Ancilladriven universal quantum computing carnegie mellon. Linear optical quantum computing or linear optics quantum computation loqc is a paradigm of quantum computation, allowing under certain conditions, described below universal quantum computation. Institute for quantum computing and department of physics and astronomy university of waterloo waterloo canada. Apply a unitary transformation to the combined system. Schemes of universal quantum computation in which the interactions between the computational elements, in a computational register, are. Quantum mechanics qm describes the behavior and properties of elementary particles ep such as electrons or photons on the atomic and subatomic levels. We present a new protocol to remotely entangle two stationary qubits by rst entangling them with propagating ancilla qubits and then performing a. Introduction the quantum computers use the quantum mechanical phenomena such as superposition and quantum entanglement to perform computations. Get started with the quantum development kit microsoft. Quantum computing faulttolerant detection of a quantum. Minimal ancilla mediated quantum computation arxiv. Let the orthonormal quantum states be represented in the vector notation heisenberg notation eq. The coupling, e ar, is xed throughout the computation while the measurements on the ancilla, indicated by the arrows, can di er.
Quantum computers will be resourceconstrained for years to come so reducing ancilla requirements is crucial. Quantum computing applications ashley montanaro department of computer science, university of bristol. A chosen transformation of an initial nqubit state is probabilistically obtained. A quantum circuit performing quantum computation in a quantum computer. A promising technology is the quantum computers, and this paper gives a general overview about this subject. Quantum logic operations can be performed using linear optical elements, additional photons ancilla, and postselection based on measurements made on the ancilla. To achieve universal quantum computing, loqc should be capable of realizing a complete set of universal gates. Quantum computing jozef gruska quantum measurement has the effect of magnifying one of the outcomes of quantum superposition probabilistic, sequential only at this point do indeterminacy and probabilities e. Quantum mechanics is a mathematical language, much like calculus.
Universal quantum computation by the unitary control of. Ancilla based quantum circuits it is wellknown that using an ancilla register eases the complexity in the implementation of quantum gates e. These lecture notes were formed in small chunks during my \quantum computing course at the university of amsterdam, febmay 2011, and compiled into one text thereafter. We demonstrate a faulttolerant errordetection scheme that suppresses spreading of ancilla errors by a. But avoid asking for help, clarification, or responding to other answers. Quantum simulation on a quantum computer would provide us with efficient algorithms to obtain. Twisted graph states for ancilladriven universal quantum. We make these results controlled on an ancilla qubit so that we can apply the phase estimation. Quantum computing, algebraic applications, operators, gates 1. In general, an arbitrary quantum state can be generated for qip with a proper set of photon sources. We introduce a new paradigm for quantum computing called ancilladriven quantum computation adqc combines aspects of the quantum circuit and the oneway model to overcome challenging issues in building largescale quantum computers. Vlad gheorghiu cmu ancilla driven universal quantum computing september 30, 2010 6 11.
An ancilla based quantum simulation framework fornon. Schemes of universal quantum computation in which the interactions between the computational elements, in a computational register, are mediated by some ancillary system are of interest due to their relevance to the physical implementation of a quantum computer. Just as classical computers can be thought of in boolean algebra terms, quantum computers are reasoned about with quantum mechanics. A critical component of any quantum errorcorrecting scheme is detection of errors by using an ancilla system. A handbook of markovian and nonmarkovian quantum stochastic methods with applications to quantum optics springer, berlin, heidelberg, 2004. However, errors occurring in the ancilla can propagate onto the logical qubit, irreversibly corrupting the encoded information. Remote entanglement of distant, noninteracting quantum entities is a key primitive for quantum information processing.
In this paper, we present square strategic quantum ancilla reuse, a compilation infrastructure that tackles allocation and reclamation of scratch qubits called ancilla in modular quantum programs. Grovers algorithm searches for a speci ed entry in an unordered database, employing an important technique in quantum algorithm design known as amplitude ampli cation to achieve a polynomial speedup over the best classical algorithms. However, this is not the case in quantum computing or classical reversible computing. In this paper, we show that it is possible to adapt a qudit scheme for creating a controlledtoffoli created by ralph et al. So far we have mentioned only the practical advantages of our proposed architecture. Quantum computers will be resourceconstrained for years to come so reducing. Ancilla bits are some extra bits being used to achieve some specific goals in computation e. We consider the transformations of quantum states obtainable by a process of the following sort. Quantum computing glossary is a glossary of some crucial terms specific to quantum computing and program development. Now, let s be the set of all accepting basis states. Quantum computing models for algebraic applications nikolay raychev. Abstractin our days the quantum computers may be used for a great number of algebraic applications exponentially faster in comparison to the classical computing equipment. In classical computation, any memory bit can be turned on or off at will, requiring no prior knowledge or extra gadgetry. Such gates are unsuitable for multistep quantum logic circuits, where the output of one gate is used as input for the next.
Quantum computing concepts includes topics such as the relevance of linear algebra to quantum computing, the nature and use of a qubit, how to read a quantum circuit, and more. On the another hand, when it comes to the realization of quantum computers. Nearly two years ago, ibm made a quantum computer available to the world. As quantum computing technology improves and quantum computers with a small but nontrivial number of n 100 qubits appear feasible in the near future the question of possible applications of small quantum computers gains importance. Pdf twisted graph states for ancilladriven quantum.
Since the computations are carried out in ways, which the classic computers can not apply for certain tasks such as decomposition of. The reason quantum computing seems more powerful than classical computing is precisely that it seems hard to estimate that tiny residue using random sampling. Application of unitary operations from the clifford group. Pdf we propose a method of manipulating a quantum register remotely with the help of a single ancilla that steers the evolution of the register. While this scheme requires more gates than standard schemes for creating large controlled gates, we show that with simple adaptations, it is directly equivalent to the standard scheme in the literature. Loqc uses photons as information carriers, mainly uses linear optical elements, or optical instruments including reciprocal mirrors and waveplates to process quantum information, and uses. Ancilladriven quantum computation with twisted graph states. We introduce a new paradigm for quantum computing called ancilla driven quantum computation adqc combines aspects of the quantum circuit and the oneway model to overcome challenging issues in building largescale quantum computers. Pdf universal quantum computation by the unitary control of. Wewillthendiscusspossible hamiltonians with which this could be implemented and in doing so give a suitable. The rst algorithm that will be explored in this tutorial is lov grovers quantum database search 5. Us7590607b2 nonunitary probabilistic quantum computing.
Hybrid quantum computing with ancillas request pdf. Instead of directly manipulating each qubit to perform universal quantum logic gates or measurements. Howell department of physics and astronomy, university of rochester, rochester, ny 14627, usa in this paper we report the. Entanglement stabilization using ancillabased parity. Furthermore, reducing the level of control required over both the ancillary and register systems has the potential to. A tutorial on quantum error correction oxford physics university.
A quantum computer is a computation device that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Hastings, matthias troyer as quantum computing technology improves and quantum computers with a small but nontrivial number of n 100 qubits appear feasible in the near future the question of possible applications of small. Minimal ancilla mediated quantum computation springerlink. The josephson junction is the basic building block of a superconducting qubit, and thus a quantum computer.
Proctor, 1, erika andersson,2 and viv kendon 1school of physics and astronomy, e c stoner building, university of leeds, leeds, ls2 9jt, united kingdom 2supa, institute for photonics and quantum sciences, heriotwatt. Vlad gheorghiu cmu ancilladriven universal quantum computing september 30, 2010 6 11. When operation on the ancilla state provides a success condition, computation is stopped. Pdf generation of entangled ancilla states for use in. Each chapter was covered in a lecture of 2 45 minutes, with an additional 45minute lecture for exercises and homework. After decades of heavy slog with no promise of success, quantum computing is suddenly buzzing with almost feverish excitement and activity. Quantum computing heisenberg notationis useful in computer calculations. Compiling highlevel quantum programs to machines that are size constrained i. Quantum computing applications ashley montanaro department of computer science, university of bristol 25 february 20. Universal quantum computation by the unitary control of ancilla qubits and using a fixed ancillaregister interaction.
Jacobs johns hopkins university applied physics laboratory laurel, md 20723 abstract. Thanks for contributing an answer to quantum computing stack exchange. Ancilla approximable quantum state transformations. The first real quantum algorithm invented by david deutsch is described. An alternative to sqpt, which we refer to as ancilla assisted process tomography aapt, introduces an extra ancilla qubit, and involves preparation and tomography of only a single twoqubit quantum state, rather than four onequbit states 4. Quantum computer architectures 2009 john kubiatowiczuc berkeley qarc. A particular type of ancilla based circuits can be described for the matrices represented as a sum of unitary matrices 12, 15. Instead of directly manipulating each qubit to perform universal quantum logic gates or measurements, adqc uses a fixed twoqubit interaction to couple the.
However, this is not the case in quantum computing or classical reversible. A possible alternative to the standard model of measurementbased quantum computation mbqc is offered by the sequential model of mbqc a particular class of quantum computation via ancillae. Instead of directly manipulating each qubit to perform universal quantum logic gates or measurements, adqc uses a fixed twoqubit interaction to couple. An alternative to sqpt, which we refer to as ancillaassisted process tomography aapt, introduces an extra ancilla qubit, and involves preparation and tomography of only a single twoqubit quantum state, rather than four onequbit states 4. In particular, when people write about constant input what they mean is that, for a given algorithm which has a purpose, such as finding the prime factors of an input number, or effecting a simple arithmetic operation between two input numbers the value of the ancilla qubits will be independent of the value of the input.
Minimal ancilla mediated quantum computation epj quantum. We introduce a new paradigm for quantum computing called ancilla driven quantum computation adqc combines aspects of the quantum circuit 1 and the oneway model 2 to overcome challenging issues in building largescale quantum computers. An ancilla based quantum simulation framework fornonunitary. Quantum world classical world quantum computation is deterministic highly exponentially parallel unitary described by. The formalisation of the computational model underlying adqc, which is the focus of the current paper, leads to the introduction of a new multi. One frequently mentioned application is feynmans original proposal of simulating quantum systems, and in. Combine the given input state with a specially prepared initial state of an auxiliary system. Institute for quantum computing the clifford group scheme for quantum computation is constructed from the following three primitives. Random sampling would work fine for say a typical us election, but estimating.
Pdf ancilladriven universal quantum computation researchgate. Many quantum algorithms make use of ancilla, additional qubits used to store temporary information during computation, to reduce the total. Hastings, matthias troyer as quantum computing technology improves and quantum computers with a small but nontrivial number of n 100 qubits appear feasible in the near future the question of possible. Quantum computing 1 is an emerging technology that is recently receiving. Building qubits phase across junction energy maximum 0 energy energy minimum energy diagram of a junction electrons weak link superconductor what are the basic principles. The circuit comprises a unitary quantum operator obtained from a nonunitary quantum operator, operating on an nqubit state and an ancilla state. In a previous work, we have shown similar improvements in generating cluster states 32, illustrating the generality of the techniques we have described here in the context.
Similarly, ancilla methods of quantum computing are more general than just the qubus, so these results are potentially applicable to a large range of physical systems. For a more complete introduction to quantum computing we refer the reader to 4 and, for a good introduction to ternary quantum gates, 5. Introduction what can we do with our quantum computers. Just as classical physics uses calculus to explain nature, quantum physics uses quantum mechanics to explain nature. Quantum entanglement is the central resource behind applications in quantum information science, from quantum computers and simulators of complex quantum systems to metrology and secure communication. The general meaning of ancilla in ancilla qubit is auxiliary.
Quantum computing has the potential to revolutionize a wide array of industries, from pharmaceuticals and materials research to finance and logistics, by offering a fundamentally different way of processing information using quantum mechanical systems. As quantum computing technology improves and quantum. Reducing the number of ancilla qubits and the gate count. Quantum computation, ancilladriven, universal quantum computation, graph states 1 introduction there are two main paradigms which have driven boththe theory and implementation of quantum computation. Can quantum chemistry be performed on a small quantum computer. Error correction is especially important in quantum computers, because. Mosca, 2007, an introduction to quantum computing, oxford university press, oxford, uk. In these models of computing, all operations on computer memory must. A joint multiqubit state can be prepared in a similar way. However, the heinsenberg notation is much more explicit when one attempts to clearly explain the principles of quantum computations. Ancilla generation memory alu quantum computer architectures 2009 john kubiatowiczuc berkeley qarc.
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