David Deutsch - Academia.edu (original) (raw)
Papers by David Deutsch
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2000
All information in quantum systems is, notwithstanding BellÕs theorem, localised. Measuring or ot... more All information in quantum systems is, notwithstanding BellÕs theorem, localised. Measuring or otherwise interacting with a quantum system S has no effect on distant systems from which S is dynamically isolated, even if they are entangled with S. Using the Heisenberg picture to analyse quantum information processing makes this locality explicit, and reveals that under some circumstances (in particular, in Einstein-Podolski-Rosen experiments and in quantum teleportation) quantum information is transmitted through ÔclassicalÕ (i.e. decoherent) information channels.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
It is argued that underlying the Church–Turing hypothesis there is an implicit physical assertion... more It is argued that underlying the Church–Turing hypothesis there is an implicit physical assertion. Here, this assertion is presented explicitly as a physical principle: ‘every finitely realizible physical system can be perfectly simulated by a universal model computing machine operating by finite means’. Classical physics and the universal Turing machine, because the former is continuous and the latter discrete, do not obey the principle, at least in the strong form above. A class of model computing machines that is the quantum generalization of the class of Turing machines is described, and it is shown that quantum theory and the 'universal quantum computer’ are compatible with the principle. Computing machines resembling the universal quantum computer could, in principle, be built and would have many remarkable properties not reproducible by any Turing machine. These do not include the computation of non-recursive functions, but they do include ‘quantum parallelism’, a method ...
Page 1. Rapid solution of problems by quantum computation BY DAVID DEUTSCH1 AND RICHARD JOZSA2t 1... more Page 1. Rapid solution of problems by quantum computation BY DAVID DEUTSCH1 AND RICHARD JOZSA2t 1 Wolfson College, Oxford 0X2 6UD, UK 2St Edmund Hall, Oxford OX1 4AR, UK A class of problems is ...
The canonical commutation relations of quantum field theory require all pairs of observables loca... more The canonical commutation relations of quantum field theory require all pairs of observables located in spacelike-separated regions to commute. In the theory as it is currently constituted, this implies that the information-carrying capacity of a finite volume of space is infinite. Yet Bekenstein's bound gives us strong reason to believe that it is finite. A class of quantum field theories is presented in which observables localised in spacelike-separated regions do not necessarily commute, but which nevertheless has no physical pathologies.
A quantum computer is a device capable of performing computational tasks that depend on character... more A quantum computer is a device capable of performing computational tasks that depend on characteristically quantum mechanical effects, in particular coherent quantum superposition. Such devices can efficiently perform classes of computation (e.g. factorisation) which are believed to be intractable on any classical computer. This makes it highly desirable to construct such devices. In this paper, we address the last remaining theoretical obstacle to such a construction, namely the problem of stability or error correction. This problem is more substantial in quantum computation than in classical computation because of the delicate nature of the interference phenomena on which quantum computation depends. We present a new, purely quantum mechanical method of error correction, which has no classical analogue, but can serve to stabilise coherent quantum computations. Like the classical methods, it utilises redundancy, but it does not depend on measuring intermediate results of the computation
S I a M Journal on Computing, 1997
We propose a method for the stabilisation of quantum computations (including quantum state storag... more We propose a method for the stabilisation of quantum computations (including quantum state storage). The method is based on the operation of projection into SYM, the symmetric subspace of the full state space of R redundant copies of the computer. We describe an efficient algorithm and quantum network effecting SYM-projection and discuss the stabilising effect of the proposed method in the context of unitary errors generated by hardware imprecision, and nonunitary errors arising from external environmental interaction. Finally, limitations of the method are discussed.
Siam Journal on Computing, 1996
We propose a method for the stabilisation of quantum computations (including quantum state storag... more We propose a method for the stabilisation of quantum computations (including quantum state storage). The method is based on the operation of projection into calSYM\cal SYMcalSYM, the symmetric subspace of the full state space of RRR redundant copies of the computer. We describe an efficient algorithm and quantum network effecting calSYM\cal SYMcalSYM--projection and discuss the stabilising effect of the proposed
Quantum Theory, Cosmology, and Complexity, 2004
Scientific American, 1994
Physical Review D, 1983
We set out the problem of constructing states for quantum field theories in nonstationary space-t... more We set out the problem of constructing states for quantum field theories in nonstationary space-time backgrounds. We stress that this problem is a fundamental one, not to be confused with the inessential question "what is a particle." We present a formalism, related to that of Ashtekhar and Magnon, in which the problem can be attacked more easily than at present. By way of illustration we express the ansatz of "energy minimization" in our formalism and thereby find its general solution for noninteracting scalar fields.
Bulletin of Symbolic Logic, 2000
Though the truths of logic and pure mathematics are objective and independent of any contingent f... more Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum theory of computation has provided practical instances of this, and forces us to abandon the classical view that computation, and hence mathematical proof, are purely logical notions independent of that of computation as a physical process. Henceforward, a proof must be regarded not as an abstract object or process but as a physical process, a species of computation, whose scope and reliability depend on our knowledge of the physics of the computer concerned.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012
In a previous paper Hayden and I proved, using the Heisenberg picture, that quantum physics satis... more In a previous paper Hayden and I proved, using the Heisenberg picture, that quantum physics satisfies Einstein's criterion of locality. Wallace and Timpson have argued that certain transformations of the Heisenbergpicture description of a quantum system must be regarded as leaving invariant the factual situation being described, and that taking this into account reveals that Einstein's criterion is violated after all. Here I vindicate the proof and explain some misconceptions that have led to this and other criticisms of it.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2002
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1995
We show that in quantum computation almost every gate that operates on two or more bits is a univ... more We show that in quantum computation almost every gate that operates on two or more bits is a universal gate. We discuss various physical considerations bearing on the proper definition of universality for computational components such as logic gates.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2000
All information in quantum systems is, notwithstanding BellÕs theorem, localised. Measuring or ot... more All information in quantum systems is, notwithstanding BellÕs theorem, localised. Measuring or otherwise interacting with a quantum system S has no effect on distant systems from which S is dynamically isolated, even if they are entangled with S. Using the Heisenberg picture to analyse quantum information processing makes this locality explicit, and reveals that under some circumstances (in particular, in Einstein-Podolski-Rosen experiments and in quantum teleportation) quantum information is transmitted through ÔclassicalÕ (i.e. decoherent) information channels.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
It is argued that underlying the Church–Turing hypothesis there is an implicit physical assertion... more It is argued that underlying the Church–Turing hypothesis there is an implicit physical assertion. Here, this assertion is presented explicitly as a physical principle: ‘every finitely realizible physical system can be perfectly simulated by a universal model computing machine operating by finite means’. Classical physics and the universal Turing machine, because the former is continuous and the latter discrete, do not obey the principle, at least in the strong form above. A class of model computing machines that is the quantum generalization of the class of Turing machines is described, and it is shown that quantum theory and the 'universal quantum computer’ are compatible with the principle. Computing machines resembling the universal quantum computer could, in principle, be built and would have many remarkable properties not reproducible by any Turing machine. These do not include the computation of non-recursive functions, but they do include ‘quantum parallelism’, a method ...
Page 1. Rapid solution of problems by quantum computation BY DAVID DEUTSCH1 AND RICHARD JOZSA2t 1... more Page 1. Rapid solution of problems by quantum computation BY DAVID DEUTSCH1 AND RICHARD JOZSA2t 1 Wolfson College, Oxford 0X2 6UD, UK 2St Edmund Hall, Oxford OX1 4AR, UK A class of problems is ...
The canonical commutation relations of quantum field theory require all pairs of observables loca... more The canonical commutation relations of quantum field theory require all pairs of observables located in spacelike-separated regions to commute. In the theory as it is currently constituted, this implies that the information-carrying capacity of a finite volume of space is infinite. Yet Bekenstein's bound gives us strong reason to believe that it is finite. A class of quantum field theories is presented in which observables localised in spacelike-separated regions do not necessarily commute, but which nevertheless has no physical pathologies.
A quantum computer is a device capable of performing computational tasks that depend on character... more A quantum computer is a device capable of performing computational tasks that depend on characteristically quantum mechanical effects, in particular coherent quantum superposition. Such devices can efficiently perform classes of computation (e.g. factorisation) which are believed to be intractable on any classical computer. This makes it highly desirable to construct such devices. In this paper, we address the last remaining theoretical obstacle to such a construction, namely the problem of stability or error correction. This problem is more substantial in quantum computation than in classical computation because of the delicate nature of the interference phenomena on which quantum computation depends. We present a new, purely quantum mechanical method of error correction, which has no classical analogue, but can serve to stabilise coherent quantum computations. Like the classical methods, it utilises redundancy, but it does not depend on measuring intermediate results of the computation
S I a M Journal on Computing, 1997
We propose a method for the stabilisation of quantum computations (including quantum state storag... more We propose a method for the stabilisation of quantum computations (including quantum state storage). The method is based on the operation of projection into SYM, the symmetric subspace of the full state space of R redundant copies of the computer. We describe an efficient algorithm and quantum network effecting SYM-projection and discuss the stabilising effect of the proposed method in the context of unitary errors generated by hardware imprecision, and nonunitary errors arising from external environmental interaction. Finally, limitations of the method are discussed.
Siam Journal on Computing, 1996
We propose a method for the stabilisation of quantum computations (including quantum state storag... more We propose a method for the stabilisation of quantum computations (including quantum state storage). The method is based on the operation of projection into calSYM\cal SYMcalSYM, the symmetric subspace of the full state space of RRR redundant copies of the computer. We describe an efficient algorithm and quantum network effecting calSYM\cal SYMcalSYM--projection and discuss the stabilising effect of the proposed
Quantum Theory, Cosmology, and Complexity, 2004
Scientific American, 1994
Physical Review D, 1983
We set out the problem of constructing states for quantum field theories in nonstationary space-t... more We set out the problem of constructing states for quantum field theories in nonstationary space-time backgrounds. We stress that this problem is a fundamental one, not to be confused with the inessential question "what is a particle." We present a formalism, related to that of Ashtekhar and Magnon, in which the problem can be attacked more easily than at present. By way of illustration we express the ansatz of "energy minimization" in our formalism and thereby find its general solution for noninteracting scalar fields.
Bulletin of Symbolic Logic, 2000
Though the truths of logic and pure mathematics are objective and independent of any contingent f... more Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum theory of computation has provided practical instances of this, and forces us to abandon the classical view that computation, and hence mathematical proof, are purely logical notions independent of that of computation as a physical process. Henceforward, a proof must be regarded not as an abstract object or process but as a physical process, a species of computation, whose scope and reliability depend on our knowledge of the physics of the computer concerned.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012
In a previous paper Hayden and I proved, using the Heisenberg picture, that quantum physics satis... more In a previous paper Hayden and I proved, using the Heisenberg picture, that quantum physics satisfies Einstein's criterion of locality. Wallace and Timpson have argued that certain transformations of the Heisenbergpicture description of a quantum system must be regarded as leaving invariant the factual situation being described, and that taking this into account reveals that Einstein's criterion is violated after all. Here I vindicate the proof and explain some misconceptions that have led to this and other criticisms of it.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2002
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1995
We show that in quantum computation almost every gate that operates on two or more bits is a univ... more We show that in quantum computation almost every gate that operates on two or more bits is a universal gate. We discuss various physical considerations bearing on the proper definition of universality for computational components such as logic gates.