Related papers: Short and useful quantum proofs for sublogarithmic…
Self-testing is a fundamental feature of quantum mechanics that allows a classical verifier to force untrusted quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two…
Recently, there are more and more organizations offering quantum-cloud services, where any client can access a quantum computer remotely through the internet. In the near future, these cloud servers may claim to offer quantum computing…
We study classical simulation of quantum computation, taking the Gottesman-Knill theorem as a starting point. We show how each Clifford circuit can be reduced to an equivalent, manifestly simulatable circuit (normal form). This provides a…
Hamiltonian quantum gates controlled by classical electromagnetic fields form the basis of any realistic model of quantum computers. In this letter, we derive a lower bound on the field energy required to implement such gates and relate…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
We study possible formulations of algebraic propositional proof systems operating with noncommutative formulas. We observe that a simple formulation gives rise to systems at least as strong as Frege---yielding a semantic way to define a…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
In the near future, there will likely be special-purpose quantum computers with 40-50 high-quality qubits. This paper lays general theoretical foundations for how to use such devices to demonstrate "quantum supremacy": that is, a clear…
In seeking out an algorithm to test out the capability of the IBM Quantum Experience quantum computer, we were given a review paper covering various algorithms for solving the subset-sum problem, including both classical and quantum…
Quantum physics is surprising in many ways. One surprise is the threat to locality implied by Bell's Theorem. Another surprise is the capacity of quantum computation, which poses a threat to the complexity-theoretic Church-Turing thesis. In…
Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order finding, which quantum mechanics lets us perform…
Quantum metric learning enhances machine learning by mapping classical data to a quantum Hilbert space with maximal separation between classes. However, on current NISQ hardware, this mapping process itself is prone to errors and could be…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
The rapid advancement of quantum hardware necessitates the development of reliable methods to certify its correct functioning. However, existing certification tests fall short, as they either suffer from systematic errors or do not…
Over a decade after its proposal, the idea of using quantum computers to sample hard distributions has remained a key path to demonstrating quantum advantage. Yet a severe drawback remains: verification seems to require classical…
In this perspective, we discuss conditions under which it would be possible for a modest fault-tolerant quantum computer to realize a runtime advantage by executing a quantum algorithm with only a small polynomial speedup over the best…
We survey recent progress in the proof complexity of strong proof systems and its connection to algebraic circuit complexity, showing how the synergy between the two gives rise to new approaches to fundamental open questions, solutions to…
Over the past few years several quantum machine learning algorithms were proposed that promise quantum speed-ups over their classical counterparts. Most of these learning algorithms either assume quantum access to data -- making it unclear…
In a model of fault-tolerant quantum computation with quick and noiseless polyloglog-time auxiliary classical computation, we construct a fault tolerance protocol with constant-space and $\widetilde{O}(\log N)$-time overhead, where…
The stabilization of a quantum computer by repeated error correction can be reduced almost entirely to repeated preparation of blocks of qubits in quantum codeword states. These are multi-particle entangled states with a high degree of…