Qudits and high-dimensional quantum computing (original) (raw)
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Efficient realization of quantum algorithms with qudits
arXiv (Cornell University), 2021
The development of a universal fault-tolerant quantum computer that can solve efficiently various difficult computational problems is an outstanding challenge for science and technology. In this work, we propose a technique for an efficient implementation of quantum algorithms with multilevel quantum systems (qudits). Our method uses a transpilation of a circuit in the standard qubit form, which depends on the parameters of a qudit-based processor, such as their number and the number of accessible levels. This approach provides a qubit-to-qudit mapping and comparison to a standard realization of quantum algorithms highlighting potential advantages of qudits. We provide an explicit scheme of transpiling qubit circuits into sequences of single-qudit and two-qudit gates taken from a particular universal set. We then illustrate our method by considering an example of an efficient implementation of a 6-qubit quantum algorithm with qudits. We expect that our findings are of relevance for ongoing experiments with noisy intermediate-scale quantum devices that operate with information carrier allowing qudit encodings, such as trapped ions and neutral atoms as well as optical and solid-state systems.
QuDiet: A Classical Simulation Platform for Qubit-Qudit Hybrid Quantum Systems
Cornell University - arXiv, 2022
In the recent years, numerous research advancements have extended the limit of classical simulation of quantum algorithms. Although, most of the state-of-the-art classical simulators are only limited to binary quantum systems, which restrict the classical simulation of higher-dimensional quantum computing systems. rough recent developments in higher-dimensional quantum computing systems, it is realized that implementing qudits improves the overall performance of a quantum algorithm by increasing memory space and reducing the asymptotic complexity of a quantum circuit. Hence, in this article, we introduce Diet, a state-of-the-art user-friendly python-based higher-dimensional quantum computing simulator. Diet o ers multi-valued logic operations by utilizing generalized quantum gates with an abstraction so that any naive user can simulate qudit systems with ease as compared to the existing ones. We simulate various benchmark quantum circuits in Diet and show the considerable speedup in simulation time as compared to the other simulators without loss in precision. Finally, Diet provides a full qubit-qudit hybrid quantum simulator package with quantum circuit templates of well-known quantum algorithms for fast prototyping and simulation. e complete code and packages of Diet is available at h ps://github.com/LegacYFTw/ Diet so that other platforms can incorporate it as a classical simulation option for qubit-qudit hybrid systems to their platforms.
Controlled gates for multi-level quantum computation
Quantum Information Processing, 2011
Multi-level (ML) quantum logic can potentially reduce the number of inputs/outputs or quantum cells in a quantum circuit which is a limitation in current quantum technology. In this paper we propose theorems about ML-quantum and reversible logic circuits. New efficient implementations for some basic controlled MLquantum logic gates, such as three-qudit controlled NOT, Cycle, and Self Shift gates are proposed. We also propose lemmas about r -level quantum arrays and the number of required gates for an arbitrary n-qudit ML gate. An equivalent definition of quantum cost (QC) of binary quantum gates for ML-quantum gates is introduced and QC of controlled quantum gates is calculated.
Parallelism for quantum computation with qudits
Physical Review A, 2006
Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high fidelity two-qudit gates. We first describe how to implement parallel single qudit operations. It is by now well known that any single-qudit unitary can be decomposed into a sequence of Givens rotations on two-dimensional subspaces of the qudit state space. Using a coupling graph to represent physically allowed couplings between pairs of qudit states, we then show that the logical depth of the parallel gate sequence is equal to the height of an associated tree. The implementation of a given unitary can then optimize the tradeoff between gate time and resources used. These ideas are illustrated for qudits encoded in the ground hyperfine states of the atomic alkalies 87 Rb and 133 Cs. Second, we provide a protocol for implementing parallelized nonlocal two-qudit gates using the assistance of entangled qubit pairs. Because the entangled qubits can be prepared non-deterministically, this offers the possibility of high fidelity two-qudit gates.
Single qudit realization of the Deutsch algorithm using superconducting many-level quantum circuits
Physics Letters A, 2015
Design of a large-scale quantum computer has paramount importance for science and technologies. We investigate a scheme for realization of quantum algorithms using noncomposite quantum systems, i.e., systems without subsystems. In this framework, n artificially allocated "subsystems" play a role of qubits in n-qubits quantum algorithms. With focus on two-qubit quantum algorithms, we demonstrate a realization of the universal set of gates using a d = 5 single qudit state. Manipulation with an ancillary level in the systems allows effective implementation of operators from U(4) group via operators from SU(5) group. Using a possible experimental realization of such systems through anharmonic superconducting many-level quantum circuits, we present a blueprint for a single qudit realization of the Deutsch algorithm, which generalizes previously studied realization based on the virtual spin representation [A.R. Kessel et al., Phys. Rev. A 66, 062322 (2002)].
arXiv (Cornell University), 2022
Qubits, which are quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g. (artificial) atoms or ions, admit encoding of more complex multilevel states-qudits. Recently, significant attention is paid to the idea of using qudit encoding as a way for further scaling quantum processors. In this work, we present an efficient decomposition of the generalized Toffoli gate on the five-level quantum systems, so-called ququints, that uses ququints' space as the space of two qubits with a joint ancillary state. The basic two-qubit operation that we use is a version of controlled-phase gate. The proposed N-qubit Toffoli gate decomposition has O(N) asymptotic depth and does not use ancillary qubits. We then apply our results for Grover's algorithm, where we indicate on the sizable advantage of the using qudit-based approach with the proposed decomposition in comparison to the standard qubit case. We expect that our results are applicable for quantum processors based on various physical platforms, such as trapped ions, neutral atoms, protonic systems, superconducting circuits, and others.
Qutrit quantum computer with trapped ions
Physical Review A, 2003
We study a physical implementation of a qutrit quantum computer. Qutrits are embodied in electronic levels of trapped ions. We concentrate our attention on a universal two-qutrit gate. Using this gate and a general gate of an individual qutrit, any gate can be decomposed into a sequence of these gates.
Using existing experimental and computational resources, a multi-institutional team has developed an effective method for measuring high-dimensional qudits encoded in quantum frequency combs, which are a type of photon source, on a single optical chip.
Ancilla-driven quantum computation for qudits and continuous variables
Physical Review A, 2017
Although qubits are the leading candidate for the basic elements in a quantum computer, there are also a range of reasons to consider using higher dimensional qudits or quantum continuous variables (QCVs). In this paper we use a general 'quantum variable' formalism to propose a method of quantum computation in which ancillas are used to mediate gates on a well-isolated 'quantum memory' register and which may be applied to the setting of qubits, qudits (for d > 2) or QCVs. More specifically, we present a model in which universal quantum computation may be implemented on a register using only: repeated applications of a single fixed two-body ancilla-register interaction gate, ancillas prepared in a single state, and local measurements of these ancillas. In order to maintain determinism in the computation, adaptive measurements via a classical-feedforward of measurement outcomes are used, with the method similar to that in measurement-based quantum computation (MBQC). We show that our model has the same hybrid quantum-classical processing advantages as MBQC, including the power to implement any Clifford circuit in essentially one layer of quantum computation. In some physical settings, high-quality measurements of the ancillas may be highly challenging or not possible, and hence we also present a globally unitary model which replaces the need for measurements of the ancillas with the requirement for ancillas to be prepared in states from a fixed orthonormal basis. Finally, we discuss settings in which these models may be of practical interest.