Related papers: Quantum interactive proofs with weak error bounds
It is known that there exist multi-prover interactive protocols ($\mathsf{MIP}$ protocols) for the complexity class $\mathsf{NEXP}$, succinct $\mathsf{MIP}$ protocols for $\mathsf{NP}$ and multi-prover interactive protocols with shared…
Low degree tests play an important role in classical complexity theory, serving as basic ingredients in foundational results such as $\mathsf{MIP} = \mathsf{NEXP}$ [BFL91] and the PCP theorem [AS98,ALM+98]. Over the last ten years, versions…
The complexity class Quantum Statistical Zero-Knowledge ($\mathsf{QSZK}$), introduced by Watrous (FOCS 2002) and later refined in Watrous (SICOMP, 2009), has the best known upper bound $\mathsf{QIP(2)} \cap \text{co-}\mathsf{QIP(2)}$, which…
We present characterisations of "exact" gap-definable classes, in terms of indeterministic models of computation which slightly modify the standard model of quantum computation. This follows on work of Aaronson [arXiv:quant-ph/0412187], who…
A longstanding goal in quantum information science is to demonstrate quantum computations that cannot be feasibly reproduced on a classical computer. Such demonstrations mark major milestones: they showcase fine control over quantum systems…
In this paper we explore the power of AM for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA)--introduced by Ambainis and Watrous in 2002--and the communications are classical. It is of…
A test of quantumness is a protocol where a classical user issues challenges to a quantum device to determine if it exhibits non-classical behavior, under certain cryptographic assumptions. Recent attempts to implement such tests on current…
The efficient certification of classically intractable quantum devices has been a central research question for some time. However, to observe a "quantum advantage", it is believed that one does not need to build a large scale universal…
The accessible information quantifies the amount of classical information that can be extracted from an ensemble of quantum states. Analogously, the informational power quantifies the amount of classical information that can be extracted by…
In this paper, we provide a simple framework for deriving one-shot achievable bounds for some problems in quantum information theory. Our framework is based on the joint convexity of the exponential of the collision relative entropy, and is…
In this paper we consider what can be computed by a user interacting with a potentially malicious server, when the server performs polynomial-time quantum computation but the user can only perform polynomial-time classical (i.e.,…
With experimental quantum computing technologies now in their infancy, the search for efficient means of testing the correctness of these quantum computations is becoming more pressing. An approach to the verification of quantum computation…
Modern SAT or QBF solvers are expected to produce correctness certificates. However, certificates have worst-case exponential size (unless NP=coNP), and at recent SAT competitions the largest certificates of unsatisfiability are starting to…
Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the…
In this thesis, we introduce a new quantum Turing machine (QTM) model that supports general quantum operators, together with its pushdown, counter, and finite automaton variants, and examine the computational power of classical and quantum…
We study the problem of approximating the commuting-operator value of a two-player non-local game. It is well-known that it is $\mathrm{NP}$-complete to decide whether the classical value of a non-local game is 1 or $1- \epsilon$.…
Quantum information science provides powerful technologies beyond the scope of classical physics. In practice, accurate control of quantum operations is a challenging task with current quantum devices. The implementation of high fidelity…
Various quantum applications can be reduced to estimating expectation values, which are inevitably deviated by operational and environmental errors. Although errors can be tackled by quantum error correction, the overheads are far from…
Complexity theory traditionally studies the hardness of solving classical computational problems. In the quantum setting, it is also natural to consider a different notion of complexity, namely the complexity of physically preparing a…
Recently, Google announced the first demonstration of quantum computational supremacy with a programmable superconducting processor. Their demonstration is based on collecting samples from the output distribution of a noisy random quantum…