Efficient Quantum Circuit Decompositions via Intermediate Qudits

Emerging Technologies for Quantum Computing

“…With a technique called "compression" we can generate the required ancilla inplace to obtain logarithmic depth, the best known depth for decompositions with ancilla. 3 The simplest example is to consider the storage of two qubits into a single ququart (four level system). The two qubits and the single ququart can each be written as a superposition of four basis states.…”

“…Using this type of compression circuit can produce clean ancilla on demand by storing unused data temporarily in higher states. Figure from Baker et al 3 transmon qubits, which suffer from fabrication inconsistency and crosstalk during parallel operations. To scale to the millions of qubits needed for error correction, a memory-based architecture can be used to decouple qubit-count from transmon count.…”

“…Here we explore a proof-of-concept demonstration of its viability by virtualizing surface code tiles (one example of quantum error correction) in a 2.5-D memory-based architecture. 3 Logical qubits can be stored at unique virtual addresses in memory cavities when not in use and are loaded to a physical address in the transmons for computation or to correct errors, similar to DRAM refresh. Figure 3 depicts the proposed architecture with surface tiles mapped to unique virtual addresses.…”

“…First, we discuss the temporary use of qudits which can be used to accelerate key circuit components, an example of evaluating a fundamental architectural question of computing radix. 3,4 Second, we explore the use of local "memory-equipped" superconducting qubits to reduce hardware requirements to implement error correction, an example of application-driven hardware design. 5 Finally, we address the use of neutral atoms as a competitive alternative to industry focuses, an example of using software to mitigate fundamental hardware limitations to both guide development and accelerate scalability.…”

Decomposing the generalized Toffoli gate with qutrits

“…Despite its simplicity and efficiency, there is a number of limitations associated with finding optimal qudit-to-qubit mappings [41]. The second approach is to employ higher qudit levels can be used for substituting ancilla qubits, which is of specific interest in the problem of decomposing multi-qubit gates [40], such as the Toffoli gate [19,26,27,29,[42][43][44][45][46]. We note that in the pioneering experimental work on the realization of the Toffoli gate, the third energy level of the superconducting transmon qubit has been used [29]; this has been further exploited in Ref.…”