow in number of qubits, determining good or even adequate parameter configurations for a given application, or for device calibration, becomes a cumbersome task. An evolutionary algorithm is presented here which allows for the automatic tuning of the parameters of any arrangement of coupled qubits, to perform a given task with high fidelity. The algorithm's use is exemplified with the generation of schemes for the distribution of quantum states and the design of multi-qubit gates. The algorithm is demonstrated to converge very rapidly, yielding unforeseeable designs of quantum devices that perform their required tasks with excellent fidelities. Given these promising results, practical scalability and application versatility, the approach has the potential to become a powerful technique to aid the design and calibration of NISQ devices., Comment: 11 pages, 15 figures (including the Supporting Information, which has been included to the end of the paper)

Entanglement is a crucial resource for quantum information processing, and so protocols to generate high fidelity entangled states on various hardware platforms are in demand. While spin chains have been extensively studied to generate entanglement, graph structures also have such potential; however, only a few classes of graphs have been explored for this specific task. In this paper, we apply a particular coupling scheme involving two different coupling strengths to a graph of two interconnected $3\times3$ square graphs such that it effectively contains three defects. We show how this structure allows generation of a Bell state whose fidelity depends on the chosen coupling ratio. We apply partitioned graph theory in order to reduce the dimension of the graph and show that, using a reduced graph or a reduced chain, we can still simulate the same protocol with identical dynamics. Finally, we investigate how fabrication errors affect the entanglement generation protocol and how the different equivalent structures are affected, finding that for some specific coupling ratios they are extremely robust., Comment: 12 pages, 15 figures

Mapping a quantum algorithm to any practical large-scale quantum computer will require a sequence of compilations and optimizations. At the level of fault-tolerant encoding, one likely requirement of this process is the translation into a topological circuit, for which braided circuits represent one candidate model. Given the large overhead associated with encoded circuits, it is paramount to reduce their size in terms of computation time and qubit number through circuit compression. While these optimizations have typically been performed in the language of three-dimensional diagrams, such a representation does not allow an efficient, general, and scalable approach to reduction or verification. We propose the use of the ZX-calculus as an intermediate language for braided circuit compression, demonstrating advantage by comparing results using this approach with those previously obtained for the compression of A- and Y-state distillation circuits. We then provide a benchmark of our method against a small set of Clifford+T circuits, yielding compression percentages of 77%. Our results suggest that the overheads of braided, defect-based circuits are comparable to those of their lattice-surgery counterparts, restoring the potential of this model for surface-code quantum computation., Comment: 13 pages, 9 figures

We investigate the ability of dimerized spin chains with defects to generate EPR pairs to very high fidelity through their natural dynamics. We propose two protocols based on different initializations of the system, which yield the same maximally entangled Bell state after a characteristic time. This entangling time can be varied through engineering the weak/strong couplings' ratio of the chain, with larger values giving rise to an exponentially faster quantum entangling operation. We demonstrate that there is a set of characteristic values of the coupling, for which the entanglement generated remains extremely high. We investigate the robustness of both protocols to diagonal and off-diagonal disorder. Our results demonstrate extremely strong robustness to both perturbation types, up to strength of 50% of the weak coupling. Robustness to disorder can be further enhanced by increasing the coupling ratio. The combination of these properties makes the use of our proposed device suitable for the rapid and robust generation of Bell states in quantum information processing applications., Comment: 15 PAGES, 8 FIGURES

Reliable quantum communication/processing links between modules are a necessary building block for various quantum processing architectures. Here we consider a spin chain system with alternating strength couplings and containing three defects, that impose three domain walls between topologically distinct regions of the chain. We show that -- in addition to its useful, high fidelity, quantum state transfer properties -- an entangling protocol can be implemented in this system, with optional localisation and storage of the entangled states. We demonstrate both numerically and analytically that, given a suitable initial product-state injection, the natural dynamics of the system produces a maximally entangled state at a given time. We present detailed investigations of the effects of fabrication errors, analyzing random static disorder both in the diagonal and off-diagonal terms of the system Hamiltonian. Our results show that the entangled state formation is very robust against perturbations of up to $\sim10\%$ the weaker chain coupling, and also robust against timing injection errors. We propose a further protocol which manipulates the chain in order to localise and store each of the entangled qubits. The engineering of a system with such characteristics would thus provide a useful device for quantum information processing tasks involving the creation and storage of entangled resources., Comment: 7 pages, 6 figures

We consider spin chain families inspired by the Su, Schrieffer and Hegger (SSH) model. We demonstrate explicitly the topologically induced spatial localisation of quantum states in our systems. We present detailed investigations of the effects of random noise, showing that these topologically protected states are very robust against this type of perturbation. Systems with such topological robustness are clearly good candidates for quantum information tasks and we discuss some potential applications. Thus, we present interesting spin chain models which show promising applications for quantum devices., Comment: 11 pages, 8 figures