It has been shown recently that parity measurement is an efficient entangler for fermions and hence is a universal resource for fermionic quantum computing with linear elements. In this article, we investigate several properties of the parity P-gate. We construct a simple quantum network model for the P-gate and derive gate identities for it. Finally, we examine entanglement generation using parity measurements.
It has been shown recently that parity measurement is an efficient entangler for fermions and hence is a universal resource for fermionic quantum computing with linear elements. In this article, we investigate several properties of the parity P-gate. We construct a simple quantum network model for the P-gate and derive gate identities for it. Finally, we examine entanglement generation using parity measurements.
The parity gate emerged recently as a promising resource for performing universal quantum computation with fermions using only linear interactions. Here we analyze the parity gate (P gate) from a theoretical point of view in the context of quantum networks. We present several schemes for entanglement generation with P gates and show that native networks simplify considerably the resources required for producing multiqubit entanglement, such as n--Greenberg-Horne-Zellinger (GHZ) states. Other applications include a Bell-state analyzer and teleportation. We also show that cluster state fusion can be performed deterministically with parity measurements. We then extend this analysis to hybrid quantum networks containing spin and mode qubits. Starting from an easy-to-prepare resource (spin-mode entanglement of single electrons) we show how to produce a spin n-GHZ state with linear elements (beam splitters and local spin flips) and charge-parity detectors; this state can be used as a resource in a spin quantum computer or as a precursor for constructing cluster states. Finally, we construct an alternative spin-controlled-Z gate by using the mode degrees of freedom as ancill\ae{}.
Measurements play an important role in quantum computing (QC), either by providing the nonlinearity required for two-qubit gates (linear optics QC), or by implementing a quantum algorithm using single-qubit measurements on a highly entangled initial state (cluster state QC). Parity measurements can be used as building blocks for preparing arbitrary stabilizer states, and, together with one-qubit gates, are universal for quantum computing. Here we generalize parity gates by using a higher-dimensional (qudit) ancilla. This enables us to go beyond the stabilizer or graph state formalism and prepare other types of multiparticle entangled states. The generalized parity module introduced here can prepare in one shot, heralded by the outcome of the ancilla, a large class of entangled states, including Greenberger-Home-Zeilinger states GHZn, Wn, Dicke states Dn,k, and, more generally, certain sums of Dicke states, like Gn states used in secret sharing. For Wn states it provides an exponential gain compared to linear-optics-based methods.
We demonstrate the applicability of a universal gate set in the parity encoding, which is a dual to the standard gate model, by exploring several quantum gate algorithms such as the quantum Fourier transform and quantum addition. Embedding these algorithms in the parity encoding reduces the circuit depth compared to conventional gate-based implementations while keeping the multiqubit gate counts comparable. We further propose simple implementations of multiqubit gates in tailored encodings and an efficient strategy to prepare graph states.
In parity quantum computing, multiqubit logical gates are implemented by single-qubit rotations on a suitably encoded state involving auxiliary qubits. Consequently, there is a correspondence between qubit count and the size of the native gate set. One might then wonder, what is the smallest number of auxiliary qubits that still allows for universal parity computing? Here, we demonstrate that the answer is 1 if the number of logical qubits is even, and 2 otherwise. Furthermore, we present a sufficient condition for a given parity gate set to be universal. This leads to a variety of different universal parity gate sets corresponding to different numbers of auxiliary qubits and more generally contributes to the understanding of which entangling gates are required to augment the set of single-qubit unitaries to perform universal quantum computing. As a consequence, we obtain (i) minimal implementations of the parity framework on, e.g., a triangular lattice, (ii) hardware-specific implementations of the parity flow framework on, e.g., a heavy-hex lattice, and (iii) novel universal resources for measurement-based quantum computation.
We proposed a new candidate for the construction of an universal quantum network, which are built from the elementary quantum gates to the elements of quantum circuit, again to quantum subnetworks and finally to a whole quantum network. The main advantages of our scheme are its simplicity and standardization in construction, facility and directness in assembly and scale, reusage and update in engineering, realizability and procedurization in an effective construction. Moreover our universal quantum networks are potentially programmable. It is proved that all the elementary quantum gates can be written as our quantum subnetwork. This implies that our scheme is compatible with the known quantum gate-assembly schemes, and so the known results from a quantum computation to a set of the elementary quantum gates can be directly inherited and used in our scheme. As the applications of our construction scheme, we obtain the whole quantum networks for Shor's algorithm, Grover's algorithm and simulating Schr\\"odinger equation in general. This means that our universal quantum network can generally describe the known main results in quantum computation.
We present a possible candidate of construction of a scalable, uniform and universal quantum network, which is built from quantum gates to elements of quantum circuit, again to quantum subnetworks and finally to an entire quantum network. Our scheme can overcome some difficulties of the existing schemes and makes improvements to different extent in the scale of quantum network, ability of computation, implementation of engineering, efficiency of quantum network, universality, compatibility, design principle, programmability, fault tolerance, error control, industrialization and commercialization {\it et. al} aspects. As the applications of this construction scheme, we obtain the entire quantum networks for Shor's algorithm, Grover's algorithm and solving Schrödinger equation in general. This implies that the scalable, uniform and universal quantum networks are able to generally describe the known main results and can be further applied to more interesting examples in quantum computations.