Scalable algorithm simplification using quantum AND logic

Abstract

Implementing quantum algorithms on realistic hardware requires translating high-level global operations into sequences of native elementary gates, a process known as quantum compiling. Physical limitations, such as constraints in connectivity and gate alphabets, often result in unacceptable implementation costs. To enable successful near-term applications, it is crucial to optimize compilation by exploiting the potential capabilities of existing hardware. Here, we implement a resource-efficient construction for a quantum version of AND logic that can reduce the cost, enabling the execution of key quantum circuits. On a high-scalability superconducting quantum processor, we demonstrate low-depth synthesis of high-fidelity generalized Toffoli gates with up to 8 qubits and Grover's search algorithm in a search space of up to 64 entries; both are the largest such implementations in scale to date. Our experimental demonstration illustrates a scalable implementation of simplifying quantum algorithms, paving the way for larger, more meaningful quantum applications on noisy devices.

Phase gadget compilation for diagonal qutrit gates

“…While some of our constructions will naturally generalise to arbitrary qudit dimension, some things are qutrit specific. It seems to be a coincidence that for qutrits, in contrast with other dimension qudits, you can derive a relation between modular multiplication and addition (17) from the same binomial as for qubits (16), which comes from having a natural way to express x 2 mod 3 thanks to Fermat's little theorem. As a result, qubit and qutrit phase multipliers admit constructions which are structurally similar, despite the fact that for qubits it applies a phase of α on only one possible input -where all n qubits are |1 -while for qutrits it applies a phase, which can be α or 2α, for 2 n of the 3 n possible input basis states.…”

“…Most work on qutrits and emulation has focussed on classical functions: those that come from a map of classical trits. For instance, using qutrits we can build logarithmic-depth Toffolis [27,41] and binary AND gates on superconducting qutrits [16]. This leaves open the question of whether there is any advantages to emulation by studying 'truly' quantum gates such as diagonal unitaries.…”

Nonunitary Gate Operations by Dissipation Engineering

“…From the combination of the paradigms of classical and quantum information processing stems the idea to perform classical logic operations in quantum systems [29][30][31]. The term logic gate commonly refers to an electronic circuit that implements a Boolean function.…”

“…To a large extent, the available realizations rely on measurements of (ancilla) qubits and conditional operations. The requirement for macroscopic measurement devices and feedforward can lead, however, to high resource overheads, as well as imperfections that are challenging with current devices [31,56].…”

Canceling microwave crosstalk with fixed-frequency qubits

“…We first demonstrate our method in a two-qubit subsystem out of a 16-qubit processor, the design of which is similar to the device presented in Ref. [23]. The two transmon qubits have frequencies: 6.2497 GHz (target qubit) and 6.2718 GHz (control qubit).…”