Abstract
Quantum random-access look-up of a string of classical bits is a necessary ingredient in several important quantum algorithms. In some cases, the cost of such quantum random-access memory (qRAM) is the limiting factor in the implementation of the algorithm. In this paper we study the cost of fault-tolerantly implementing a qRAM. We construct and analyze generic families of circuits that function as a qRAM, discuss opportunities for qubit-time tradeoffs, and estimate their resource costs when embedded in a surface code.
Highlights
Random-access memory (RAM) is an essential component of classical computing architectures
A memory that stores classical information but allows queries in superposition is required for quantum algorithms such as Grover’s search on a classical database [1], collision finding [2], element distinctness [3], dihedral hidden subgroup problem [4], phase estimation for electronic structure simulation [5], and various practical applications mentioned in [6]
There are many natural ways to interpolate between the two approaches, for example, using the same fan-out like operation to make 2k copies of the first k index bits, and use 2k parallel logical circuits to explore the remaining n − k index bits. We outline these various questions and approaches, and consider their costs and tradeoffs. Such an analysis is important for optimizing the physical resources needed to implement in practice quantum algorithms that use a quantum random-access memory (qRAM) repeatedly, using the best-known methods
Summary
Random-access memory (RAM) is an essential component of classical computing architectures. A memory that stores classical information but allows queries in superposition is required for quantum algorithms such as Grover’s search on a classical database [1], collision finding [2], element distinctness [3], dihedral hidden subgroup problem [4], phase estimation for electronic structure simulation [5], and various practical applications mentioned in [6]. We outline these various questions and approaches, and consider their costs and tradeoffs Such an analysis is important for optimizing the physical resources needed to implement in practice quantum algorithms that use a qRAM repeatedly, using the best-known methods. We note that we have made available a code repository including our data as well as circuit details and resource estimation procedures [16]
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