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arXiv:2203.08993 · Physica Scripta

Measurement-based quantum computation using two-component BECs

Genji Fujii

Published Apr 20, 2023• 2 citations
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Abstract

Abstract Measurement-based quantum computation (MBQC) using two-component Bose–Einstein condensates (BECs) is proposed in this paper. An arbitrary state for one logical qubit is obtained by three-body measurement. Furthermore, a method is proposed for implementing controlled-Z gates for logical qubits in a graph state using BEC qubits and controlled-Z gates for BEC-type encoding. Results showed that the state after a measurement depends on the number of particles. These results pave the way for a novel quantum computing process based on particle control.

DOI
10.1088/1402-4896/accede

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Abstract Measurement-based quantum computation (MBQC) using two-component Bose–Einstein condensates (BECs) is proposed in this paper. An arbitrary state for one logical qubit is obtained by three-body measurement. Furthermore, a method is proposed for implementing controlled-Z gates for logical qubits in a graph state using BEC qubits and controlled-Z gates for BEC-type encoding. Results showed that the state after a measurement depends on the number of particles. These results pave the way for a novel quantum computing process based on particle control.
Abstract Measurement-based quantum computation (MBQC) is a protocol for quantum computation that represents a model distinct from the circuit-based approach. MBQC has been proposed not only for qubits but also for qudits, continuous-variable (CV) qubits, and Bose–Einstein condensates (BECs) qubits. In qubit-based MBQC, arbitrary rotations on the Bloch sphere can be performed by measuring a graph state. This naturally raises the question of whether arbitrary rotations on the Bloch sphere can similarly be achieved through measurements in other types of quantum bits. We have demonstrated that this can indeed be realized for BECs qubits by considering composite graph states involving CV qubits and BECs qubits.
Quantum computation using qubits made of two component Bose-Einstein condensates (BECs) is analyzed. We construct a general framework for quantum algorithms to be executed using the collective states of the BECs. The use of BECs allows for an increase of energy scales via bosonic enhancement, resulting in two qubit gate operations that can be performed at a time reduced by a factor of N, where N is the number of bosons per qubit. We illustrate the scheme by an application to Deutsch-s and Grover-s algorithms, and discuss possible experimental implementations. Decoherence effects are analyzed under both general conditions and for the experimental implementation proposed.
Abstract The measurement-based quantum computing paradigm relies on entangling the qubits of a register into a graph state and on measuring subsets of such register in order to condition the unmeasured qubits. The computation therefore, instead of being carried on only by one-qubit and two-qubits logic gates, is largely based on entanglement and measurement processes. Compared to the gate model architecture, in MBQC the overhead in terms of computation resources to synthesize logical qubits is higher. While gate model relies on a register of logical qubits whose number is set at the beginning of the computation and remains constant during the computation, in the MBQC the input qubits outnumber the output ones, due to the destructive nature of measurement processes. Still, we analytically prove and experimentally confirm that MBQC can be efficiently emulated on a classical software, reaching equal loads with respect to the gate-based approach in terms of average runtime and storage of memory. The numerical results confirm that despite the potential computational overhead due to the high entanglement of the initial graph state, the MBQC paradigm carries similar computational complexity, both in terms of time and memory, with respect to the gate-based approach.
We propose a new scheme of measurement-based quantum computation (MBQC) using an error-correcting code against photon-loss in circuit quantum electrodynamics. We describe a specific protocol of logical single-qubit gates given by sequential cavity measurements for logical MBQC and a generalised Schrödinger cat state is used for a continuous-variable (CV) logical qubit captured in a microwave cavity. To apply an error-correcting scheme on the logical qubit, we utilise a d-dimensional quantum system called a qudit. It is assumed that a three CV-qudit entangled state is initially prepared in three jointed cavities and the microwave qudit states are individually controlled, operated, and measured through a readout resonator coupled with an ancillary superconducting qubit. We then examine a practical approach of how to create the CV-qudit cluster state via a cross-Kerr interaction induced by intermediary superconducting qubits between neighbouring cavities under the Jaynes-Cummings Hamiltonian. This approach could be scalable for building 2D logical cluster states and therefore will pave a new pathway of logical MBQC in superconducting circuits toward fault-tolerant quantum computing.
Integrated photonics provides a scalable platform for quantum information processing. In this context, measurement-based quantum computing (MBQC) offers an attractive approach in which quantum computation is realised by adaptive measurements on highly entangled graph states, circumventing the need for deterministic photon-photon interactions. Here, we demonstrate MBQC on an integrated silicon photonic chip capable of generating photonic graph states with up to four qubits. We achieve fidelities of FStar=(83.5±1.8) %F_{Star} = (83.5 \pm 1.8)\,\%FStar​=(83.5±1.8)% and FLin=(75.6±1.1) %F_{Lin} = (75.6 \pm 1.1)\,\%FLin​=(75.6±1.1)% for four-photon star and linear graph states, respectively. We use these resource states to implement MBQC-based single- and two-qubit gates and to demonstrate Grover's search algorithm and the Deutsch-Jozsa algorithm. These results establish the feasibility of reconfigurable four-photon MBQC on an integrated photonic platform and provide a foundation for future larger-scale implementations.
We analyze quantum computation using quantum information stored on two component Bose-Einstein condensates (BECs). We construct a general framework for quantum algorithms to be executed using the collective states of the BECs. The use of BECs allows for an increase of energy scales via bosonic enhancement, resulting in two-qubit gate operations that can be performed at a time reduced by a factor of NNN, where NNN is the number of bosons in the BEC. We illustrate the scheme by an application to Grover's algorithm, and discuss possible experimental implementations and decoherence effects.