# Questions tagged [quantum-computing]

Quantum computation and computational issues related to quantum mechanics

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### How much computational power fits into a cubic centimeter?

This question is a followup on the question about DNA algorithms asked by Aadita Mehra. In comments there, Joe Fitzsimmons said, in part: [T]he radius of the system must scale proportionately to ...
4k views

### Physics results in TCS?

It seems clear that a number of subfields of theoretical computer science have been significantly impacted by results from theoretical physics. Two examples of this are Quantum computation ...
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### NP-intermediate problems with efficient quantum solutions

Peter Shor showed that two of the most important NP-intermediate problems, factoring and the discrete log problem, are in BQP. In contrast, the best known quantum algorithm for SAT (Grover's search) ...
960 views

### Reading up on $BQP = BPP^{BQNC}$

What should I read to understand this problem? The power of small-depth quantum circuits. Is $BQP = BPP^{BQNC}$? In other words, can the "quantum" part of any quantum algorithm be compressed ...
2k views

### What is the quantum computational model?

I have occasionally heard people talk about quantum algorithms and about states and the ability to consider multiple possibilities at once, but I have never managed to get someone to explain the ...
1k views

### Is there a Quantum equivalent of the Time hierarchy theorem ?

My favourite theorem in complexity theory is the Time hierarchy theorem. However, this was done in 1965. I wanted to know then if there was anything similar for Quantum Computing. Also, if not ...
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### Quantum computing project ideas

I'm undergraduate computer science student and I'm currently planning for my graduation project. I need some ideas in quantum computing field. any help?
1k views

### Quantum analogues of SPACE complexity classes

We often consider complexity classes where we are bounded in the amount of space our Turing machine can use, for example: $\textbf{DSPACE}(f(n))$ or $\textbf{NSPACE}(f(n))$. It seems that early in ...
933 views

### What is known about multi-prover interactive proofs with short messages?

Beigi, Shor and Watrous have a very nice paper on the power of quantum interactive proofs with short messages. They consider three variants of 'short messages', and the specific one I care about is ...
730 views

### What is the proof that quantum computers can efficiently simulate arbitrary quantum mechanical systems?

JBV suggested I turn some comments into a question, so here goes. Another question  asks about applications of QM computing. One answer  was "efficiently simulating quantum mechanics". ...
755 views

### Bounding the gap between quantum and deterministic query complexity

Although exponential separations between bounded-error quantum query complexity ($Q(f)$) and deterministic query complexity ($D(f)$) or bounded-error randomized query complexity ($R(f)$) are known, ...
614 views

### Learning quantum CS [duplicate]

Possible Duplicate: What is the quantum computational model? What is the best way to study quantum branch of CS for the person with rather advanced background in classical CS? Does one need to ...
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### Was the reduction in Shor's algorithm originally discovered by Shor?

This is a "historical question" more than it is a research question, but was the classical reduction to order-finding in Shor's algorithm for factorization initially discovered by Peter Shor, or was ... 2k views

### Rigorous security proof for Wiesner's quantum money?

In his celebrated paper "Conjugate Coding" (written around 1970), Stephen Wiesner proposed a scheme for quantum money that is unconditionally impossible to counterfeit, assuming that the issuing bank ...
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### Consequences of $SAT \in BQP$

As a TCS amateur, I'm reading some popular, very introductory material on quantum computing. Here are the few elementary bits of information I've learned so far: Quantum computers are not known to ...
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### Quantum proofs of classical theorems

I'm interested in examples of problems where a theorem which seemingly has nothing to do with quantum mechanics/information (e.g. states something about purely classical objects) can nevertheless be ...
966 views

### Universal sets of gates for SU(3)?

In quantum computing we are often interested in cases where group of special unitary operators, G, for some d-dimensional system gives either the whole group SU(d) exactly or even just an ... 8k views

### Is there any connection between the diamond norm and the distance of the associated states?

In quantum information theory, the distance between two quantum channels is often measured using the diamond norm. There are also a number of ways to measure distance between two quantum states, such ...
2k views

### How does the BosonSampling paper avoid easy classes of complex matrices?

In The computational complexity of linear optics (ECCC TR10-170), Scott Aaronson and Alex Arkhipov argue that if quantum computers can be efficiently simulated by classical computers then the ...
28k views

### Universities for Quantum Computing / Information?

Which universities have a strong quantum computing curriculum, and offer some type of quantum computing/information courses/research? The aim here is to collect a useful list for someone considering ...
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While Adleman's theorem shows, that $\mathsf{BPP} \subseteq \mathsf{P}/\text{poly}$, I'm not aware of any literature investigating the possible inclusion of $\mathsf{BQP} \subseteq \mathsf{P}/\text{... 20 votes 2 answers 1k views ###$\ell_p$-norm preserving Turing machines Reading some recent threads on quantum computing (here,here, and here), make me remember an interesting question about the power of some kind of$\ell_p$-norm preserving machine. For people working ... 20 votes 4 answers 815 views ### Is there an equivalent to derandomization for quantum algorithms? With some randomized algorithms you can derandomize the algorithm, removing (at a possible cost in run time) the use of random bits and maximizing some lower bound on the objective (usually computed ... 19 votes 1 answer 1k views ### Why does Odlyzko improvement of Shor's Algorithm reduces the number of trials to$O(1)$In his 1995 paper Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer, Peter W. Shor discusses an improvement on the order-finding part of his ... 17 votes 5 answers 3k views ### Real world applications of quantum computing (except for security) Let's assume that we have built an universal quantum computer. Except for security-related issues (cryptography, privacy, ...) which current real world problems can benefit from using it? I am ... 15 votes 1 answer 858 views ### Is there a quantum NC algorithm for computing GCD? From the comments on one of my questions on MathOverflow I get the feeling that the question regarding GCD being in$\mathsf{NC}$vs.$\mathsf{P}$is akin to the question regarding Integer ... 11 votes 1 answer 307 views ### Fast classical simulation of quantum algorithms Are there examples of cases where the classical simulation of a quantum algorithm for a problem outperforms the best previously known classical algorithm for this problem? "Outperforms" doesn't have ... 10 votes 1 answer 317 views ### Lower bounds for quantum circuits using the geodesic framework Some of us have been reading Michael Nielsen's paper on a geometric approach to using quantum lower bounds (in brief, the construction of a Finsler metric on$SU(2^n)$such that the geodesic distance ... 10 votes 2 answers 518 views ### Restricting entries of unitary operators to real numbers and universal gate sets In Bernstein and Vazirani's seminal paper "Quantum Complexity Theory", they show that a$d$-dimensional unitary transformation can be efficiently approximated by a product of what they call "near-... 10 votes 1 answer 495 views ### Span programs, witness size, and certificate complexity A span program is a linear-algebraic way of specifying a boolean function introduced here. Recently, this model was used to show that the negative adversary method provides a tight characterization (... 9 votes 2 answers 858 views ### Is adiabatic quantum computing as powerful as the circuit model? Much of the quantum computing literature focuses on the circuit model. Adiabatic quantum computing is not based on applying a sequence of unitary operators, but on changing a time-dependent ... 9 votes 2 answers 778 views ### Understanding QMA This question comes out of an answer Joe Fitzsimons gave to a different question. Most natural complexity classes have a one-line "intuitive description" that helps characterize core problems in that ... 8 votes 1 answer 466 views ### Quantum Money where not even the Bank can counterfeit The Quantum Money system proposed in "Quantum Copy-Protection and Quantum Money" has the following properties: The bank can produce bank notes in the form of quantum states. Anyone can verify that ... 7 votes 2 answers 356 views ### Given a subset of the hypercube and a copy translated by s, find s Problem: Suppose we are given an$n$element subset$A\subseteq\{0,1\}^d$of the$d$dimensional hypercube and a translated copy$B= A+s$by some secret$s\in\{0,1\}^d$. Find$s$as fast as possible ... 7 votes 1 answer 196 views ### Quantum complexity of TQBF There is no classical algorithm for$n$-bit TQBF with better than$O(2^n)$complexity. Is that also the best known bound for quantum algorithms / circuits? Edit: As pointed out by Huck Bennett, in ... 7 votes 2 answers 443 views ### Energy cost of adiabatic quantum computation I'm not sure whether this question is completely on-topic, since it is a physics-related question. But I'll ask anyway and apologize if I'm off-topic. In Adiabatic Quantum Computation is Equivalent ... 7 votes 2 answers 584 views ### Quantum query complexity and certificate complexity A certificate for an input$x$is a subset of bits$S \subseteq \{1,...,n\}$such that for all inputs$y$,$(\forall i \in S \quad y_i = x_i) \rightarrow f(y) = f(x)$. Then$C_x(f)$is the minimum ... 6 votes 1 answer 254 views ### Are there problems that can be solved in time$2^{n-q^c}$with$q$qubits? This is another attempt to formalize my former question on the topic. I'm looking for a problem for which all known classical algorithms take exponential time, but given ANY number of few qubits (... 5 votes 0 answers 191 views ### Do the quantum communication complexity lower bounds hold when parties can send a "duplicated" qubits? This question continues from the previous question where I mistakenly asked a question that is too general. In quantum communication complexity, we always assume that Alice and Bob have unlimited ... 5 votes 2 answers 307 views ### Witness verifiable quantum advantage Update: A slightly different version of this question has been answered here. As far as I can see, a major issue with Google's recent quantum supremacy claim is that it is hard to verify the results. ... 4 votes 6 answers 6k views ### Ternary (and beyond) computation and quantum computing? Binary math is at the heart of most computing, in large part because of the ease with which two energy states can be achieved. I have always thought that having more states could improve computing ... 3 votes 1 answer 173 views ### How well can an arbitrary (unknown) quantum state be imperfectly cloned? How well can an arbitrary unknown (quantum) state$\rvert \psi \rangle = \alpha\rvert 0 \rangle + \beta \rvert 1 \rangle$, be imperfectly/approximately cloned? Given an unknown state${\rvert \psi \...
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I have been going through Eddie Farhi's 6-pages long pre-Adiabatic paper, An Analog Analogue of a Digital Quantum Computation. I guess I understand most of the math and physics but I am struggling ...
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### Is unbounded quantum fanout operation experimentally feasible?

It is known that the "unbounded quantum fanout operation" is very powerful: (See, for example, Hoyer et al. : http://theoryofcomputing.org/articles/v001a005/v001a005.pdf). In particular, it is known ...
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In quantum communication complexity, we always assume that Alice and Bob have unlimited computational power and are still prove lower bounds such as the $\Omega(n)$ lower bounds of parity. What ...
This is a follow up to Quantum complexity of TQBF, trying to model the situation where we have good heuristics. Let $L$ be the language of true, fully alternating totally quantified boolean formulas ...