Quantum random access memory

A random access memory (RAM) uses n bits to randomly address N=2^n distinct memory cells. A quantum random access memory (qRAM) uses n qubits to address any quantum superposition of N memory cells. We present an architecture that exponentially reduces the requirements for a memory call: O(log N) switches need be thrown instead of the N used in conventional (classical or quantum) RAM designs. This yields a more robust qRAM algorithm, as it in general requires entanglement among exponentially less gates, and leads to an exponential decrease in the power needed for addressing. A quantum optical implementation is presented.Comment: 4 pages, 3 figures. Accepted for publication on Phys. Rev. Let

A Robust Quantum Random Access Memory

A "bucket brigade" architecture for a quantum random memory of $N=2^n$ memory cells needs $n(n+5)/2$ times of quantum manipulation on control circuit nodes per memory call. Here we propose a scheme, in which only average $n/2$ times manipulation is required to accomplish a memory call. This scheme may significantly decrease the time spent on a memory call and the average overall error rate per memory call. A physical implementation scheme for storing an arbitrary state in a selected memory cell followed by reading it out is discussed.Comment: 5 pages, 3 figure

Quantum Certificate Complexity

Given a Boolean function f, we study two natural generalizations of the certificate complexity C(f): the randomized certificate complexity RC(f) and the quantum certificate complexity QC(f). Using Ambainis' adversary method, we exactly characterize QC(f) as the square root of RC(f). We then use this result to prove the new relation R0(f) = O(Q2(f)^2 Q0(f) log n) for total f, where R0, Q2, and Q0 are zero-error randomized, bounded-error quantum, and zero-error quantum query complexities respectively. Finally we give asymptotic gaps between the measures, including a total f for which C(f) is superquadratic in QC(f), and a symmetric partial f for which QC(f) = O(1) yet Q2(f) = Omega(n/log n).Comment: 9 page

Defeating classical bit commitments with a quantum computer

It has been recently shown by Mayers that no bit commitment scheme is secure if the participants have unlimited computational power and technology. However it was noticed that a secure protocol could be obtained by forcing the cheater to perform a measurement. Similar situations had been encountered previously in the design of Quantum Oblivious Transfer. The question is whether a classical bit commitment could be used for this specific purpose. We demonstrate that, surprisingly, classical unconditionally concealing bit commitments do not help.Comment: 13 pages. Supersedes quant-ph/971202

Optimizing the Number of Gates in Quantum Search

$$In its usual form, Grover's quantum search algorithm uses $O(\sqrt{N})$ queries and $O(\sqrt{N} \log N)$ other elementary gates to find a solution in an $N$-bit database. Grover in 2002 showed how to reduce the number of other gates to $O(\sqrt{N}\log\log N)$ for the special case where the database has a unique solution, without significantly increasing the number of queries. We show how to reduce this further to $O(\sqrt{N}\log^{(r)} N)$ gates for any constant $r$, and sufficiently large $N$. This means that, on average, the gates between two queries barely touch more than a constant number of the $\log N$ qubits on which the algorithm acts. For a very large $N$ that is a power of 2, we can choose $r$ such that the algorithm uses essentially the minimal number $\frac{\pi}{4}\sqrt{N}$ of queries, and only $O(\sqrt{N}\log(\log^{\star} N))$ other gates.Comment: 11 pages LaTeX. Version 2: small improvements in the proof

A brief review on the impossibility of quantum bit commitment

The desire to obtain an unconditionally secure bit commitment protocol in quantum cryptography was expressed for the first time thirteen years ago. Bit commitment is sufficient in quantum cryptography to realize a variety of applications with unconditional security. In 1993, a quantum bit commitment protocol was proposed together with a security proof. However, a basic flaw in the protocol was discovered by Mayers in 1995 and subsequently by Lo and Chau. Later the result was generalized by Mayers who showed that unconditionally secure bit commitment is impossible. A brief review on quantum bit commitment which focuses on the general impossibility theorem and on recent attempts to bypass this result is provided.Comment: 11 page