Exploiting Dynamic Quantum Circuits in a Quantum Algorithm with Superconducting Qubits

A. D. Córcoles, Maika Takita, Ken Inoue, Scott Lekuch, Zlatko K. Minev, Jerry M. Chow, and Jay M. Gambetta

Phys. Rev. Lett. 127, 100501 – Published 31 August 2021

Abstract

To date, quantum computation on real, physical devices has largely been limited to simple, time-ordered sequences of unitary operations followed by a final projective measurement. As hardware platforms for quantum computing continue to mature in size and capability, it is imperative to enable quantum circuits beyond their conventional construction. Here we break into the realm of dynamic quantum circuits on a superconducting-based quantum system. Dynamic quantum circuits not only involve the evolution of the quantum state throughout the computation but also periodic measurements of qubits midcircuit and concurrent processing of the resulting classical information on timescales shorter than the execution times of the circuits. Using noisy quantum hardware, we explore one of the most fundamental quantum algorithms, quantum phase estimation, in its adaptive version, which exploits dynamic circuits, and compare the results to a nonadaptive implementation of the same algorithm. We demonstrate that the version of real-time quantum computing with dynamic circuits can yield results comparable to an approach involving classical asynchronous postprocessing, thus opening the door to a new realm of available algorithms on real quantum systems.

Received 2 March 2021
Accepted 6 August 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.100501

Physics Subject Headings (PhySH)

Quantum computation Quantum information processing Quantum information with solid state qubits

Superconducting qubits

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

A. D. Córcoles, Maika Takita, Ken Inoue , Scott Lekuch, Zlatko K. Minev, Jerry M. Chow, and Jay M. Gambetta

IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA

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Vol. 127, Iss. 10 — 3 September 2021

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Figure 1
Circuit diagrams for $m$ -bit implementations of QPE using the two approaches described in this Letter: Kitaev’s QPE (top) and IPE (bottom). The variable $s$ guides the cumulative average of each circuit sampling up to its final amount determined by the total number of resources (measurements). Note that for the IPE case (top right gray box) a resource includes the conditional reset of the qubit, which is run twice. The Kitaev circuits do not need previous knowledge of other bits at the expense of running and measuring one extra circuit per bit and needing additional near-time computing resources [48]. The iterative version uses a $Z$ rotation conditional on all the previous measured bits before measuring the auxiliary qubit in the $X$ basis.
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Figure 2
Qubit measurement and reset of the pointer qubit. (a) I/Q traces (upper plot) and discriminator kernel (lower plot). The readout signal is sampled for 360 ns (dashed in I/Q traces) and the kernel is applied for 320 ns (solid in I/Q traces). (b) Experimental sequences to assess qubit reset quality. The sequences are played in order from top to bottom at a repetition rate of 100 kHz. After each computational state is prepared, the first measurement is used to build the histograms in the bottom panel of (c). The shaded $X$ gates are applied conditionally to the preceding measurement outcome being 1. (c) Histograms from preparing each computational state 10 000 times at 1 kHz (top) and 100 kHz (bottom). From the histograms, we extract an assignment error of $3 \times 10^{- 3}$ (top) and $8.3 \times 10^{- 3}$ (bottom). The insets show the integrated samples in the I/Q plane.
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Figure 3
Latency breakdown in a measurement and reset cycle. The control electronics entire latency to determine the qubit state, send a conditional marker to a blanking switch, and determine the IPE branching path, is comparable to the latency due to resonator dynamics (population and emptying). This cycle is repeated twice during the algorithm, yielding a total qubit reset latency of $1.4 μ s$ .
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Figure 4
(a) (Top) Decomposition of a controlled- $U$ , where $U$ is a parametrized element of $S U (2)$ , in terms of single-qubit unitaries ( $U$ rotations and the phase gate $P$ -see Supplemental Material [47] for details on the $P$ -gate) and CNOTs. (Bottom) Phase estimation error up to 10-bit accuracy for both algorithms when the total number of resources are kept constant at 50, 70, and 200. The lower bound of the error is shown for each bit as a dash-dotted black line. (b) Algorithm error as a function of the number of available resources for IPE (blue) and Kitaev (red). The lowest error is chosen among the available number of bits for a given number of resources for both algorithms. The optimal number of bits for a discrete set of resources for both protocols is shown in the inset.
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