SIGEST

Abstract

This issue's SIGEST paper, from the SIAM Journal on Computing (SICOMP), takes SIAM readers into the world of quantum computing, a world with its roots in physics that still probably is better known to many physicists and theoretical computer scientists than to a good portion of SIAM readers. Quantum computation is a form of computing based upon quantum mechanics, rather than the classical physics that conventional computers utilize. The distinction between conventional and quantum computers starts to become apparent at the most basic level of bits: whereas standard computers utilize binary bits that may have either the state 0 or 1, quantum computers are based upon “qubits” (quantum binary digits) that may have the state 0, 1, or a superposition of these two states with a complex number that specifies the probability for being in each state. Mathematically, the state of a quantum computer can change through a sequence of unitary transformations to the initial state. One reason for the great interest in quantum computation is that it has been shown that quantum computers can solve some important problems, such as the factorization of very large integers (which has important implications for cryptography), far more efficiently than we currently are able to solve these problems on conventional computers. The selected paper, “Adiabatic Quantum Computation Is Equivalent to Standard Quantum Computation” by Dorit Aharonov, Wim van Dam, Julia Kempe, Zeph Landau, Seth Lloyd, and Oded Regev, which was originally published in SICOMP in 2007, establishes an important theoretical result in the field of quantum computation. As the title indicates, it involves adiabatic quantum computation, a form of quantum computing that has attracted interest in recent years in part because it may offer promise in the effort to build effective quantum computers. Adiabatic quantum computation is distinctly different from standard quantum computation. In the standard model, computations are represented similarly to classical circuits, except that the circuits carry qubits instead of bits. In contrast, the adiabatic model is inspired by the adiabatic theorem in quantum mechanics which states that a system in its lowest energy or ground state will remain in that state if it is subjected to conditions that change sufficiently slowly. It already was known that standard quantum computers can efficiently simulate adiabatic quantum computers. The key contribution of this paper is to show the reverse: that adiabatic quantum computation can efficiently simulate standard quantum computation. In the words of the SICOMP editorial board in nominating this paper, “This is a surprising result that continues to be very influential.” It established that the two forms of quantum computation are theoretically equivalent, one implication of which is to bolster the potential practical importance of adiabatic quantum computation. The paper by Aharonov et al. is very nicely suited to SIGEST—it is important in its field, it is nicely and accessibly written, it offers a glimpse into an area of applied mathematics and computation that is of growing importance, and it touches on many areas of applied mathematics, including linear algebra, Markov chains, and optimization. We hope it will provide SIAM readers a glimpse of current theoretical research that may, some day, help lead to a brave new world of practical computation.