Hardware-Efficient Quantum Random Access Memory with Hybrid Quantum Acoustic Systems

Connor T. Hann, Chang-Ling Zou, Yaxing Zhang, Yiwen Chu, Robert J. Schoelkopf, S. M. Girvin, and Liang Jiang

Phys. Rev. Lett. 123, 250501 – Published 17 December 2019

Abstract

Hybrid quantum systems in which acoustic resonators couple to superconducting qubits are promising quantum information platforms. High quality factors and small mode volumes make acoustic modes ideal quantum memories, while the qubit-phonon coupling enables the initialization and manipulation of quantum states. We present a scheme for quantum computing with multimode quantum acoustic systems, and based on this scheme, propose a hardware-efficient implementation of a quantum random access memory (QRAM). Quantum information is stored in high- $Q$ phonon modes, and couplings between modes are engineered by applying off-resonant drives to a transmon qubit. In comparison to existing proposals that involve directly exciting the qubit, this scheme can offer a substantial improvement in gate fidelity for long-lived acoustic modes. We show how these engineered phonon-phonon couplings can be used to access data in superposition according to the state of designated address modes—implementing a QRAM on a single chip.

Received 9 July 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.250501

Physics Subject Headings (PhySH)

Acoustics Quantum computation Quantum gates Quantum information architectures & platforms Quantum information with hybrid systems

Superconducting qubits

Quantum Information, Science & Technology

Authors & Affiliations

Connor T. Hann ¹, Chang-Ling Zou², Yaxing Zhang¹, Yiwen Chu³, Robert J. Schoelkopf¹, S. M. Girvin ¹, and Liang Jiang¹

¹Departments of Applied Physics and Physics, Yale University, New Haven, Connecticut 06511, USA
²Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
³Department of Physics, ETH Zürich, 8093 Zürich, Switzerland

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Vol. 123, Iss. 25 — 20 December 2019

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Images

Figure 1
Multimode cQAD. A transmon qubit (red) is piezoelectrically coupled to (a) a bulk acoustic wave resonator, (b) a surface acoustic wave resonator, or (c) an array of phononic crystal resonators.
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Figure 2
Phonon-phonon gates. swap: Applying two drives with $ω_{2} - ω_{1} = ω_{B} - ω_{A}$ creates an effective coupling between modes $A$ and $B$ . CZ: Applying a single drive with $ω_{1} = ω_{A} + ω_{B} - ω_{C}$ creates an effective three-mode coupling between modes $A$ , $B$ , and $C$ . Frequency shifts of strongly hybridized modes (dark blue) can enable selective coupling when the modes are otherwise uniformly spaced (dashed lines denote uniform spacing) [56].
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Figure 3
Comparison of direct and virtual operations. (a),(b) $\log_{10} (1 - F)$ for the direct and virtual swap operations, respectively. The couplings are optimized subject to constraints ( $g_{d} \in [0, g]$ , constraints on $g_{v}$ are discussed in Ref. [56]). (c) Comparison of direct and virtual swap operations. The log ratio of the infidelities is plotted, with the virtual operations attaining higher fidelities in the blue region. (d),(e) ${Log}_{10}$ infidelity for the direct and virtual CZ operations. (f) Comparison of CZ operations. For reference, the symbols circle, square, triangle, diamond, star, respectively, denote the decoherence rates $κ$ (phonon) and $γ$ (transmon) measured in Refs. [17, 19, 21, 22, 25]. Note, however, that the plots are generated using typical parameter values, not specific values from any one experiment. Parameters: $g / 2 π = 10$ , $δ / 2 π = 100$ , $ν / 2 π = 10$ , and $Δ ν / 2 π = 1 MHz$ .
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Figure 4
cQAD implementation of QRAM. (a) Quantum router. Each circle represents a phonon mode. The router directs the qubit $| ψ ⟩$ in the incoming mode (top) to either the right or left mode conditioned on the state of the routing qubit $| ϕ ⟩$ . (b) Controlled swap. Note that this circuit implements the gate only within the relevant subspace of $< 2$ total phonons in the modes to be swapped. (c) QRAM implementation. Address qubits (green) are routed into position one by one, carving out a path to the database. The bus qubit (red) follows this path to retrieve the data $D_{j}$ . The bus and address qubits are then routed back out of the tree to complete the query. The database (blue squares) can be either classical or quantum. In the former case, the bus is initially prepared in $| + ⟩$ , and classical bits are copied to the bus by applying phase shifts to each mode at the bottom of the tree. In the latter case, the data qubit is extracted through a sequence of controlled swap operations. See Ref. [56] for details.
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